%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SWW272+1 : TPTP v8.1.2. Released v5.2.0.
% 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 : Sun May  5 11:35:36 EDT 2024

% Result   : Theorem 0.95s 0.64s
% Output   : Refutation 1.61s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      : 1196
% Syntax   : Number of formulae    : 3492 (1156 unt;   0 def)
%            Number of atoms       : 7672 (1873 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives : 6498 (2318   ~;2322   |; 343   &)
%                                         ( 874 <=>; 641  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Maximal term depth    :    9 (   1 avg)
%            Number of predicates  :  730 ( 728 usr; 642 prp; 0-5 aty)
%            Number of functors    :   50 (  50 usr;  14 con; 0-3 aty)
%            Number of variables   : 4708 (4677   !;  31   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f10625,plain,
    $false,
    inference(avatar_sat_refutation,[],[f5899,f5904,f5909,f5914,f5919,f5924,f5929,f5934,f5939,f5944,f5949,f5954,f5959,f5964,f5969,f5974,f5979,f5984,f5989,f5994,f5999,f6004,f6009,f6014,f6019,f6024,f6029,f6034,f6039,f6044,f6049,f6054,f6059,f6064,f6069,f6074,f6079,f6084,f6089,f6094,f6099,f6104,f6109,f6114,f6119,f6124,f6129,f6134,f6139,f6144,f6149,f6154,f6159,f6164,f6169,f6174,f6179,f6184,f6189,f6194,f6199,f6204,f6209,f6214,f6219,f6224,f6229,f6234,f6239,f6244,f6249,f6254,f6259,f6264,f6269,f6274,f6279,f6284,f6289,f6294,f6299,f6304,f6309,f6314,f6319,f6324,f6329,f6334,f6339,f6344,f6349,f6354,f6359,f6364,f6369,f6374,f6379,f6384,f6389,f6394,f6399,f6404,f6409,f6414,f6419,f6424,f6429,f6434,f6439,f6444,f6449,f6454,f6459,f6464,f6469,f6474,f6479,f6484,f6489,f6494,f6499,f6504,f6509,f6514,f6519,f6524,f6529,f6534,f6539,f6544,f6549,f6554,f6559,f6564,f6569,f6574,f6579,f6584,f6589,f6594,f6599,f6604,f6609,f6614,f6619,f6624,f6629,f6634,f6638,f6642,f6646,f6650,f6654,f6659,f6664,f6669,f6674,f6679,f6684,f6688,f6692,f6696,f6700,f6704,f6708,f6712,f6716,f6720,f6724,f6728,f6732,f6736,f6740,f6744,f6748,f6752,f6756,f6760,f6764,f6768,f6772,f6776,f6780,f6784,f6788,f6792,f6796,f6800,f6804,f6808,f6812,f6816,f6820,f6824,f6828,f6832,f6836,f6840,f6844,f6848,f6852,f6856,f6860,f6864,f6868,f6872,f6876,f6880,f6884,f6888,f6892,f6896,f6900,f6904,f6908,f6912,f6916,f6920,f6924,f6928,f6933,f6938,f6943,f6948,f6953,f6958,f6962,f6966,f6970,f6974,f6978,f6982,f6986,f6990,f6994,f6998,f7002,f7006,f7010,f7014,f7018,f7023,f7030,f7034,f7039,f7044,f7049,f7054,f7058,f7062,f7066,f7070,f7074,f7078,f7082,f7086,f7090,f7094,f7098,f7102,f7106,f7110,f7114,f7118,f7122,f7126,f7130,f7134,f7138,f7142,f7146,f7150,f7173,f7179,f7185,f7190,f7194,f7198,f7202,f7206,f7210,f7214,f7218,f7222,f7226,f7230,f7234,f7238,f7242,f7246,f7250,f7254,f7258,f7262,f7266,f7270,f7279,f7310,f7311,f7315,f7319,f7323,f7327,f7331,f7335,f7339,f7343,f7347,f7351,f7355,f7359,f7363,f7367,f7371,f7375,f7379,f7383,f7387,f7391,f7395,f7399,f7403,f7407,f7411,f7415,f7419,f7423,f7427,f7431,f7435,f7439,f7443,f7447,f7451,f7455,f7459,f7528,f7594,f7608,f7612,f7616,f7620,f7624,f7628,f7632,f7637,f7641,f7645,f7649,f7653,f7657,f7661,f7665,f7669,f7673,f7677,f7681,f7685,f7689,f7693,f7697,f7701,f7705,f7709,f7713,f7718,f7722,f7726,f7730,f7734,f7738,f7742,f7758,f7927,f7952,f7957,f7961,f7965,f7969,f7973,f7977,f7981,f7985,f7989,f7993,f7998,f8002,f8006,f8010,f8014,f8018,f8022,f8026,f8030,f8034,f8038,f8042,f8046,f8050,f8054,f8058,f8062,f8066,f8070,f8074,f8078,f8084,f8088,f8092,f8096,f8100,f8104,f8108,f8112,f8116,f8120,f8128,f8132,f8136,f8140,f8144,f8148,f8152,f8156,f8160,f8164,f8168,f8173,f8177,f8181,f8185,f8189,f8237,f8408,f8448,f8592,f8644,f8650,f8654,f8658,f8662,f8666,f8670,f8674,f8678,f8682,f8686,f8690,f8694,f8698,f8702,f8706,f8710,f8714,f8718,f8722,f8727,f8731,f8735,f8739,f8743,f8747,f8751,f8755,f8759,f8763,f8769,f8773,f8777,f8781,f8785,f8789,f8793,f8797,f8801,f8805,f8809,f8813,f8817,f8821,f8825,f8829,f8833,f8837,f8841,f8845,f8850,f8854,f8858,f8862,f8866,f8870,f8874,f8878,f8882,f8886,f8890,f8894,f8898,f8902,f8906,f8910,f8914,f8918,f8922,f8926,f8930,f8934,f8938,f8965,f9066,f9180,f9280,f9399,f9527,f9531,f9535,f9539,f9543,f9547,f9551,f9555,f9559,f9563,f9567,f9571,f9575,f9579,f9583,f9587,f9591,f9595,f9599,f9603,f9607,f9611,f9615,f9619,f9623,f9627,f9631,f9635,f9639,f9643,f9647,f9651,f9655,f9659,f9663,f9667,f9671,f9675,f9679,f9683,f9687,f9882,f10276,f10289,f10293,f10297,f10301,f10305,f10309,f10313,f10317,f10321,f10325,f10329,f10333,f10337,f10341,f10345,f10349,f10353,f10357,f10362,f10366,f10370,f10374,f10378,f10382,f10386,f10390,f10394,f10398,f10403,f10407,f10411,f10415,f10419,f10423,f10427,f10431,f10435,f10439,f10444,f10448,f10452,f10456,f10460,f10464,f10468,f10472,f10476,f10480,f10484,f10488,f10492,f10496,f10500,f10504,f10508,f10512,f10516,f10520,f10524,f10528,f10532,f10536,f10540,f10544,f10548,f10552,f10556,f10560,f10564,f10568,f10572,f10587,f10591,f10595,f10599,f10603,f10607,f10611,f10615,f10619,f10623,f10624]) ).

fof(f10624,plain,
    ( spl38_1
    | ~ spl38_3
    | ~ spl38_245
    | ~ spl38_420
    | ~ spl38_468
    | ~ spl38_599 ),
    inference(avatar_split_clause,[],[f10581,f10441,f8757,f8122,f7036,f5906,f5896]) ).

fof(f5896,plain,
    ( spl38_1
  <=> v_pa____ = v_s____ ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_1])]) ).

fof(f5906,plain,
    ( spl38_3
  <=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_s____ ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_3])]) ).

fof(f7036,plain,
    ( spl38_245
  <=> v_pa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),v_s____))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),v_s____) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_245])]) ).

fof(f8122,plain,
    ( spl38_420
  <=> class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_420])]) ).

fof(f8757,plain,
    ( spl38_468
  <=> ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Ozero__class_Ozero(X1))
        | ~ class_Rings_Ocomm__semiring__1(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_468])]) ).

fof(f10441,plain,
    ( spl38_599
  <=> c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),v_s____) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_599])]) ).

fof(f10581,plain,
    ( v_pa____ = v_s____
    | ~ spl38_3
    | ~ spl38_245
    | ~ spl38_420
    | ~ spl38_468
    | ~ spl38_599 ),
    inference(forward_demodulation,[],[f10577,f9062]) ).

fof(f9062,plain,
    ( ! [X0] : v_s____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0),v_s____)
    | ~ spl38_3
    | ~ spl38_420
    | ~ spl38_468 ),
    inference(forward_demodulation,[],[f9059,f5908]) ).

fof(f5908,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_s____
    | ~ spl38_3 ),
    inference(avatar_component_clause,[],[f5906]) ).

fof(f9059,plain,
    ( ! [X0] : c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
    | ~ spl38_420
    | ~ spl38_468 ),
    inference(resolution,[],[f8758,f8123]) ).

fof(f8123,plain,
    ( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl38_420 ),
    inference(avatar_component_clause,[],[f8122]) ).

fof(f8758,plain,
    ( ! [X0,X1] :
        ( ~ class_Rings_Ocomm__semiring__1(X1)
        | c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Ozero__class_Ozero(X1)) )
    | ~ spl38_468 ),
    inference(avatar_component_clause,[],[f8757]) ).

fof(f10577,plain,
    ( v_pa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),v_s____)
    | ~ spl38_245
    | ~ spl38_599 ),
    inference(superposition,[],[f7038,f10443]) ).

fof(f10443,plain,
    ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),v_s____) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl38_599 ),
    inference(avatar_component_clause,[],[f10441]) ).

fof(f7038,plain,
    ( v_pa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),v_s____))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),v_s____)
    | ~ spl38_245 ),
    inference(avatar_component_clause,[],[f7036]) ).

fof(f10623,plain,
    spl38_641,
    inference(avatar_split_clause,[],[f5124,f10621]) ).

fof(f10621,plain,
    ( spl38_641
  <=> ! [X0,X3,X2,X1] :
        ( c_Orderings_Oord__class_Oless(X2,X1,X0)
        | c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X3)
        | ~ sP13(X0,X1,X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_641])]) ).

fof(f5124,plain,
    ! [X2,X3,X0,X1] :
      ( c_Orderings_Oord__class_Oless(X2,X1,X0)
      | c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X3)
      | ~ sP13(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f3793]) ).

fof(f3793,plain,
    ! [X0,X1,X2,X3] :
      ( ( sP13(X0,X1,X2,X3)
        | ( ( ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
            | ~ c_Orderings_Oord__class_Oless(X2,X3,c_Groups_Ozero__class_Ozero(X2)) )
          & ( ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
            | ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X3) ) ) )
      & ( ( c_Orderings_Oord__class_Oless(X2,X1,X0)
          & c_Orderings_Oord__class_Oless(X2,X3,c_Groups_Ozero__class_Ozero(X2)) )
        | ( c_Orderings_Oord__class_Oless(X2,X0,X1)
          & c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X3) )
        | ~ sP13(X0,X1,X2,X3) ) ),
    inference(rectify,[],[f3792]) ).

fof(f3792,plain,
    ! [X2,X0,X3,X1] :
      ( ( sP13(X2,X0,X3,X1)
        | ( ( ~ c_Orderings_Oord__class_Oless(X3,X0,X2)
            | ~ c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Ozero__class_Ozero(X3)) )
          & ( ~ c_Orderings_Oord__class_Oless(X3,X2,X0)
            | ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1) ) ) )
      & ( ( c_Orderings_Oord__class_Oless(X3,X0,X2)
          & c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Ozero__class_Ozero(X3)) )
        | ( c_Orderings_Oord__class_Oless(X3,X2,X0)
          & c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1) )
        | ~ sP13(X2,X0,X3,X1) ) ),
    inference(flattening,[],[f3791]) ).

fof(f3791,plain,
    ! [X2,X0,X3,X1] :
      ( ( sP13(X2,X0,X3,X1)
        | ( ( ~ c_Orderings_Oord__class_Oless(X3,X0,X2)
            | ~ c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Ozero__class_Ozero(X3)) )
          & ( ~ c_Orderings_Oord__class_Oless(X3,X2,X0)
            | ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1) ) ) )
      & ( ( c_Orderings_Oord__class_Oless(X3,X0,X2)
          & c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Ozero__class_Ozero(X3)) )
        | ( c_Orderings_Oord__class_Oless(X3,X2,X0)
          & c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1) )
        | ~ sP13(X2,X0,X3,X1) ) ),
    inference(nnf_transformation,[],[f3472]) ).

fof(f3472,plain,
    ! [X2,X0,X3,X1] :
      ( sP13(X2,X0,X3,X1)
    <=> ( ( c_Orderings_Oord__class_Oless(X3,X0,X2)
          & c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Ozero__class_Ozero(X3)) )
        | ( c_Orderings_Oord__class_Oless(X3,X2,X0)
          & c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP13])]) ).

fof(f10619,plain,
    spl38_640,
    inference(avatar_split_clause,[],[f5123,f10617]) ).

fof(f10617,plain,
    ( spl38_640
  <=> ! [X0,X3,X2,X1] :
        ( c_Orderings_Oord__class_Oless(X2,X3,c_Groups_Ozero__class_Ozero(X2))
        | c_Orderings_Oord__class_Oless(X2,X0,X1)
        | ~ sP13(X0,X1,X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_640])]) ).

fof(f5123,plain,
    ! [X2,X3,X0,X1] :
      ( c_Orderings_Oord__class_Oless(X2,X3,c_Groups_Ozero__class_Ozero(X2))
      | c_Orderings_Oord__class_Oless(X2,X0,X1)
      | ~ sP13(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f3793]) ).

fof(f10615,plain,
    spl38_639,
    inference(avatar_split_clause,[],[f5118,f10613]) ).

fof(f10613,plain,
    ( spl38_639
  <=> ! [X0,X3,X2,X1] :
        ( sP11(X0,X1,X2,X3)
        | ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
        | ~ c_Orderings_Oord__class_Oless(X2,X3,c_Groups_Ozero__class_Ozero(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_639])]) ).

fof(f5118,plain,
    ! [X2,X3,X0,X1] :
      ( sP11(X0,X1,X2,X3)
      | ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(X2,X3,c_Groups_Ozero__class_Ozero(X2)) ),
    inference(cnf_transformation,[],[f3788]) ).

fof(f3788,plain,
    ! [X0,X1,X2,X3] :
      ( ( sP11(X0,X1,X2,X3)
        | ( ( ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
            | ~ c_Orderings_Oord__class_Oless(X2,X3,c_Groups_Ozero__class_Ozero(X2)) )
          & ( ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
            | ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X3) ) ) )
      & ( ( c_Orderings_Oord__class_Oless(X2,X1,X0)
          & c_Orderings_Oord__class_Oless(X2,X3,c_Groups_Ozero__class_Ozero(X2)) )
        | ( c_Orderings_Oord__class_Oless(X2,X0,X1)
          & c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X3) )
        | ~ sP11(X0,X1,X2,X3) ) ),
    inference(rectify,[],[f3787]) ).

fof(f3787,plain,
    ! [X1,X0,X3,X2] :
      ( ( sP11(X1,X0,X3,X2)
        | ( ( ~ c_Orderings_Oord__class_Oless(X3,X0,X1)
            | ~ c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3)) )
          & ( ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
            | ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2) ) ) )
      & ( ( c_Orderings_Oord__class_Oless(X3,X0,X1)
          & c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3)) )
        | ( c_Orderings_Oord__class_Oless(X3,X1,X0)
          & c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2) )
        | ~ sP11(X1,X0,X3,X2) ) ),
    inference(flattening,[],[f3786]) ).

fof(f3786,plain,
    ! [X1,X0,X3,X2] :
      ( ( sP11(X1,X0,X3,X2)
        | ( ( ~ c_Orderings_Oord__class_Oless(X3,X0,X1)
            | ~ c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3)) )
          & ( ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
            | ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2) ) ) )
      & ( ( c_Orderings_Oord__class_Oless(X3,X0,X1)
          & c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3)) )
        | ( c_Orderings_Oord__class_Oless(X3,X1,X0)
          & c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2) )
        | ~ sP11(X1,X0,X3,X2) ) ),
    inference(nnf_transformation,[],[f3469]) ).

fof(f3469,plain,
    ! [X1,X0,X3,X2] :
      ( sP11(X1,X0,X3,X2)
    <=> ( ( c_Orderings_Oord__class_Oless(X3,X0,X1)
          & c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3)) )
        | ( c_Orderings_Oord__class_Oless(X3,X1,X0)
          & c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP11])]) ).

fof(f10611,plain,
    spl38_638,
    inference(avatar_split_clause,[],[f5117,f10609]) ).

fof(f10609,plain,
    ( spl38_638
  <=> ! [X0,X3,X2,X1] :
        ( sP11(X0,X1,X2,X3)
        | ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
        | ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_638])]) ).

fof(f5117,plain,
    ! [X2,X3,X0,X1] :
      ( sP11(X0,X1,X2,X3)
      | ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
      | ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X3) ),
    inference(cnf_transformation,[],[f3788]) ).

fof(f10607,plain,
    spl38_637,
    inference(avatar_split_clause,[],[f5115,f10605]) ).

fof(f10605,plain,
    ( spl38_637
  <=> ! [X0,X3,X2,X1] :
        ( c_Orderings_Oord__class_Oless(X2,X1,X0)
        | c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X3)
        | ~ sP11(X0,X1,X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_637])]) ).

fof(f5115,plain,
    ! [X2,X3,X0,X1] :
      ( c_Orderings_Oord__class_Oless(X2,X1,X0)
      | c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X3)
      | ~ sP11(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f3788]) ).

fof(f10603,plain,
    spl38_636,
    inference(avatar_split_clause,[],[f5114,f10601]) ).

fof(f10601,plain,
    ( spl38_636
  <=> ! [X0,X3,X2,X1] :
        ( c_Orderings_Oord__class_Oless(X2,X3,c_Groups_Ozero__class_Ozero(X2))
        | c_Orderings_Oord__class_Oless(X2,X0,X1)
        | ~ sP11(X0,X1,X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_636])]) ).

fof(f5114,plain,
    ! [X2,X3,X0,X1] :
      ( c_Orderings_Oord__class_Oless(X2,X3,c_Groups_Ozero__class_Ozero(X2))
      | c_Orderings_Oord__class_Oless(X2,X0,X1)
      | ~ sP11(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f3788]) ).

fof(f10599,plain,
    spl38_635,
    inference(avatar_split_clause,[],[f5016,f10597]) ).

fof(f10597,plain,
    ( spl38_635
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_635])]) ).

fof(f5016,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
    inference(cnf_transformation,[],[f3741]) ).

fof(f3741,plain,
    ! [X0,X1,X2] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)) ) ),
    inference(nnf_transformation,[],[f1979]) ).

fof(f1979,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0))
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
    inference(rectify,[],[f645]) ).

fof(f645,axiom,
    ! [X11,X34,X35] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X35,X34),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X35,X11))
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X34,X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel__less) ).

fof(f10595,plain,
    spl38_634,
    inference(avatar_split_clause,[],[f5015,f10593]) ).

fof(f10593,plain,
    ( spl38_634
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_634])]) ).

fof(f5015,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)) ),
    inference(cnf_transformation,[],[f3741]) ).

fof(f10591,plain,
    spl38_633,
    inference(avatar_split_clause,[],[f5014,f10589]) ).

fof(f10589,plain,
    ( spl38_633
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_633])]) ).

fof(f5014,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
    inference(cnf_transformation,[],[f3740]) ).

fof(f3740,plain,
    ! [X0,X1,X2] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)) ) ),
    inference(nnf_transformation,[],[f1978]) ).

fof(f1978,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
    inference(rectify,[],[f656]) ).

fof(f656,axiom,
    ! [X11,X34,X35] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X35,X34),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X35,X11))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel__le) ).

fof(f10587,plain,
    spl38_632,
    inference(avatar_split_clause,[],[f5013,f10585]) ).

fof(f10585,plain,
    ( spl38_632
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_632])]) ).

fof(f5013,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)) ),
    inference(cnf_transformation,[],[f3740]) ).

fof(f10572,plain,
    spl38_631,
    inference(avatar_split_clause,[],[f5008,f10570]) ).

fof(f10570,plain,
    ( spl38_631
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_631])]) ).

fof(f5008,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0),X1) ),
    inference(cnf_transformation,[],[f3737]) ).

fof(f3737,plain,
    ! [X0,X1,X2] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0),X1) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0),X1)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) ) ),
    inference(nnf_transformation,[],[f1975]) ).

fof(f1975,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0),X1) ),
    inference(rectify,[],[f988]) ).

fof(f988,axiom,
    ! [X35,X88,X89] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X89,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X88,X35))
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X89,X35),X88) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__diff__conv) ).

fof(f10568,plain,
    spl38_630,
    inference(avatar_split_clause,[],[f5007,f10566]) ).

fof(f10566,plain,
    ( spl38_630
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0),X1)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_630])]) ).

fof(f5007,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0),X1)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) ),
    inference(cnf_transformation,[],[f3737]) ).

fof(f10564,plain,
    spl38_629,
    inference(avatar_split_clause,[],[f5006,f10562]) ).

fof(f10562,plain,
    ( spl38_629
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X0)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_629])]) ).

fof(f5006,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
    inference(cnf_transformation,[],[f3736]) ).

fof(f3736,plain,
    ! [X0,X1,X2] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X0)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X0) ) ),
    inference(nnf_transformation,[],[f1974]) ).

fof(f1974,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X0)
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
    inference(rectify,[],[f989]) ).

fof(f989,axiom,
    ! [X89,X35,X88] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X88,X35),X89)
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X88,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X89,X35)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__diff__conv) ).

fof(f10560,plain,
    spl38_628,
    inference(avatar_split_clause,[],[f5005,f10558]) ).

fof(f10558,plain,
    ( spl38_628
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_628])]) ).

fof(f5005,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X0) ),
    inference(cnf_transformation,[],[f3736]) ).

fof(f10556,plain,
    spl38_627,
    inference(avatar_split_clause,[],[f4985,f10554]) ).

fof(f10554,plain,
    ( spl38_627
  <=> ! [X2,X0,X1] :
        ( X0 = X1
        | c_Polynomial_Opoly(X2,X1) != c_Polynomial_Opoly(X2,X0)
        | ~ class_Rings_Oidom(X2)
        | ~ class_Int_Oring__char__0(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_627])]) ).

fof(f4985,plain,
    ! [X2,X0,X1] :
      ( X0 = X1
      | c_Polynomial_Opoly(X2,X1) != c_Polynomial_Opoly(X2,X0)
      | ~ class_Rings_Oidom(X2)
      | ~ class_Int_Oring__char__0(X2) ),
    inference(cnf_transformation,[],[f3726]) ).

fof(f3726,plain,
    ! [X0,X1,X2] :
      ( ( ( c_Polynomial_Opoly(X2,X1) = c_Polynomial_Opoly(X2,X0)
          | X0 != X1 )
        & ( X0 = X1
          | c_Polynomial_Opoly(X2,X1) != c_Polynomial_Opoly(X2,X0) ) )
      | ~ class_Rings_Oidom(X2)
      | ~ class_Int_Oring__char__0(X2) ),
    inference(nnf_transformation,[],[f3045]) ).

fof(f3045,plain,
    ! [X0,X1,X2] :
      ( ( c_Polynomial_Opoly(X2,X1) = c_Polynomial_Opoly(X2,X0)
      <=> X0 = X1 )
      | ~ class_Rings_Oidom(X2)
      | ~ class_Int_Oring__char__0(X2) ),
    inference(flattening,[],[f3044]) ).

fof(f3044,plain,
    ! [X0,X1,X2] :
      ( ( c_Polynomial_Opoly(X2,X1) = c_Polynomial_Opoly(X2,X0)
      <=> X0 = X1 )
      | ~ class_Rings_Oidom(X2)
      | ~ class_Int_Oring__char__0(X2) ),
    inference(ennf_transformation,[],[f1967]) ).

fof(f1967,plain,
    ! [X0,X1,X2] :
      ( ( class_Rings_Oidom(X2)
        & class_Int_Oring__char__0(X2) )
     => ( c_Polynomial_Opoly(X2,X1) = c_Polynomial_Opoly(X2,X0)
      <=> X0 = X1 ) ),
    inference(rectify,[],[f20]) ).

fof(f20,axiom,
    ! [X15,X7,X4] :
      ( ( class_Rings_Oidom(X4)
        & class_Int_Oring__char__0(X4) )
     => ( c_Polynomial_Opoly(X4,X7) = c_Polynomial_Opoly(X4,X15)
      <=> X7 = X15 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__eq__iff) ).

fof(f10552,plain,
    spl38_626,
    inference(avatar_split_clause,[],[f4945,f10550]) ).

fof(f10550,plain,
    ( spl38_626
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_626])]) ).

fof(f4945,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
    inference(cnf_transformation,[],[f2987]) ).

fof(f2987,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
    inference(ennf_transformation,[],[f1934]) ).

fof(f1934,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) ),
    inference(rectify,[],[f648]) ).

fof(f648,axiom,
    ! [X30,X37,X38] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X38,X37)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X38,X30),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X37,X30)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__mono1) ).

fof(f10548,plain,
    spl38_625,
    inference(avatar_split_clause,[],[f4938,f10546]) ).

fof(f10546,plain,
    ( spl38_625
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X0),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_625])]) ).

fof(f4938,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X0),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1) ),
    inference(cnf_transformation,[],[f2979]) ).

fof(f2979,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X0),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1) ),
    inference(ennf_transformation,[],[f1927]) ).

fof(f1927,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
     => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X0),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) ),
    inference(rectify,[],[f726]) ).

fof(f726,axiom,
    ! [X30,X37,X38] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X38,X37)
     => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X38,X30),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X37,X30)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__strict__right__mono) ).

fof(f10544,plain,
    spl38_624,
    inference(avatar_split_clause,[],[f4923,f10542]) ).

fof(f10542,plain,
    ( spl38_624
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_624])]) ).

fof(f4923,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    inference(cnf_transformation,[],[f2963]) ).

fof(f2963,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    inference(ennf_transformation,[],[f1916]) ).

fof(f1916,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) ),
    inference(rectify,[],[f659]) ).

fof(f659,axiom,
    ! [X30,X37,X38] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X38,X37)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X38,X30),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X37,X30)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__mono1) ).

fof(f10540,plain,
    spl38_623,
    inference(avatar_split_clause,[],[f4922,f10538]) ).

fof(f10538,plain,
    ( spl38_623
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_623])]) ).

fof(f4922,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    inference(cnf_transformation,[],[f2962]) ).

fof(f2962,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    inference(ennf_transformation,[],[f1915]) ).

fof(f1915,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) ),
    inference(rectify,[],[f982]) ).

fof(f982,axiom,
    ! [X36,X10,X19] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X10)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X36),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X10,X36)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__le__mono) ).

fof(f10536,plain,
    spl38_622,
    inference(avatar_split_clause,[],[f4921,f10534]) ).

fof(f10534,plain,
    ( spl38_622
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_622])]) ).

fof(f4921,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    inference(cnf_transformation,[],[f2961]) ).

fof(f2961,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    inference(ennf_transformation,[],[f1914]) ).

fof(f1914,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2)) ),
    inference(rectify,[],[f981]) ).

fof(f981,axiom,
    ! [X36,X10,X19] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X10)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X36,X10),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X36,X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__le__mono2) ).

fof(f10532,plain,
    ( spl38_621
    | ~ spl38_3
    | ~ spl38_558 ),
    inference(avatar_split_clause,[],[f10285,f9685,f5906,f10530]) ).

fof(f10530,plain,
    ( spl38_621
  <=> ! [X2,X0,X1] :
        ( ~ sP16(X0,tc_Complex_Ocomplex,v_s____,X1,X2)
        | v_s____ = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_621])]) ).

fof(f9685,plain,
    ( spl38_558
  <=> ! [X4,X0,X1,X3] :
        ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X3
        | ~ sP16(X0,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_558])]) ).

fof(f10285,plain,
    ( ! [X2,X0,X1] :
        ( ~ sP16(X0,tc_Complex_Ocomplex,v_s____,X1,X2)
        | v_s____ = X1 )
    | ~ spl38_3
    | ~ spl38_558 ),
    inference(superposition,[],[f9686,f5908]) ).

fof(f9686,plain,
    ( ! [X3,X0,X1,X4] :
        ( ~ sP16(X0,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X3,X4)
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X3 )
    | ~ spl38_558 ),
    inference(avatar_component_clause,[],[f9685]) ).

fof(f10528,plain,
    spl38_620,
    inference(avatar_split_clause,[],[f4920,f10526]) ).

fof(f10526,plain,
    ( spl38_620
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X2))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_620])]) ).

fof(f4920,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X2))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    inference(cnf_transformation,[],[f2960]) ).

fof(f2960,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X2))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    inference(ennf_transformation,[],[f1913]) ).

fof(f1913,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X2)) ),
    inference(rectify,[],[f991]) ).

fof(f991,axiom,
    ! [X19,X10,X30] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30,X10)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X19),X30)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__diff) ).

fof(f10524,plain,
    spl38_619,
    inference(avatar_split_clause,[],[f4914,f10522]) ).

fof(f10522,plain,
    ( spl38_619
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_619])]) ).

fof(f4914,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1) ),
    inference(cnf_transformation,[],[f2953]) ).

fof(f2953,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1) ),
    inference(ennf_transformation,[],[f1907]) ).

fof(f1907,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1)
     => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1)) ),
    inference(rectify,[],[f725]) ).

fof(f725,axiom,
    ! [X30,X37,X38] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X38,X37)
     => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X30,X38),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X30,X37)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__left__mono) ).

fof(f10520,plain,
    spl38_618,
    inference(avatar_split_clause,[],[f4882,f10518]) ).

fof(f10518,plain,
    ( spl38_618
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless(X2,X1,X0)
        | c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
        | ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
        | ~ class_Orderings_Opreorder(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_618])]) ).

fof(f4882,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless(X2,X1,X0)
      | c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
      | ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
      | ~ class_Orderings_Opreorder(X2) ),
    inference(cnf_transformation,[],[f3704]) ).

fof(f3704,plain,
    ! [X0,X1,X2] :
      ( ( ( c_Orderings_Oord__class_Oless(X2,X1,X0)
          | c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
          | ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0) )
        & ( ( ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
            & c_Orderings_Oord__class_Oless__eq(X2,X1,X0) )
          | ~ c_Orderings_Oord__class_Oless(X2,X1,X0) ) )
      | ~ class_Orderings_Opreorder(X2) ),
    inference(flattening,[],[f3703]) ).

fof(f3703,plain,
    ! [X0,X1,X2] :
      ( ( ( c_Orderings_Oord__class_Oless(X2,X1,X0)
          | c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
          | ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0) )
        & ( ( ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
            & c_Orderings_Oord__class_Oless__eq(X2,X1,X0) )
          | ~ c_Orderings_Oord__class_Oless(X2,X1,X0) ) )
      | ~ class_Orderings_Opreorder(X2) ),
    inference(nnf_transformation,[],[f2918]) ).

fof(f2918,plain,
    ! [X0,X1,X2] :
      ( ( c_Orderings_Oord__class_Oless(X2,X1,X0)
      <=> ( ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
          & c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ) )
      | ~ class_Orderings_Opreorder(X2) ),
    inference(ennf_transformation,[],[f1886]) ).

fof(f1886,plain,
    ! [X0,X1,X2] :
      ( class_Orderings_Opreorder(X2)
     => ( c_Orderings_Oord__class_Oless(X2,X1,X0)
      <=> ( ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
          & c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ) ) ),
    inference(rectify,[],[f621]) ).

fof(f621,axiom,
    ! [X17,X3,X4] :
      ( class_Orderings_Opreorder(X4)
     => ( c_Orderings_Oord__class_Oless(X4,X3,X17)
      <=> ( ~ c_Orderings_Oord__class_Oless__eq(X4,X17,X3)
          & c_Orderings_Oord__class_Oless__eq(X4,X3,X17) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__le__not__le) ).

fof(f10516,plain,
    spl38_617,
    inference(avatar_split_clause,[],[f4862,f10514]) ).

fof(f10514,plain,
    ( spl38_617
  <=> ! [X2,X0,X1] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1)))
        | ~ class_Rings_Ocomm__semiring__1(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_617])]) ).

fof(f4862,plain,
    ! [X2,X0,X1] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1)))
      | ~ class_Rings_Ocomm__semiring__1(X2) ),
    inference(cnf_transformation,[],[f2894]) ).

fof(f2894,plain,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1)))
      | ~ class_Rings_Ocomm__semiring__1(X2) ),
    inference(ennf_transformation,[],[f1869]) ).

fof(f1869,plain,
    ! [X0,X1,X2] :
      ( class_Rings_Ocomm__semiring__1(X2)
     => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1))) ),
    inference(rectify,[],[f176]) ).

fof(f176,axiom,
    ! [X27,X18,X4] :
      ( class_Rings_Ocomm__semiring__1(X4)
     => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),X18),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X27),X18))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__triv__right) ).

fof(f10512,plain,
    spl38_616,
    inference(avatar_split_clause,[],[f4861,f10510]) ).

fof(f10510,plain,
    ( spl38_616
  <=> ! [X2,X0,X1] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)))
        | ~ class_Rings_Ocomm__semiring__1(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_616])]) ).

fof(f4861,plain,
    ! [X2,X0,X1] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)))
      | ~ class_Rings_Ocomm__semiring__1(X2) ),
    inference(cnf_transformation,[],[f2893]) ).

fof(f2893,plain,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)))
      | ~ class_Rings_Ocomm__semiring__1(X2) ),
    inference(ennf_transformation,[],[f1868]) ).

fof(f1868,plain,
    ! [X0,X1,X2] :
      ( class_Rings_Ocomm__semiring__1(X2)
     => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))) ),
    inference(rectify,[],[f175]) ).

fof(f175,axiom,
    ! [X27,X18,X4] :
      ( class_Rings_Ocomm__semiring__1(X4)
     => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),X18),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X18),X27))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__triv__left) ).

fof(f10508,plain,
    spl38_615,
    inference(avatar_split_clause,[],[f4846,f10506]) ).

fof(f10506,plain,
    ( spl38_615
  <=> ! [X2,X0,X1] :
        ( c_Groups_Ozero__class_Ozero(X2) = X1
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != c_Polynomial_OpCons(X2,X1,X0)
        | ~ class_Groups_Ozero(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_615])]) ).

fof(f4846,plain,
    ! [X2,X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X2) = X1
      | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != c_Polynomial_OpCons(X2,X1,X0)
      | ~ class_Groups_Ozero(X2) ),
    inference(cnf_transformation,[],[f3700]) ).

fof(f3700,plain,
    ! [X0,X1,X2] :
      ( ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_OpCons(X2,X1,X0)
          | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X0
          | c_Groups_Ozero__class_Ozero(X2) != X1 )
        & ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
            & c_Groups_Ozero__class_Ozero(X2) = X1 )
          | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != c_Polynomial_OpCons(X2,X1,X0) ) )
      | ~ class_Groups_Ozero(X2) ),
    inference(flattening,[],[f3699]) ).

fof(f3699,plain,
    ! [X0,X1,X2] :
      ( ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_OpCons(X2,X1,X0)
          | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X0
          | c_Groups_Ozero__class_Ozero(X2) != X1 )
        & ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
            & c_Groups_Ozero__class_Ozero(X2) = X1 )
          | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != c_Polynomial_OpCons(X2,X1,X0) ) )
      | ~ class_Groups_Ozero(X2) ),
    inference(nnf_transformation,[],[f2882]) ).

fof(f2882,plain,
    ! [X0,X1,X2] :
      ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_OpCons(X2,X1,X0)
      <=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
          & c_Groups_Ozero__class_Ozero(X2) = X1 ) )
      | ~ class_Groups_Ozero(X2) ),
    inference(ennf_transformation,[],[f1857]) ).

fof(f1857,plain,
    ! [X0,X1,X2] :
      ( class_Groups_Ozero(X2)
     => ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_OpCons(X2,X1,X0)
      <=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
          & c_Groups_Ozero__class_Ozero(X2) = X1 ) ) ),
    inference(rectify,[],[f45]) ).

fof(f45,axiom,
    ! [X7,X12,X4] :
      ( class_Groups_Ozero(X4)
     => ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = c_Polynomial_OpCons(X4,X12,X7)
      <=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X7
          & c_Groups_Ozero__class_Ozero(X4) = X12 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pCons__eq__0__iff) ).

fof(f10504,plain,
    spl38_614,
    inference(avatar_split_clause,[],[f4844,f10502]) ).

fof(f10502,plain,
    ( spl38_614
  <=> ! [X2,X0,X1] :
        ( c_Groups_Ozero__class_Ozero(X2) = X1
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != c_Polynomial_Omonom(X2,X1,X0)
        | ~ class_Groups_Ozero(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_614])]) ).

fof(f4844,plain,
    ! [X2,X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X2) = X1
      | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != c_Polynomial_Omonom(X2,X1,X0)
      | ~ class_Groups_Ozero(X2) ),
    inference(cnf_transformation,[],[f3698]) ).

fof(f3698,plain,
    ! [X0,X1,X2] :
      ( ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_Omonom(X2,X1,X0)
          | c_Groups_Ozero__class_Ozero(X2) != X1 )
        & ( c_Groups_Ozero__class_Ozero(X2) = X1
          | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != c_Polynomial_Omonom(X2,X1,X0) ) )
      | ~ class_Groups_Ozero(X2) ),
    inference(nnf_transformation,[],[f2881]) ).

fof(f2881,plain,
    ! [X0,X1,X2] :
      ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_Omonom(X2,X1,X0)
      <=> c_Groups_Ozero__class_Ozero(X2) = X1 )
      | ~ class_Groups_Ozero(X2) ),
    inference(ennf_transformation,[],[f1856]) ).

fof(f1856,plain,
    ! [X0,X1,X2] :
      ( class_Groups_Ozero(X2)
     => ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_Omonom(X2,X1,X0)
      <=> c_Groups_Ozero__class_Ozero(X2) = X1 ) ),
    inference(rectify,[],[f10]) ).

fof(f10,axiom,
    ! [X11,X12,X4] :
      ( class_Groups_Ozero(X4)
     => ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = c_Polynomial_Omonom(X4,X12,X11)
      <=> c_Groups_Ozero__class_Ozero(X4) = X12 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_monom__eq__0__iff) ).

fof(f10500,plain,
    spl38_613,
    inference(avatar_split_clause,[],[f4831,f10498]) ).

fof(f10498,plain,
    ( spl38_613
  <=> ! [X2,X0,X1] :
        ( c_Polynomial_Odegree(X2,c_Polynomial_Omonom(X2,X1,X0)) = X0
        | c_Groups_Ozero__class_Ozero(X2) = X1
        | ~ class_Groups_Ozero(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_613])]) ).

fof(f4831,plain,
    ! [X2,X0,X1] :
      ( c_Polynomial_Odegree(X2,c_Polynomial_Omonom(X2,X1,X0)) = X0
      | c_Groups_Ozero__class_Ozero(X2) = X1
      | ~ class_Groups_Ozero(X2) ),
    inference(cnf_transformation,[],[f2866]) ).

fof(f2866,plain,
    ! [X0,X1,X2] :
      ( c_Polynomial_Odegree(X2,c_Polynomial_Omonom(X2,X1,X0)) = X0
      | c_Groups_Ozero__class_Ozero(X2) = X1
      | ~ class_Groups_Ozero(X2) ),
    inference(flattening,[],[f2865]) ).

fof(f2865,plain,
    ! [X0,X1,X2] :
      ( c_Polynomial_Odegree(X2,c_Polynomial_Omonom(X2,X1,X0)) = X0
      | c_Groups_Ozero__class_Ozero(X2) = X1
      | ~ class_Groups_Ozero(X2) ),
    inference(ennf_transformation,[],[f1847]) ).

fof(f1847,plain,
    ! [X0,X1,X2] :
      ( class_Groups_Ozero(X2)
     => ( c_Groups_Ozero__class_Ozero(X2) != X1
       => c_Polynomial_Odegree(X2,c_Polynomial_Omonom(X2,X1,X0)) = X0 ) ),
    inference(rectify,[],[f51]) ).

fof(f51,axiom,
    ! [X10,X18,X4] :
      ( class_Groups_Ozero(X4)
     => ( c_Groups_Ozero__class_Ozero(X4) != X18
       => c_Polynomial_Odegree(X4,c_Polynomial_Omonom(X4,X18,X10)) = X10 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__monom__eq) ).

fof(f10496,plain,
    spl38_612,
    inference(avatar_split_clause,[],[f4798,f10494]) ).

fof(f10494,plain,
    ( spl38_612
  <=> ! [X2,X0,X1] :
        ( c_Divides_Odiv__class_Omod(X2,X0,X1) = c_Divides_Odiv__class_Omod(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),X1)
        | ~ class_Divides_Osemiring__div(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_612])]) ).

fof(f4798,plain,
    ! [X2,X0,X1] :
      ( c_Divides_Odiv__class_Omod(X2,X0,X1) = c_Divides_Odiv__class_Omod(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),X1)
      | ~ class_Divides_Osemiring__div(X2) ),
    inference(cnf_transformation,[],[f2818]) ).

fof(f2818,plain,
    ! [X0,X1,X2] :
      ( c_Divides_Odiv__class_Omod(X2,X0,X1) = c_Divides_Odiv__class_Omod(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),X1)
      | ~ class_Divides_Osemiring__div(X2) ),
    inference(ennf_transformation,[],[f1817]) ).

fof(f1817,plain,
    ! [X0,X1,X2] :
      ( class_Divides_Osemiring__div(X2)
     => c_Divides_Odiv__class_Omod(X2,X0,X1) = c_Divides_Odiv__class_Omod(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),X1) ),
    inference(rectify,[],[f884]) ).

fof(f884,axiom,
    ! [X18,X27,X4] :
      ( class_Divides_Osemiring__div(X4)
     => c_Divides_Odiv__class_Omod(X4,X18,X27) = c_Divides_Odiv__class_Omod(X4,c_Groups_Oplus__class_Oplus(X4,X27,X18),X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__add__self1) ).

fof(f10492,plain,
    spl38_611,
    inference(avatar_split_clause,[],[f4797,f10490]) ).

fof(f10490,plain,
    ( spl38_611
  <=> ! [X2,X0,X1] :
        ( c_Divides_Odiv__class_Omod(X2,X1,X0) = c_Divides_Odiv__class_Omod(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),X0)
        | ~ class_Divides_Osemiring__div(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_611])]) ).

fof(f4797,plain,
    ! [X2,X0,X1] :
      ( c_Divides_Odiv__class_Omod(X2,X1,X0) = c_Divides_Odiv__class_Omod(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),X0)
      | ~ class_Divides_Osemiring__div(X2) ),
    inference(cnf_transformation,[],[f2817]) ).

fof(f2817,plain,
    ! [X0,X1,X2] :
      ( c_Divides_Odiv__class_Omod(X2,X1,X0) = c_Divides_Odiv__class_Omod(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),X0)
      | ~ class_Divides_Osemiring__div(X2) ),
    inference(ennf_transformation,[],[f1816]) ).

fof(f1816,plain,
    ! [X0,X1,X2] :
      ( class_Divides_Osemiring__div(X2)
     => c_Divides_Odiv__class_Omod(X2,X1,X0) = c_Divides_Odiv__class_Omod(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),X0) ),
    inference(rectify,[],[f883]) ).

fof(f883,axiom,
    ! [X27,X18,X4] :
      ( class_Divides_Osemiring__div(X4)
     => c_Divides_Odiv__class_Omod(X4,X18,X27) = c_Divides_Odiv__class_Omod(X4,c_Groups_Oplus__class_Oplus(X4,X18,X27),X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__add__self2) ).

fof(f10488,plain,
    ( spl38_610
    | ~ spl38_3
    | ~ spl38_122
    | ~ spl38_533 ),
    inference(avatar_split_clause,[],[f9875,f9585,f6501,f5906,f10486]) ).

fof(f10486,plain,
    ( spl38_610
  <=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,v_s____)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_610])]) ).

fof(f6501,plain,
    ( spl38_122
  <=> class_Groups_Ozero(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_122])]) ).

fof(f9585,plain,
    ( spl38_533
  <=> ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X1,c_Polynomial_OpCons(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))))
        | ~ class_Groups_Ozero(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_533])]) ).

fof(f9875,plain,
    ( ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,v_s____))
    | ~ spl38_3
    | ~ spl38_122
    | ~ spl38_533 ),
    inference(forward_demodulation,[],[f9871,f5908]) ).

fof(f9871,plain,
    ( ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))
    | ~ spl38_122
    | ~ spl38_533 ),
    inference(resolution,[],[f9586,f6503]) ).

fof(f6503,plain,
    ( class_Groups_Ozero(tc_Complex_Ocomplex)
    | ~ spl38_122 ),
    inference(avatar_component_clause,[],[f6501]) ).

fof(f9586,plain,
    ( ! [X0,X1] :
        ( ~ class_Groups_Ozero(X1)
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X1,c_Polynomial_OpCons(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))) )
    | ~ spl38_533 ),
    inference(avatar_component_clause,[],[f9585]) ).

fof(f10484,plain,
    spl38_609,
    inference(avatar_split_clause,[],[f4796,f10482]) ).

fof(f10482,plain,
    ( spl38_609
  <=> ! [X2,X0,X1] :
        ( c_Divides_Odiv__class_Omod(X2,X1,X0) = c_Divides_Odiv__class_Omod(X2,c_Divides_Odiv__class_Omod(X2,X1,X0),X0)
        | ~ class_Divides_Osemiring__div(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_609])]) ).

fof(f4796,plain,
    ! [X2,X0,X1] :
      ( c_Divides_Odiv__class_Omod(X2,X1,X0) = c_Divides_Odiv__class_Omod(X2,c_Divides_Odiv__class_Omod(X2,X1,X0),X0)
      | ~ class_Divides_Osemiring__div(X2) ),
    inference(cnf_transformation,[],[f2816]) ).

fof(f2816,plain,
    ! [X0,X1,X2] :
      ( c_Divides_Odiv__class_Omod(X2,X1,X0) = c_Divides_Odiv__class_Omod(X2,c_Divides_Odiv__class_Omod(X2,X1,X0),X0)
      | ~ class_Divides_Osemiring__div(X2) ),
    inference(ennf_transformation,[],[f1815]) ).

fof(f1815,plain,
    ! [X0,X1,X2] :
      ( class_Divides_Osemiring__div(X2)
     => c_Divides_Odiv__class_Omod(X2,X1,X0) = c_Divides_Odiv__class_Omod(X2,c_Divides_Odiv__class_Omod(X2,X1,X0),X0) ),
    inference(rectify,[],[f863]) ).

fof(f863,axiom,
    ! [X27,X18,X4] :
      ( class_Divides_Osemiring__div(X4)
     => c_Divides_Odiv__class_Omod(X4,X18,X27) = c_Divides_Odiv__class_Omod(X4,c_Divides_Odiv__class_Omod(X4,X18,X27),X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mod__trivial) ).

fof(f10480,plain,
    spl38_608,
    inference(avatar_split_clause,[],[f4795,f10478]) ).

fof(f10478,plain,
    ( spl38_608
  <=> ! [X2,X0,X1] :
        ( c_Groups_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),X0)
        | ~ class_Divides_Osemiring__div(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_608])]) ).

fof(f4795,plain,
    ! [X2,X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),X0)
      | ~ class_Divides_Osemiring__div(X2) ),
    inference(cnf_transformation,[],[f2815]) ).

fof(f2815,plain,
    ! [X0,X1,X2] :
      ( c_Groups_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),X0)
      | ~ class_Divides_Osemiring__div(X2) ),
    inference(ennf_transformation,[],[f1814]) ).

fof(f1814,plain,
    ! [X0,X1,X2] :
      ( class_Divides_Osemiring__div(X2)
     => c_Groups_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),X0) ),
    inference(rectify,[],[f875]) ).

fof(f875,axiom,
    ! [X27,X18,X4] :
      ( class_Divides_Osemiring__div(X4)
     => c_Groups_Ozero__class_Ozero(X4) = c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X18),X27),X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__self2__is__0) ).

fof(f10476,plain,
    spl38_607,
    inference(avatar_split_clause,[],[f4794,f10474]) ).

fof(f10474,plain,
    ( spl38_607
  <=> ! [X2,X0,X1] :
        ( c_Groups_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),X1)
        | ~ class_Divides_Osemiring__div(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_607])]) ).

fof(f4794,plain,
    ! [X2,X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),X1)
      | ~ class_Divides_Osemiring__div(X2) ),
    inference(cnf_transformation,[],[f2814]) ).

fof(f2814,plain,
    ! [X0,X1,X2] :
      ( c_Groups_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),X1)
      | ~ class_Divides_Osemiring__div(X2) ),
    inference(ennf_transformation,[],[f1813]) ).

fof(f1813,plain,
    ! [X0,X1,X2] :
      ( class_Divides_Osemiring__div(X2)
     => c_Groups_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),X1) ),
    inference(rectify,[],[f874]) ).

fof(f874,axiom,
    ! [X18,X27,X4] :
      ( class_Divides_Osemiring__div(X4)
     => c_Groups_Ozero__class_Ozero(X4) = c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X27),X18),X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__self1__is__0) ).

fof(f10472,plain,
    spl38_606,
    inference(avatar_split_clause,[],[f4761,f10470]) ).

fof(f10470,plain,
    ( spl38_606
  <=> ! [X2,X0,X1] :
        ( c_Groups_Ouminus__class_Ouminus(X2,X0) = X1
        | c_Groups_Ozero__class_Ozero(X2) != c_Groups_Oplus__class_Oplus(X2,X1,X0)
        | ~ class_Groups_Ogroup__add(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_606])]) ).

fof(f4761,plain,
    ! [X2,X0,X1] :
      ( c_Groups_Ouminus__class_Ouminus(X2,X0) = X1
      | c_Groups_Ozero__class_Ozero(X2) != c_Groups_Oplus__class_Oplus(X2,X1,X0)
      | ~ class_Groups_Ogroup__add(X2) ),
    inference(cnf_transformation,[],[f3673]) ).

fof(f3673,plain,
    ! [X0,X1,X2] :
      ( ( ( c_Groups_Ouminus__class_Ouminus(X2,X0) = X1
          | c_Groups_Ozero__class_Ozero(X2) != c_Groups_Oplus__class_Oplus(X2,X1,X0) )
        & ( c_Groups_Ozero__class_Ozero(X2) = c_Groups_Oplus__class_Oplus(X2,X1,X0)
          | c_Groups_Ouminus__class_Ouminus(X2,X0) != X1 ) )
      | ~ class_Groups_Ogroup__add(X2) ),
    inference(nnf_transformation,[],[f2790]) ).

fof(f2790,plain,
    ! [X0,X1,X2] :
      ( ( c_Groups_Ouminus__class_Ouminus(X2,X0) = X1
      <=> c_Groups_Ozero__class_Ozero(X2) = c_Groups_Oplus__class_Oplus(X2,X1,X0) )
      | ~ class_Groups_Ogroup__add(X2) ),
    inference(ennf_transformation,[],[f1795]) ).

fof(f1795,plain,
    ! [X0,X1,X2] :
      ( class_Groups_Ogroup__add(X2)
     => ( c_Groups_Ouminus__class_Ouminus(X2,X0) = X1
      <=> c_Groups_Ozero__class_Ozero(X2) = c_Groups_Oplus__class_Oplus(X2,X1,X0) ) ),
    inference(rectify,[],[f538]) ).

fof(f538,axiom,
    ! [X20,X12,X4] :
      ( class_Groups_Ogroup__add(X4)
     => ( c_Groups_Ouminus__class_Ouminus(X4,X20) = X12
      <=> c_Groups_Ozero__class_Ozero(X4) = c_Groups_Oplus__class_Oplus(X4,X12,X20) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__neg__iff__add__eq__0) ).

fof(f10468,plain,
    spl38_605,
    inference(avatar_split_clause,[],[f4755,f10466]) ).

fof(f10466,plain,
    ( spl38_605
  <=> ! [X2,X0,X1] :
        ( c_Groups_Ouminus__class_Ouminus(X2,X1) = X0
        | c_Groups_Ozero__class_Ozero(X2) != c_Groups_Oplus__class_Oplus(X2,X1,X0)
        | ~ class_Groups_Ogroup__add(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_605])]) ).

fof(f4755,plain,
    ! [X2,X0,X1] :
      ( c_Groups_Ouminus__class_Ouminus(X2,X1) = X0
      | c_Groups_Ozero__class_Ozero(X2) != c_Groups_Oplus__class_Oplus(X2,X1,X0)
      | ~ class_Groups_Ogroup__add(X2) ),
    inference(cnf_transformation,[],[f2787]) ).

fof(f2787,plain,
    ! [X0,X1,X2] :
      ( c_Groups_Ouminus__class_Ouminus(X2,X1) = X0
      | c_Groups_Ozero__class_Ozero(X2) != c_Groups_Oplus__class_Oplus(X2,X1,X0)
      | ~ class_Groups_Ogroup__add(X2) ),
    inference(flattening,[],[f2786]) ).

fof(f2786,plain,
    ! [X0,X1,X2] :
      ( c_Groups_Ouminus__class_Ouminus(X2,X1) = X0
      | c_Groups_Ozero__class_Ozero(X2) != c_Groups_Oplus__class_Oplus(X2,X1,X0)
      | ~ class_Groups_Ogroup__add(X2) ),
    inference(ennf_transformation,[],[f1792]) ).

fof(f1792,plain,
    ! [X0,X1,X2] :
      ( class_Groups_Ogroup__add(X2)
     => ( c_Groups_Ozero__class_Ozero(X2) = c_Groups_Oplus__class_Oplus(X2,X1,X0)
       => c_Groups_Ouminus__class_Ouminus(X2,X1) = X0 ) ),
    inference(rectify,[],[f535]) ).

fof(f535,axiom,
    ! [X27,X18,X4] :
      ( class_Groups_Ogroup__add(X4)
     => ( c_Groups_Ozero__class_Ozero(X4) = c_Groups_Oplus__class_Oplus(X4,X18,X27)
       => c_Groups_Ouminus__class_Ouminus(X4,X18) = X27 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__unique) ).

fof(f10464,plain,
    spl38_604,
    inference(avatar_split_clause,[],[f4670,f10462]) ).

fof(f10462,plain,
    ( spl38_604
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
        | ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
        | ~ class_Groups_Oordered__ab__group__add(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_604])]) ).

fof(f4670,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
      | ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
      | ~ class_Groups_Oordered__ab__group__add(X2) ),
    inference(cnf_transformation,[],[f3652]) ).

fof(f3652,plain,
    ! [X0,X1,X2] :
      ( ( ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
          | ~ c_Orderings_Oord__class_Oless(X2,X0,X1) )
        & ( c_Orderings_Oord__class_Oless(X2,X0,X1)
          | ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0)) ) )
      | ~ class_Groups_Oordered__ab__group__add(X2) ),
    inference(nnf_transformation,[],[f2683]) ).

fof(f2683,plain,
    ! [X0,X1,X2] :
      ( ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
      <=> c_Orderings_Oord__class_Oless(X2,X0,X1) )
      | ~ class_Groups_Oordered__ab__group__add(X2) ),
    inference(ennf_transformation,[],[f1727]) ).

fof(f1727,plain,
    ! [X0,X1,X2] :
      ( class_Groups_Oordered__ab__group__add(X2)
     => ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
      <=> c_Orderings_Oord__class_Oless(X2,X0,X1) ) ),
    inference(rectify,[],[f135]) ).

fof(f135,axiom,
    ! [X12,X20,X4] :
      ( class_Groups_Oordered__ab__group__add(X4)
     => ( c_Orderings_Oord__class_Oless(X4,c_Groups_Ouminus__class_Ouminus(X4,X20),c_Groups_Ouminus__class_Ouminus(X4,X12))
      <=> c_Orderings_Oord__class_Oless(X4,X12,X20) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__less__iff__less) ).

fof(f10460,plain,
    spl38_603,
    inference(avatar_split_clause,[],[f4669,f10458]) ).

fof(f10458,plain,
    ( spl38_603
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless(X2,X0,X1)
        | ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
        | ~ class_Groups_Oordered__ab__group__add(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_603])]) ).

fof(f4669,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless(X2,X0,X1)
      | ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
      | ~ class_Groups_Oordered__ab__group__add(X2) ),
    inference(cnf_transformation,[],[f3652]) ).

fof(f10456,plain,
    spl38_602,
    inference(avatar_split_clause,[],[f4667,f10454]) ).

fof(f10454,plain,
    ( spl38_602
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
        | ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
        | ~ class_Groups_Oordered__ab__group__add(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_602])]) ).

fof(f4667,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
      | ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
      | ~ class_Groups_Oordered__ab__group__add(X2) ),
    inference(cnf_transformation,[],[f3651]) ).

fof(f3651,plain,
    ! [X0,X1,X2] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
          | ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1) )
        & ( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
          | ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0)) ) )
      | ~ class_Groups_Oordered__ab__group__add(X2) ),
    inference(nnf_transformation,[],[f2682]) ).

fof(f2682,plain,
    ! [X0,X1,X2] :
      ( ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
      <=> c_Orderings_Oord__class_Oless__eq(X2,X0,X1) )
      | ~ class_Groups_Oordered__ab__group__add(X2) ),
    inference(ennf_transformation,[],[f1726]) ).

fof(f1726,plain,
    ! [X0,X1,X2] :
      ( class_Groups_Oordered__ab__group__add(X2)
     => ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
      <=> c_Orderings_Oord__class_Oless__eq(X2,X0,X1) ) ),
    inference(rectify,[],[f134]) ).

fof(f134,axiom,
    ! [X12,X20,X4] :
      ( class_Groups_Oordered__ab__group__add(X4)
     => ( c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ouminus__class_Ouminus(X4,X20),c_Groups_Ouminus__class_Ouminus(X4,X12))
      <=> c_Orderings_Oord__class_Oless__eq(X4,X12,X20) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__le__iff__le) ).

fof(f10452,plain,
    spl38_601,
    inference(avatar_split_clause,[],[f4666,f10450]) ).

fof(f10450,plain,
    ( spl38_601
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)
        | ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),X1)
        | ~ class_Groups_Oordered__ab__group__add(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_601])]) ).

fof(f4666,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)
      | ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),X1)
      | ~ class_Groups_Oordered__ab__group__add(X2) ),
    inference(cnf_transformation,[],[f3650]) ).

fof(f3650,plain,
    ! [X0,X1,X2] :
      ( ( ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)
          | ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),X1) )
        & ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),X1)
          | ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0) ) )
      | ~ class_Groups_Oordered__ab__group__add(X2) ),
    inference(nnf_transformation,[],[f2681]) ).

fof(f2681,plain,
    ! [X0,X1,X2] :
      ( ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)
      <=> c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),X1) )
      | ~ class_Groups_Oordered__ab__group__add(X2) ),
    inference(ennf_transformation,[],[f1725]) ).

fof(f1725,plain,
    ! [X0,X1,X2] :
      ( class_Groups_Oordered__ab__group__add(X2)
     => ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)
      <=> c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),X1) ) ),
    inference(rectify,[],[f138]) ).

fof(f138,axiom,
    ! [X20,X12,X4] :
      ( class_Groups_Oordered__ab__group__add(X4)
     => ( c_Orderings_Oord__class_Oless(X4,c_Groups_Ouminus__class_Ouminus(X4,X12),X20)
      <=> c_Orderings_Oord__class_Oless(X4,c_Groups_Ouminus__class_Ouminus(X4,X20),X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__less__iff) ).

fof(f10448,plain,
    spl38_600,
    inference(avatar_split_clause,[],[f4664,f10446]) ).

fof(f10446,plain,
    ( spl38_600
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
        | ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ouminus__class_Ouminus(X2,X1))
        | ~ class_Groups_Oordered__ab__group__add(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_600])]) ).

fof(f4664,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
      | ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ouminus__class_Ouminus(X2,X1))
      | ~ class_Groups_Oordered__ab__group__add(X2) ),
    inference(cnf_transformation,[],[f3649]) ).

fof(f3649,plain,
    ! [X0,X1,X2] :
      ( ( ( c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
          | ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ouminus__class_Ouminus(X2,X1)) )
        & ( c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ouminus__class_Ouminus(X2,X1))
          | ~ c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0)) ) )
      | ~ class_Groups_Oordered__ab__group__add(X2) ),
    inference(nnf_transformation,[],[f2680]) ).

fof(f2680,plain,
    ! [X0,X1,X2] :
      ( ( c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
      <=> c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ouminus__class_Ouminus(X2,X1)) )
      | ~ class_Groups_Oordered__ab__group__add(X2) ),
    inference(ennf_transformation,[],[f1724]) ).

fof(f1724,plain,
    ! [X0,X1,X2] :
      ( class_Groups_Oordered__ab__group__add(X2)
     => ( c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
      <=> c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ouminus__class_Ouminus(X2,X1)) ) ),
    inference(rectify,[],[f141]) ).

fof(f141,axiom,
    ! [X20,X12,X4] :
      ( class_Groups_Oordered__ab__group__add(X4)
     => ( c_Orderings_Oord__class_Oless(X4,X12,c_Groups_Ouminus__class_Ouminus(X4,X20))
      <=> c_Orderings_Oord__class_Oless(X4,X20,c_Groups_Ouminus__class_Ouminus(X4,X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__minus__iff) ).

fof(f10444,plain,
    ( spl38_599
    | ~ spl38_3
    | ~ spl38_128
    | ~ spl38_519 ),
    inference(avatar_split_clause,[],[f9698,f9529,f6531,f5906,f10441]) ).

fof(f6531,plain,
    ( spl38_128
  <=> class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_128])]) ).

fof(f9529,plain,
    ( spl38_519
  <=> ! [X0] :
        ( c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))
        | ~ class_Rings_Ocomm__semiring__1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_519])]) ).

fof(f9698,plain,
    ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),v_s____) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl38_3
    | ~ spl38_128
    | ~ spl38_519 ),
    inference(forward_demodulation,[],[f9693,f5908]) ).

fof(f9693,plain,
    ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl38_128
    | ~ spl38_519 ),
    inference(resolution,[],[f9530,f6533]) ).

fof(f6533,plain,
    ( class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)
    | ~ spl38_128 ),
    inference(avatar_component_clause,[],[f6531]) ).

fof(f9530,plain,
    ( ! [X0] :
        ( ~ class_Rings_Ocomm__semiring__1(X0)
        | c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) )
    | ~ spl38_519 ),
    inference(avatar_component_clause,[],[f9529]) ).

fof(f10439,plain,
    spl38_598,
    inference(avatar_split_clause,[],[f4662,f10437]) ).

fof(f10437,plain,
    ( spl38_598
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)
        | ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),X1)
        | ~ class_Groups_Oordered__ab__group__add(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_598])]) ).

fof(f4662,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)
      | ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),X1)
      | ~ class_Groups_Oordered__ab__group__add(X2) ),
    inference(cnf_transformation,[],[f3648]) ).

fof(f3648,plain,
    ! [X0,X1,X2] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)
          | ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),X1) )
        & ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),X1)
          | ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0) ) )
      | ~ class_Groups_Oordered__ab__group__add(X2) ),
    inference(nnf_transformation,[],[f2679]) ).

fof(f2679,plain,
    ! [X0,X1,X2] :
      ( ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)
      <=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),X1) )
      | ~ class_Groups_Oordered__ab__group__add(X2) ),
    inference(ennf_transformation,[],[f1723]) ).

fof(f1723,plain,
    ! [X0,X1,X2] :
      ( class_Groups_Oordered__ab__group__add(X2)
     => ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)
      <=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),X1) ) ),
    inference(rectify,[],[f137]) ).

fof(f137,axiom,
    ! [X20,X12,X4] :
      ( class_Groups_Oordered__ab__group__add(X4)
     => ( c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ouminus__class_Ouminus(X4,X12),X20)
      <=> c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ouminus__class_Ouminus(X4,X20),X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__le__iff) ).

fof(f10435,plain,
    spl38_597,
    inference(avatar_split_clause,[],[f4660,f10433]) ).

fof(f10433,plain,
    ( spl38_597
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
        | ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ouminus__class_Ouminus(X2,X1))
        | ~ class_Groups_Oordered__ab__group__add(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_597])]) ).

fof(f4660,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
      | ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ouminus__class_Ouminus(X2,X1))
      | ~ class_Groups_Oordered__ab__group__add(X2) ),
    inference(cnf_transformation,[],[f3647]) ).

fof(f3647,plain,
    ! [X0,X1,X2] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
          | ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ouminus__class_Ouminus(X2,X1)) )
        & ( c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ouminus__class_Ouminus(X2,X1))
          | ~ c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0)) ) )
      | ~ class_Groups_Oordered__ab__group__add(X2) ),
    inference(nnf_transformation,[],[f2678]) ).

fof(f2678,plain,
    ! [X0,X1,X2] :
      ( ( c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
      <=> c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ouminus__class_Ouminus(X2,X1)) )
      | ~ class_Groups_Oordered__ab__group__add(X2) ),
    inference(ennf_transformation,[],[f1722]) ).

fof(f1722,plain,
    ! [X0,X1,X2] :
      ( class_Groups_Oordered__ab__group__add(X2)
     => ( c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
      <=> c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ouminus__class_Ouminus(X2,X1)) ) ),
    inference(rectify,[],[f140]) ).

fof(f140,axiom,
    ! [X20,X12,X4] :
      ( class_Groups_Oordered__ab__group__add(X4)
     => ( c_Orderings_Oord__class_Oless__eq(X4,X12,c_Groups_Ouminus__class_Ouminus(X4,X20))
      <=> c_Orderings_Oord__class_Oless__eq(X4,X20,c_Groups_Ouminus__class_Ouminus(X4,X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__minus__iff) ).

fof(f10431,plain,
    spl38_596,
    inference(avatar_split_clause,[],[f4658,f10429]) ).

fof(f10429,plain,
    ( spl38_596
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless(X2,X1,X0)
        | ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2))
        | ~ class_Groups_Oordered__ab__group__add(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_596])]) ).

fof(f4658,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless(X2,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2))
      | ~ class_Groups_Oordered__ab__group__add(X2) ),
    inference(cnf_transformation,[],[f3646]) ).

fof(f3646,plain,
    ! [X0,X1,X2] :
      ( ( ( c_Orderings_Oord__class_Oless(X2,X1,X0)
          | ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2)) )
        & ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2))
          | ~ c_Orderings_Oord__class_Oless(X2,X1,X0) ) )
      | ~ class_Groups_Oordered__ab__group__add(X2) ),
    inference(nnf_transformation,[],[f2677]) ).

fof(f2677,plain,
    ! [X0,X1,X2] :
      ( ( c_Orderings_Oord__class_Oless(X2,X1,X0)
      <=> c_Orderings_Oord__class_Oless(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2)) )
      | ~ class_Groups_Oordered__ab__group__add(X2) ),
    inference(ennf_transformation,[],[f1721]) ).

fof(f1721,plain,
    ! [X0,X1,X2] :
      ( class_Groups_Oordered__ab__group__add(X2)
     => ( c_Orderings_Oord__class_Oless(X2,X1,X0)
      <=> c_Orderings_Oord__class_Oless(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2)) ) ),
    inference(rectify,[],[f960]) ).

fof(f960,axiom,
    ! [X20,X12,X4] :
      ( class_Groups_Oordered__ab__group__add(X4)
     => ( c_Orderings_Oord__class_Oless(X4,X12,X20)
      <=> c_Orderings_Oord__class_Oless(X4,c_Groups_Ominus__class_Ominus(X4,X12,X20),c_Groups_Ozero__class_Ozero(X4)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__iff__diff__less__0) ).

fof(f10427,plain,
    spl38_595,
    inference(avatar_split_clause,[],[f4657,f10425]) ).

fof(f10425,plain,
    ( spl38_595
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2))
        | ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
        | ~ class_Groups_Oordered__ab__group__add(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_595])]) ).

fof(f4657,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2))
      | ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
      | ~ class_Groups_Oordered__ab__group__add(X2) ),
    inference(cnf_transformation,[],[f3646]) ).

fof(f10423,plain,
    spl38_594,
    inference(avatar_split_clause,[],[f4656,f10421]) ).

fof(f10421,plain,
    ( spl38_594
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
        | ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2))
        | ~ class_Groups_Oordered__ab__group__add(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_594])]) ).

fof(f4656,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2))
      | ~ class_Groups_Oordered__ab__group__add(X2) ),
    inference(cnf_transformation,[],[f3645]) ).

fof(f3645,plain,
    ! [X0,X1,X2] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
          | ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2)) )
        & ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2))
          | ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ) )
      | ~ class_Groups_Oordered__ab__group__add(X2) ),
    inference(nnf_transformation,[],[f2676]) ).

fof(f2676,plain,
    ! [X0,X1,X2] :
      ( ( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
      <=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2)) )
      | ~ class_Groups_Oordered__ab__group__add(X2) ),
    inference(ennf_transformation,[],[f1720]) ).

fof(f1720,plain,
    ! [X0,X1,X2] :
      ( class_Groups_Oordered__ab__group__add(X2)
     => ( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
      <=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2)) ) ),
    inference(rectify,[],[f961]) ).

fof(f961,axiom,
    ! [X20,X12,X4] :
      ( class_Groups_Oordered__ab__group__add(X4)
     => ( c_Orderings_Oord__class_Oless__eq(X4,X12,X20)
      <=> c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ominus__class_Ominus(X4,X12,X20),c_Groups_Ozero__class_Ozero(X4)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__iff__diff__le__0) ).

fof(f10419,plain,
    spl38_593,
    inference(avatar_split_clause,[],[f4655,f10417]) ).

fof(f10417,plain,
    ( spl38_593
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2))
        | ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
        | ~ class_Groups_Oordered__ab__group__add(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_593])]) ).

fof(f4655,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2))
      | ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
      | ~ class_Groups_Oordered__ab__group__add(X2) ),
    inference(cnf_transformation,[],[f3645]) ).

fof(f10415,plain,
    spl38_592,
    inference(avatar_split_clause,[],[f4654,f10413]) ).

fof(f10413,plain,
    ( spl38_592
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Groups_Ouminus__class_Ouminus(X2,X1))
        | ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
        | ~ class_Groups_Oordered__ab__group__add(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_592])]) ).

fof(f4654,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Groups_Ouminus__class_Ouminus(X2,X1))
      | ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
      | ~ class_Groups_Oordered__ab__group__add(X2) ),
    inference(cnf_transformation,[],[f2675]) ).

fof(f2675,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Groups_Ouminus__class_Ouminus(X2,X1))
      | ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
      | ~ class_Groups_Oordered__ab__group__add(X2) ),
    inference(flattening,[],[f2674]) ).

fof(f2674,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Groups_Ouminus__class_Ouminus(X2,X1))
      | ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
      | ~ class_Groups_Oordered__ab__group__add(X2) ),
    inference(ennf_transformation,[],[f1719]) ).

fof(f1719,plain,
    ! [X0,X1,X2] :
      ( class_Groups_Oordered__ab__group__add(X2)
     => ( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
       => c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Groups_Ouminus__class_Ouminus(X2,X1)) ) ),
    inference(rectify,[],[f132]) ).

fof(f132,axiom,
    ! [X27,X18,X4] :
      ( class_Groups_Oordered__ab__group__add(X4)
     => ( c_Orderings_Oord__class_Oless__eq(X4,X18,X27)
       => c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ouminus__class_Ouminus(X4,X27),c_Groups_Ouminus__class_Ouminus(X4,X18)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__neg__le) ).

fof(f10411,plain,
    spl38_591,
    inference(avatar_split_clause,[],[f4643,f10409]) ).

fof(f10409,plain,
    ( spl38_591
  <=> ! [X2,X0,X1] :
        ( sP4(X0,X1,X2)
        | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
        | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_591])]) ).

fof(f4643,plain,
    ! [X2,X0,X1] :
      ( sP4(X0,X1,X2)
      | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
      | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(cnf_transformation,[],[f3638]) ).

fof(f3638,plain,
    ! [X0,X1,X2] :
      ( ( sP4(X0,X1,X2)
        | ( ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
            | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) )
          & ( ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
            | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ) ) )
      & ( ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
          & c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) )
        | ( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
          & c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) )
        | ~ sP4(X0,X1,X2) ) ),
    inference(rectify,[],[f3637]) ).

fof(f3637,plain,
    ! [X0,X2,X1] :
      ( ( sP4(X0,X2,X1)
        | ( ( ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
            | ~ c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2)) )
          & ( ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
            | ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1) ) ) )
      & ( ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
          & c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2)) )
        | ( c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
          & c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1) )
        | ~ sP4(X0,X2,X1) ) ),
    inference(flattening,[],[f3636]) ).

fof(f3636,plain,
    ! [X0,X2,X1] :
      ( ( sP4(X0,X2,X1)
        | ( ( ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
            | ~ c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2)) )
          & ( ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
            | ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1) ) ) )
      & ( ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
          & c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2)) )
        | ( c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
          & c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1) )
        | ~ sP4(X0,X2,X1) ) ),
    inference(nnf_transformation,[],[f3458]) ).

fof(f3458,plain,
    ! [X0,X2,X1] :
      ( sP4(X0,X2,X1)
    <=> ( ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
          & c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2)) )
        | ( c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
          & c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).

fof(f10407,plain,
    spl38_590,
    inference(avatar_split_clause,[],[f4642,f10405]) ).

fof(f10405,plain,
    ( spl38_590
  <=> ! [X2,X0,X1] :
        ( sP4(X0,X1,X2)
        | ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
        | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_590])]) ).

fof(f4642,plain,
    ! [X2,X0,X1] :
      ( sP4(X0,X1,X2)
      | ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
      | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(cnf_transformation,[],[f3638]) ).

fof(f10403,plain,
    spl38_589,
    inference(avatar_split_clause,[],[f4641,f10401]) ).

fof(f10401,plain,
    ( spl38_589
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
        | c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
        | ~ sP4(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_589])]) ).

fof(f4641,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
      | c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
      | ~ sP4(X0,X1,X2) ),
    inference(cnf_transformation,[],[f3638]) ).

fof(f10398,plain,
    spl38_588,
    inference(avatar_split_clause,[],[f4640,f10396]) ).

fof(f10396,plain,
    ( spl38_588
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
        | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
        | ~ sP4(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_588])]) ).

fof(f4640,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
      | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
      | ~ sP4(X0,X1,X2) ),
    inference(cnf_transformation,[],[f3638]) ).

fof(f10394,plain,
    spl38_587,
    inference(avatar_split_clause,[],[f4639,f10392]) ).

fof(f10392,plain,
    ( spl38_587
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
        | c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
        | ~ sP4(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_587])]) ).

fof(f4639,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
      | c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
      | ~ sP4(X0,X1,X2) ),
    inference(cnf_transformation,[],[f3638]) ).

fof(f10390,plain,
    spl38_586,
    inference(avatar_split_clause,[],[f4638,f10388]) ).

fof(f10388,plain,
    ( spl38_586
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
        | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
        | ~ sP4(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_586])]) ).

fof(f4638,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
      | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
      | ~ sP4(X0,X1,X2) ),
    inference(cnf_transformation,[],[f3638]) ).

fof(f10386,plain,
    spl38_585,
    inference(avatar_split_clause,[],[f4634,f10384]) ).

fof(f10384,plain,
    ( spl38_585
  <=> ! [X2,X0,X1] :
        ( sP2(X0,X1,X2)
        | ~ c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0))
        | ~ c_Orderings_Oord__class_Oless__eq(X0,X2,c_Groups_Ozero__class_Ozero(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_585])]) ).

fof(f4634,plain,
    ! [X2,X0,X1] :
      ( sP2(X0,X1,X2)
      | ~ c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0))
      | ~ c_Orderings_Oord__class_Oless__eq(X0,X2,c_Groups_Ozero__class_Ozero(X0)) ),
    inference(cnf_transformation,[],[f3633]) ).

fof(f3633,plain,
    ! [X0,X1,X2] :
      ( ( sP2(X0,X1,X2)
        | ( ( ~ c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0))
            | ~ c_Orderings_Oord__class_Oless__eq(X0,X2,c_Groups_Ozero__class_Ozero(X0)) )
          & ( ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1)
            | ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X2) ) ) )
      & ( ( c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0))
          & c_Orderings_Oord__class_Oless__eq(X0,X2,c_Groups_Ozero__class_Ozero(X0)) )
        | ( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1)
          & c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X2) )
        | ~ sP2(X0,X1,X2) ) ),
    inference(rectify,[],[f3632]) ).

fof(f3632,plain,
    ! [X2,X0,X1] :
      ( ( sP2(X2,X0,X1)
        | ( ( ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
            | ~ c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2)) )
          & ( ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
            | ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1) ) ) )
      & ( ( c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
          & c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2)) )
        | ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
          & c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1) )
        | ~ sP2(X2,X0,X1) ) ),
    inference(flattening,[],[f3631]) ).

fof(f3631,plain,
    ! [X2,X0,X1] :
      ( ( sP2(X2,X0,X1)
        | ( ( ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
            | ~ c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2)) )
          & ( ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
            | ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1) ) ) )
      & ( ( c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
          & c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2)) )
        | ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
          & c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1) )
        | ~ sP2(X2,X0,X1) ) ),
    inference(nnf_transformation,[],[f3455]) ).

fof(f3455,plain,
    ! [X2,X0,X1] :
      ( sP2(X2,X0,X1)
    <=> ( ( c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
          & c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2)) )
        | ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
          & c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).

fof(f10382,plain,
    spl38_584,
    inference(avatar_split_clause,[],[f4633,f10380]) ).

fof(f10380,plain,
    ( spl38_584
  <=> ! [X2,X0,X1] :
        ( sP2(X0,X1,X2)
        | ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1)
        | ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_584])]) ).

fof(f4633,plain,
    ! [X2,X0,X1] :
      ( sP2(X0,X1,X2)
      | ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1)
      | ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X2) ),
    inference(cnf_transformation,[],[f3633]) ).

fof(f10378,plain,
    spl38_583,
    inference(avatar_split_clause,[],[f4632,f10376]) ).

fof(f10376,plain,
    ( spl38_583
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0))
        | c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1)
        | ~ sP2(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_583])]) ).

fof(f4632,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0))
      | c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1)
      | ~ sP2(X0,X1,X2) ),
    inference(cnf_transformation,[],[f3633]) ).

fof(f10374,plain,
    spl38_582,
    inference(avatar_split_clause,[],[f4631,f10372]) ).

fof(f10372,plain,
    ( spl38_582
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0))
        | c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X2)
        | ~ sP2(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_582])]) ).

fof(f4631,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0))
      | c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X2)
      | ~ sP2(X0,X1,X2) ),
    inference(cnf_transformation,[],[f3633]) ).

fof(f10370,plain,
    spl38_581,
    inference(avatar_split_clause,[],[f4630,f10368]) ).

fof(f10368,plain,
    ( spl38_581
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X0,X2,c_Groups_Ozero__class_Ozero(X0))
        | c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1)
        | ~ sP2(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_581])]) ).

fof(f4630,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X0,X2,c_Groups_Ozero__class_Ozero(X0))
      | c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1)
      | ~ sP2(X0,X1,X2) ),
    inference(cnf_transformation,[],[f3633]) ).

fof(f10366,plain,
    spl38_580,
    inference(avatar_split_clause,[],[f4629,f10364]) ).

fof(f10364,plain,
    ( spl38_580
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X0,X2,c_Groups_Ozero__class_Ozero(X0))
        | c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X2)
        | ~ sP2(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_580])]) ).

fof(f4629,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X0,X2,c_Groups_Ozero__class_Ozero(X0))
      | c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X2)
      | ~ sP2(X0,X1,X2) ),
    inference(cnf_transformation,[],[f3633]) ).

fof(f10362,plain,
    spl38_579,
    inference(avatar_split_clause,[],[f4620,f10360]) ).

fof(f10360,plain,
    ( spl38_579
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
        | ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
        | ~ class_Lattices_Oboolean__algebra(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_579])]) ).

fof(f4620,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
      | ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
      | ~ class_Lattices_Oboolean__algebra(X2) ),
    inference(cnf_transformation,[],[f3628]) ).

fof(f3628,plain,
    ! [X0,X1,X2] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
          | ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1) )
        & ( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
          | ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0)) ) )
      | ~ class_Lattices_Oboolean__algebra(X2) ),
    inference(nnf_transformation,[],[f2661]) ).

fof(f2661,plain,
    ! [X0,X1,X2] :
      ( ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
      <=> c_Orderings_Oord__class_Oless__eq(X2,X0,X1) )
      | ~ class_Lattices_Oboolean__algebra(X2) ),
    inference(ennf_transformation,[],[f1709]) ).

fof(f1709,plain,
    ! [X0,X1,X2] :
      ( class_Lattices_Oboolean__algebra(X2)
     => ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
      <=> c_Orderings_Oord__class_Oless__eq(X2,X0,X1) ) ),
    inference(rectify,[],[f783]) ).

fof(f783,axiom,
    ! [X17,X3,X4] :
      ( class_Lattices_Oboolean__algebra(X4)
     => ( c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ouminus__class_Ouminus(X4,X3),c_Groups_Ouminus__class_Ouminus(X4,X17))
      <=> c_Orderings_Oord__class_Oless__eq(X4,X17,X3) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__le__compl__iff) ).

fof(f10357,plain,
    spl38_578,
    inference(avatar_split_clause,[],[f4617,f10355]) ).

fof(f10355,plain,
    ( spl38_578
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Groups_Ouminus__class_Ouminus(X2,X1))
        | ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
        | ~ class_Lattices_Oboolean__algebra(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_578])]) ).

fof(f4617,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Groups_Ouminus__class_Ouminus(X2,X1))
      | ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
      | ~ class_Lattices_Oboolean__algebra(X2) ),
    inference(cnf_transformation,[],[f2659]) ).

fof(f2659,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Groups_Ouminus__class_Ouminus(X2,X1))
      | ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
      | ~ class_Lattices_Oboolean__algebra(X2) ),
    inference(flattening,[],[f2658]) ).

fof(f2658,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Groups_Ouminus__class_Ouminus(X2,X1))
      | ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
      | ~ class_Lattices_Oboolean__algebra(X2) ),
    inference(ennf_transformation,[],[f1707]) ).

fof(f1707,plain,
    ! [X0,X1,X2] :
      ( class_Lattices_Oboolean__algebra(X2)
     => ( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
       => c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Groups_Ouminus__class_Ouminus(X2,X1)) ) ),
    inference(rectify,[],[f776]) ).

fof(f776,axiom,
    ! [X28,X13,X4] :
      ( class_Lattices_Oboolean__algebra(X4)
     => ( c_Orderings_Oord__class_Oless__eq(X4,X13,X28)
       => c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ouminus__class_Ouminus(X4,X28),c_Groups_Ouminus__class_Ouminus(X4,X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__mono) ).

fof(f10353,plain,
    spl38_577,
    inference(avatar_split_clause,[],[f4600,f10351]) ).

fof(f10351,plain,
    ( spl38_577
  <=> ! [X2,X0,X1] :
        ( c_Polynomial_Opoly__gcd(X2,X1,X0) = c_Polynomial_Opoly__gcd(X2,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),X1),X0)
        | ~ class_Fields_Ofield(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_577])]) ).

fof(f4600,plain,
    ! [X2,X0,X1] :
      ( c_Polynomial_Opoly__gcd(X2,X1,X0) = c_Polynomial_Opoly__gcd(X2,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),X1),X0)
      | ~ class_Fields_Ofield(X2) ),
    inference(cnf_transformation,[],[f2641]) ).

fof(f2641,plain,
    ! [X0,X1,X2] :
      ( c_Polynomial_Opoly__gcd(X2,X1,X0) = c_Polynomial_Opoly__gcd(X2,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),X1),X0)
      | ~ class_Fields_Ofield(X2) ),
    inference(ennf_transformation,[],[f1695]) ).

fof(f1695,plain,
    ! [X0,X1,X2] :
      ( class_Fields_Ofield(X2)
     => c_Polynomial_Opoly__gcd(X2,X1,X0) = c_Polynomial_Opoly__gcd(X2,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),X1),X0) ),
    inference(rectify,[],[f790]) ).

fof(f790,axiom,
    ! [X28,X13,X4] :
      ( class_Fields_Ofield(X4)
     => c_Polynomial_Opoly__gcd(X4,X13,X28) = c_Polynomial_Opoly__gcd(X4,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4),X13),X28) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__gcd__minus__left) ).

fof(f10349,plain,
    spl38_576,
    inference(avatar_split_clause,[],[f4599,f10347]) ).

fof(f10347,plain,
    ( spl38_576
  <=> ! [X2,X0,X1] :
        ( c_Polynomial_Opoly__gcd(X2,X1,X0) = c_Polynomial_Opoly__gcd(X2,X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),X0))
        | ~ class_Fields_Ofield(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_576])]) ).

fof(f4599,plain,
    ! [X2,X0,X1] :
      ( c_Polynomial_Opoly__gcd(X2,X1,X0) = c_Polynomial_Opoly__gcd(X2,X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),X0))
      | ~ class_Fields_Ofield(X2) ),
    inference(cnf_transformation,[],[f2640]) ).

fof(f2640,plain,
    ! [X0,X1,X2] :
      ( c_Polynomial_Opoly__gcd(X2,X1,X0) = c_Polynomial_Opoly__gcd(X2,X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),X0))
      | ~ class_Fields_Ofield(X2) ),
    inference(ennf_transformation,[],[f1694]) ).

fof(f1694,plain,
    ! [X0,X1,X2] :
      ( class_Fields_Ofield(X2)
     => c_Polynomial_Opoly__gcd(X2,X1,X0) = c_Polynomial_Opoly__gcd(X2,X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),X0)) ),
    inference(rectify,[],[f791]) ).

fof(f791,axiom,
    ! [X28,X13,X4] :
      ( class_Fields_Ofield(X4)
     => c_Polynomial_Opoly__gcd(X4,X13,X28) = c_Polynomial_Opoly__gcd(X4,X13,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4),X28)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__gcd__minus__right) ).

fof(f10345,plain,
    spl38_575,
    inference(avatar_split_clause,[],[f4433,f10343]) ).

fof(f10343,plain,
    ( spl38_575
  <=> ! [X0,X1] :
        ( X0 = X1
        | hAPP(X1,sK23(X0,X1)) != hAPP(X0,sK23(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_575])]) ).

fof(f4433,plain,
    ! [X0,X1] :
      ( X0 = X1
      | hAPP(X1,sK23(X0,X1)) != hAPP(X0,sK23(X0,X1)) ),
    inference(cnf_transformation,[],[f3535]) ).

fof(f3535,plain,
    ! [X0,X1] :
      ( X0 = X1
      | hAPP(X1,sK23(X0,X1)) != hAPP(X0,sK23(X0,X1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK23])],[f2617,f3534]) ).

fof(f3534,plain,
    ! [X0,X1] :
      ( ? [X2] : hAPP(X1,X2) != hAPP(X0,X2)
     => hAPP(X1,sK23(X0,X1)) != hAPP(X0,sK23(X0,X1)) ),
    introduced(choice_axiom,[]) ).

fof(f2617,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ? [X2] : hAPP(X1,X2) != hAPP(X0,X2) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0,X1] :
      ( ! [X2] : hAPP(X1,X2) = hAPP(X0,X2)
     => X0 = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ext) ).

fof(f10341,plain,
    spl38_574,
    inference(avatar_split_clause,[],[f4327,f10339]) ).

fof(f10339,plain,
    ( spl38_574
  <=> ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(X1) = X0
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),c_Groups_Ozero__class_Ozero(X1)),X0))
        | ~ class_Rings_Ocomm__semiring__1(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_574])]) ).

fof(f4327,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X1) = X0
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),c_Groups_Ozero__class_Ozero(X1)),X0))
      | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(cnf_transformation,[],[f2486]) ).

fof(f2486,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X1) = X0
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),c_Groups_Ozero__class_Ozero(X1)),X0))
      | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(flattening,[],[f2485]) ).

fof(f2485,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X1) = X0
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),c_Groups_Ozero__class_Ozero(X1)),X0))
      | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(ennf_transformation,[],[f1510]) ).

fof(f1510,plain,
    ! [X0,X1] :
      ( class_Rings_Ocomm__semiring__1(X1)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),c_Groups_Ozero__class_Ozero(X1)),X0))
       => c_Groups_Ozero__class_Ozero(X1) = X0 ) ),
    inference(rectify,[],[f59]) ).

fof(f59,axiom,
    ! [X18,X4] :
      ( class_Rings_Ocomm__semiring__1(X4)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),c_Groups_Ozero__class_Ozero(X4)),X18))
       => c_Groups_Ozero__class_Ozero(X4) = X18 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__0__left) ).

fof(f10337,plain,
    spl38_573,
    inference(avatar_split_clause,[],[f4293,f10335]) ).

fof(f10335,plain,
    ( spl38_573
  <=> ! [X0,X1] :
        ( c_Polynomial_OpCons(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Polynomial_Omonom(X1,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ class_Groups_Ozero(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_573])]) ).

fof(f4293,plain,
    ! [X0,X1] :
      ( c_Polynomial_OpCons(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Polynomial_Omonom(X1,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      | ~ class_Groups_Ozero(X1) ),
    inference(cnf_transformation,[],[f2455]) ).

fof(f2455,plain,
    ! [X0,X1] :
      ( c_Polynomial_OpCons(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Polynomial_Omonom(X1,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      | ~ class_Groups_Ozero(X1) ),
    inference(ennf_transformation,[],[f1481]) ).

fof(f1481,plain,
    ! [X0,X1] :
      ( class_Groups_Ozero(X1)
     => c_Polynomial_OpCons(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Polynomial_Omonom(X1,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(rectify,[],[f32]) ).

fof(f32,axiom,
    ! [X18,X4] :
      ( class_Groups_Ozero(X4)
     => c_Polynomial_Omonom(X4,X18,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(X4,X18,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_monom__0) ).

fof(f10333,plain,
    spl38_572,
    inference(avatar_split_clause,[],[f4244,f10331]) ).

fof(f10331,plain,
    ( spl38_572
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),c_Groups_Ozero__class_Ozero(X1))
        | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
        | ~ class_Groups_Oordered__ab__group__add(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_572])]) ).

fof(f4244,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),c_Groups_Ozero__class_Ozero(X1))
      | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
      | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(cnf_transformation,[],[f3512]) ).

fof(f3512,plain,
    ! [X0,X1] :
      ( ( ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),c_Groups_Ozero__class_Ozero(X1))
          | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
        & ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
          | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),c_Groups_Ozero__class_Ozero(X1)) ) )
      | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(nnf_transformation,[],[f2413]) ).

fof(f2413,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),c_Groups_Ozero__class_Ozero(X1))
      <=> c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
      | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(ennf_transformation,[],[f1440]) ).

fof(f1440,plain,
    ! [X0,X1] :
      ( class_Groups_Oordered__ab__group__add(X1)
     => ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),c_Groups_Ozero__class_Ozero(X1))
      <=> c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) ) ),
    inference(rectify,[],[f150]) ).

fof(f150,axiom,
    ! [X12,X4] :
      ( class_Groups_Oordered__ab__group__add(X4)
     => ( c_Orderings_Oord__class_Oless(X4,c_Groups_Ouminus__class_Ouminus(X4,X12),c_Groups_Ozero__class_Ozero(X4))
      <=> c_Orderings_Oord__class_Oless(X4,c_Groups_Ozero__class_Ozero(X4),X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__less__0__iff__less) ).

fof(f10329,plain,
    spl38_571,
    inference(avatar_split_clause,[],[f4243,f10327]) ).

fof(f10327,plain,
    ( spl38_571
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
        | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),c_Groups_Ozero__class_Ozero(X1))
        | ~ class_Groups_Oordered__ab__group__add(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_571])]) ).

fof(f4243,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
      | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),c_Groups_Ozero__class_Ozero(X1))
      | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(cnf_transformation,[],[f3512]) ).

fof(f10325,plain,
    spl38_570,
    inference(avatar_split_clause,[],[f4242,f10323]) ).

fof(f10323,plain,
    ( spl38_570
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X0))
        | ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
        | ~ class_Groups_Oordered__ab__group__add(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_570])]) ).

fof(f4242,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X0))
      | ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
      | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(cnf_transformation,[],[f3511]) ).

fof(f3511,plain,
    ! [X0,X1] :
      ( ( ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X0))
          | ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1)) )
        & ( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
          | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X0)) ) )
      | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(nnf_transformation,[],[f2412]) ).

fof(f2412,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X0))
      <=> c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1)) )
      | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(ennf_transformation,[],[f1439]) ).

fof(f1439,plain,
    ! [X0,X1] :
      ( class_Groups_Oordered__ab__group__add(X1)
     => ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X0))
      <=> c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ) ),
    inference(rectify,[],[f149]) ).

fof(f149,axiom,
    ! [X12,X4] :
      ( class_Groups_Oordered__ab__group__add(X4)
     => ( c_Orderings_Oord__class_Oless(X4,c_Groups_Ozero__class_Ozero(X4),c_Groups_Ouminus__class_Ouminus(X4,X12))
      <=> c_Orderings_Oord__class_Oless(X4,X12,c_Groups_Ozero__class_Ozero(X4)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__0__less__iff__less) ).

fof(f10321,plain,
    spl38_569,
    inference(avatar_split_clause,[],[f4241,f10319]) ).

fof(f10319,plain,
    ( spl38_569
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
        | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X0))
        | ~ class_Groups_Oordered__ab__group__add(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_569])]) ).

fof(f4241,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
      | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X0))
      | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(cnf_transformation,[],[f3511]) ).

fof(f10317,plain,
    ( spl38_568
    | ~ spl38_3
    | ~ spl38_125
    | ~ spl38_461 ),
    inference(avatar_split_clause,[],[f9026,f8729,f6516,f5906,f10315]) ).

fof(f10315,plain,
    ( spl38_568
  <=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_568])]) ).

fof(f6516,plain,
    ( spl38_125
  <=> class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_125])]) ).

fof(f8729,plain,
    ( spl38_461
  <=> ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X0)
        | ~ class_Rings_Ocomm__semiring__0(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_461])]) ).

fof(f9026,plain,
    ( ! [X0] : c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),X0)
    | ~ spl38_3
    | ~ spl38_125
    | ~ spl38_461 ),
    inference(forward_demodulation,[],[f9022,f5908]) ).

fof(f9022,plain,
    ( ! [X0] : c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),X0)
    | ~ spl38_125
    | ~ spl38_461 ),
    inference(resolution,[],[f8730,f6518]) ).

fof(f6518,plain,
    ( class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex)
    | ~ spl38_125 ),
    inference(avatar_component_clause,[],[f6516]) ).

fof(f8730,plain,
    ( ! [X0,X1] :
        ( ~ class_Rings_Ocomm__semiring__0(X1)
        | c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X0) )
    | ~ spl38_461 ),
    inference(avatar_component_clause,[],[f8729]) ).

fof(f10313,plain,
    spl38_567,
    inference(avatar_split_clause,[],[f4240,f10311]) ).

fof(f10311,plain,
    ( spl38_567
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),c_Groups_Ozero__class_Ozero(X1))
        | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
        | ~ class_Groups_Oordered__ab__group__add(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_567])]) ).

fof(f4240,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),c_Groups_Ozero__class_Ozero(X1))
      | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
      | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(cnf_transformation,[],[f3510]) ).

fof(f3510,plain,
    ! [X0,X1] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),c_Groups_Ozero__class_Ozero(X1))
          | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
        & ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
          | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),c_Groups_Ozero__class_Ozero(X1)) ) )
      | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(nnf_transformation,[],[f2411]) ).

fof(f2411,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),c_Groups_Ozero__class_Ozero(X1))
      <=> c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
      | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(ennf_transformation,[],[f1438]) ).

fof(f1438,plain,
    ! [X0,X1] :
      ( class_Groups_Oordered__ab__group__add(X1)
     => ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),c_Groups_Ozero__class_Ozero(X1))
      <=> c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0) ) ),
    inference(rectify,[],[f154]) ).

fof(f154,axiom,
    ! [X12,X4] :
      ( class_Groups_Oordered__ab__group__add(X4)
     => ( c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ouminus__class_Ouminus(X4,X12),c_Groups_Ozero__class_Ozero(X4))
      <=> c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__le__0__iff__le) ).

fof(f10309,plain,
    spl38_566,
    inference(avatar_split_clause,[],[f4239,f10307]) ).

fof(f10307,plain,
    ( spl38_566
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
        | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),c_Groups_Ozero__class_Ozero(X1))
        | ~ class_Groups_Oordered__ab__group__add(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_566])]) ).

fof(f4239,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
      | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),c_Groups_Ozero__class_Ozero(X1))
      | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(cnf_transformation,[],[f3510]) ).

fof(f10305,plain,
    spl38_565,
    inference(avatar_split_clause,[],[f4238,f10303]) ).

fof(f10303,plain,
    ( spl38_565
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X0))
        | ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
        | ~ class_Groups_Oordered__ab__group__add(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_565])]) ).

fof(f4238,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X0))
      | ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
      | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(cnf_transformation,[],[f3509]) ).

fof(f3509,plain,
    ! [X0,X1] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X0))
          | ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1)) )
        & ( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
          | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X0)) ) )
      | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(nnf_transformation,[],[f2410]) ).

fof(f2410,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X0))
      <=> c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1)) )
      | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(ennf_transformation,[],[f1437]) ).

fof(f1437,plain,
    ! [X0,X1] :
      ( class_Groups_Oordered__ab__group__add(X1)
     => ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X0))
      <=> c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ) ),
    inference(rectify,[],[f152]) ).

fof(f152,axiom,
    ! [X12,X4] :
      ( class_Groups_Oordered__ab__group__add(X4)
     => ( c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),c_Groups_Ouminus__class_Ouminus(X4,X12))
      <=> c_Orderings_Oord__class_Oless__eq(X4,X12,c_Groups_Ozero__class_Ozero(X4)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__0__le__iff__le) ).

fof(f10301,plain,
    spl38_564,
    inference(avatar_split_clause,[],[f4237,f10299]) ).

fof(f10299,plain,
    ( spl38_564
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
        | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X0))
        | ~ class_Groups_Oordered__ab__group__add(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_564])]) ).

fof(f4237,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
      | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X0))
      | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(cnf_transformation,[],[f3509]) ).

fof(f10297,plain,
    spl38_563,
    inference(avatar_split_clause,[],[f4208,f10295]) ).

fof(f10295,plain,
    ( spl38_563
  <=> ! [X0,X1] :
        ( c_Polynomial_Opdivmod__rel(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
        | ~ class_Fields_Ofield(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_563])]) ).

fof(f4208,plain,
    ! [X0,X1] :
      ( c_Polynomial_Opdivmod__rel(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
      | ~ class_Fields_Ofield(X1) ),
    inference(cnf_transformation,[],[f2391]) ).

fof(f2391,plain,
    ! [X0,X1] :
      ( c_Polynomial_Opdivmod__rel(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
      | ~ class_Fields_Ofield(X1) ),
    inference(ennf_transformation,[],[f1419]) ).

fof(f1419,plain,
    ! [X0,X1] :
      ( class_Fields_Ofield(X1)
     => c_Polynomial_Opdivmod__rel(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) ),
    inference(rectify,[],[f673]) ).

fof(f673,axiom,
    ! [X28,X4] :
      ( class_Fields_Ofield(X4)
     => c_Polynomial_Opdivmod__rel(X4,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X28,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__rel__0) ).

fof(f10293,plain,
    spl38_562,
    inference(avatar_split_clause,[],[f4058,f10291]) ).

fof(f10291,plain,
    ( spl38_562
  <=> ! [X0] :
        ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Opoly__gcd(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))
        | ~ class_Fields_Ofield(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_562])]) ).

fof(f4058,plain,
    ! [X0] :
      ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Opoly__gcd(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))
      | ~ class_Fields_Ofield(X0) ),
    inference(cnf_transformation,[],[f2285]) ).

fof(f2285,plain,
    ! [X0] :
      ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Opoly__gcd(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))
      | ~ class_Fields_Ofield(X0) ),
    inference(ennf_transformation,[],[f1266]) ).

fof(f1266,plain,
    ! [X0] :
      ( class_Fields_Ofield(X0)
     => c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Opoly__gcd(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) ),
    inference(rectify,[],[f793]) ).

fof(f793,axiom,
    ! [X4] :
      ( class_Fields_Ofield(X4)
     => c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = c_Polynomial_Opoly__gcd(X4,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__gcd__0__0) ).

fof(f10289,plain,
    spl38_561,
    inference(avatar_split_clause,[],[f4052,f10287]) ).

fof(f10287,plain,
    ( spl38_561
  <=> ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_561])]) ).

fof(f4052,plain,
    ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X0))),
    inference(cnf_transformation,[],[f1260]) ).

fof(f1260,plain,
    ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X0))),
    inference(rectify,[],[f275]) ).

fof(f275,axiom,
    ! [X19] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),X19))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__cube) ).

fof(f10276,plain,
    ( spl38_560
    | ~ spl38_3
    | ~ spl38_122
    | ~ spl38_460 ),
    inference(avatar_split_clause,[],[f9021,f8725,f6501,f5906,f10274]) ).

fof(f10274,plain,
    ( spl38_560
  <=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,v_s____),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_560])]) ).

fof(f8725,plain,
    ( spl38_460
  <=> ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Polynomial_Ocoeff(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X0)
        | ~ class_Groups_Ozero(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_460])]) ).

fof(f9021,plain,
    ( ! [X0] : c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,v_s____),X0)
    | ~ spl38_3
    | ~ spl38_122
    | ~ spl38_460 ),
    inference(forward_demodulation,[],[f9017,f5908]) ).

fof(f9017,plain,
    ( ! [X0] : c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),X0)
    | ~ spl38_122
    | ~ spl38_460 ),
    inference(resolution,[],[f8726,f6503]) ).

fof(f8726,plain,
    ( ! [X0,X1] :
        ( ~ class_Groups_Ozero(X1)
        | c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Polynomial_Ocoeff(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X0) )
    | ~ spl38_460 ),
    inference(avatar_component_clause,[],[f8725]) ).

fof(f9882,plain,
    ( spl38_559
    | ~ spl38_3
    | ~ spl38_122
    | ~ spl38_518 ),
    inference(avatar_split_clause,[],[f9692,f9525,f6501,f5906,f9879]) ).

fof(f9879,plain,
    ( spl38_559
  <=> v_s____ = c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),v_s____) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_559])]) ).

fof(f9525,plain,
    ( spl38_518
  <=> ! [X0] :
        ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))
        | ~ class_Groups_Ozero(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_518])]) ).

fof(f9692,plain,
    ( v_s____ = c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),v_s____)
    | ~ spl38_3
    | ~ spl38_122
    | ~ spl38_518 ),
    inference(forward_demodulation,[],[f9688,f5908]) ).

fof(f9688,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
    | ~ spl38_122
    | ~ spl38_518 ),
    inference(resolution,[],[f9526,f6503]) ).

fof(f9526,plain,
    ( ! [X0] :
        ( ~ class_Groups_Ozero(X0)
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) )
    | ~ spl38_518 ),
    inference(avatar_component_clause,[],[f9525]) ).

fof(f9687,plain,
    spl38_558,
    inference(avatar_split_clause,[],[f5735,f9685]) ).

fof(f5735,plain,
    ! [X3,X0,X1,X4] :
      ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X3
      | ~ sP16(X0,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X3,X4) ),
    inference(equality_resolution,[],[f5314]) ).

fof(f5314,plain,
    ! [X2,X3,X0,X1,X4] :
      ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X3
      | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) != X2
      | ~ sP16(X0,X1,X2,X3,X4) ),
    inference(cnf_transformation,[],[f3819]) ).

fof(f3819,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ( sP16(X0,X1,X2,X3,X4)
        | ~ sP15(X2,X1,X0)
        | ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) != X3
          & c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X2 )
        | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X3),X2),X0) != X4 )
      & ( ( sP15(X2,X1,X0)
          & ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X3
            | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) != X2 )
          & c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X3),X2),X0) = X4 )
        | ~ sP16(X0,X1,X2,X3,X4) ) ),
    inference(rectify,[],[f3818]) ).

fof(f3818,plain,
    ! [X0,X4,X2,X1,X3] :
      ( ( sP16(X0,X4,X2,X1,X3)
        | ~ sP15(X2,X4,X0)
        | ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) != X1
          & c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X2 )
        | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4)),X1),X2),X0) != X3 )
      & ( ( sP15(X2,X4,X0)
          & ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X1
            | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) != X2 )
          & c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4)),X1),X2),X0) = X3 )
        | ~ sP16(X0,X4,X2,X1,X3) ) ),
    inference(flattening,[],[f3817]) ).

fof(f3817,plain,
    ! [X0,X4,X2,X1,X3] :
      ( ( sP16(X0,X4,X2,X1,X3)
        | ~ sP15(X2,X4,X0)
        | ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) != X1
          & c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X2 )
        | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4)),X1),X2),X0) != X3 )
      & ( ( sP15(X2,X4,X0)
          & ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X1
            | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) != X2 )
          & c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4)),X1),X2),X0) = X3 )
        | ~ sP16(X0,X4,X2,X1,X3) ) ),
    inference(nnf_transformation,[],[f3476]) ).

fof(f3476,plain,
    ! [X0,X4,X2,X1,X3] :
      ( sP16(X0,X4,X2,X1,X3)
    <=> ( sP15(X2,X4,X0)
        & ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X1
          | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) != X2 )
        & c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4)),X1),X2),X0) = X3 ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP16])]) ).

fof(f9683,plain,
    spl38_557,
    inference(avatar_split_clause,[],[f5564,f9681]) ).

fof(f9681,plain,
    ( spl38_557
  <=> ! [X1] :
        ( c_Groups_Oone__class_Oone(X1) = hAPP(c_Polynomial_Ocoeff(X1,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ class_Rings_Ocomm__semiring__1(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_557])]) ).

fof(f5564,plain,
    ! [X1] :
      ( c_Groups_Oone__class_Oone(X1) = hAPP(c_Polynomial_Ocoeff(X1,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(equality_resolution,[],[f4325]) ).

fof(f4325,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(X1) = hAPP(c_Polynomial_Ocoeff(X1,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1))),X0)
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
      | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(cnf_transformation,[],[f2484]) ).

fof(f2484,plain,
    ! [X0,X1] :
      ( ( ( c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Polynomial_Ocoeff(X1,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1))),X0)
          | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
        & ( c_Groups_Oone__class_Oone(X1) = hAPP(c_Polynomial_Ocoeff(X1,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1))),X0)
          | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) )
      | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(ennf_transformation,[],[f1509]) ).

fof(f1509,plain,
    ! [X0,X1] :
      ( class_Rings_Ocomm__semiring__1(X1)
     => ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
         => c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Polynomial_Ocoeff(X1,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1))),X0) )
        & ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
         => c_Groups_Oone__class_Oone(X1) = hAPP(c_Polynomial_Ocoeff(X1,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1))),X0) ) ) ),
    inference(rectify,[],[f203]) ).

fof(f203,axiom,
    ! [X10,X4] :
      ( class_Rings_Ocomm__semiring__1(X4)
     => ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X10
         => c_Groups_Ozero__class_Ozero(X4) = hAPP(c_Polynomial_Ocoeff(X4,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X4))),X10) )
        & ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X10
         => c_Groups_Oone__class_Oone(X4) = hAPP(c_Polynomial_Ocoeff(X4,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X4))),X10) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__1) ).

fof(f9679,plain,
    spl38_556,
    inference(avatar_split_clause,[],[f5554,f9677]) ).

fof(f9677,plain,
    ( spl38_556
  <=> ! [X1] :
        ( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1))
        | ~ class_Rings_Oring__1__no__zero__divisors(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_556])]) ).

fof(f5554,plain,
    ! [X1] :
      ( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1))
      | ~ class_Rings_Oring__1__no__zero__divisors(X1) ),
    inference(equality_resolution,[],[f4253]) ).

fof(f4253,plain,
    ! [X0,X1] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) = c_Groups_Oone__class_Oone(X1)
      | c_Groups_Oone__class_Oone(X1) != X0
      | ~ class_Rings_Oring__1__no__zero__divisors(X1) ),
    inference(cnf_transformation,[],[f3517]) ).

fof(f3517,plain,
    ! [X0,X1] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) = c_Groups_Oone__class_Oone(X1)
          | ( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1)) != X0
            & c_Groups_Oone__class_Oone(X1) != X0 ) )
        & ( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1)) = X0
          | c_Groups_Oone__class_Oone(X1) = X0
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) != c_Groups_Oone__class_Oone(X1) ) )
      | ~ class_Rings_Oring__1__no__zero__divisors(X1) ),
    inference(flattening,[],[f3516]) ).

fof(f3516,plain,
    ! [X0,X1] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) = c_Groups_Oone__class_Oone(X1)
          | ( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1)) != X0
            & c_Groups_Oone__class_Oone(X1) != X0 ) )
        & ( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1)) = X0
          | c_Groups_Oone__class_Oone(X1) = X0
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) != c_Groups_Oone__class_Oone(X1) ) )
      | ~ class_Rings_Oring__1__no__zero__divisors(X1) ),
    inference(nnf_transformation,[],[f2419]) ).

fof(f2419,plain,
    ! [X0,X1] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) = c_Groups_Oone__class_Oone(X1)
      <=> ( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1)) = X0
          | c_Groups_Oone__class_Oone(X1) = X0 ) )
      | ~ class_Rings_Oring__1__no__zero__divisors(X1) ),
    inference(ennf_transformation,[],[f1445]) ).

fof(f1445,plain,
    ! [X0,X1] :
      ( class_Rings_Oring__1__no__zero__divisors(X1)
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) = c_Groups_Oone__class_Oone(X1)
      <=> ( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1)) = X0
          | c_Groups_Oone__class_Oone(X1) = X0 ) ) ),
    inference(rectify,[],[f128]) ).

fof(f128,axiom,
    ! [X3,X4] :
      ( class_Rings_Oring__1__no__zero__divisors(X4)
     => ( c_Groups_Oone__class_Oone(X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X3)
      <=> ( c_Groups_Ouminus__class_Ouminus(X4,c_Groups_Oone__class_Oone(X4)) = X3
          | c_Groups_Oone__class_Oone(X4) = X3 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_square__eq__1__iff) ).

fof(f9675,plain,
    ( ~ spl38_8
    | spl38_555
    | ~ spl38_3
    | ~ spl38_451 ),
    inference(avatar_split_clause,[],[f8968,f8688,f5906,f9673,f5931]) ).

fof(f5931,plain,
    ( spl38_8
  <=> class_Fields_Ofield(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_8])]) ).

fof(f9673,plain,
    ( spl38_555
  <=> ! [X0] : c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,X0,v_s____,v_s____,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_555])]) ).

fof(f8688,plain,
    ( spl38_451
  <=> ! [X0,X1] :
        ( c_Polynomial_Opdivmod__rel(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0)
        | ~ class_Fields_Ofield(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_451])]) ).

fof(f8968,plain,
    ( ! [X0] :
        ( c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,X0,v_s____,v_s____,X0)
        | ~ class_Fields_Ofield(tc_Complex_Ocomplex) )
    | ~ spl38_3
    | ~ spl38_451 ),
    inference(superposition,[],[f8689,f5908]) ).

fof(f8689,plain,
    ( ! [X0,X1] :
        ( c_Polynomial_Opdivmod__rel(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0)
        | ~ class_Fields_Ofield(X1) )
    | ~ spl38_451 ),
    inference(avatar_component_clause,[],[f8688]) ).

fof(f9671,plain,
    spl38_554,
    inference(avatar_split_clause,[],[f5414,f9669]) ).

fof(f9669,plain,
    ( spl38_554
  <=> ! [X0] :
        ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK21(X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_554])]) ).

fof(f5414,plain,
    ! [X0] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK21(X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
    inference(definition_unfolding,[],[f4144,f4035]) ).

fof(f4035,plain,
    ! [X0] : c_Nat_OSuc(X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(cnf_transformation,[],[f1243]) ).

fof(f1243,plain,
    ! [X0] : c_Nat_OSuc(X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(rectify,[],[f688]) ).

fof(f688,axiom,
    ! [X10] : c_Nat_OSuc(X10) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).

fof(f4144,plain,
    ! [X0] :
      ( c_Nat_OSuc(sK21(X0)) = X0
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
    inference(cnf_transformation,[],[f3491]) ).

fof(f3491,plain,
    ! [X0] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
        | ! [X1] : c_Nat_OSuc(X1) != X0 )
      & ( c_Nat_OSuc(sK21(X0)) = X0
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK21])],[f3489,f3490]) ).

fof(f3490,plain,
    ! [X0] :
      ( ? [X2] : c_Nat_OSuc(X2) = X0
     => c_Nat_OSuc(sK21(X0)) = X0 ),
    introduced(choice_axiom,[]) ).

fof(f3489,plain,
    ! [X0] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
        | ! [X1] : c_Nat_OSuc(X1) != X0 )
      & ( ? [X2] : c_Nat_OSuc(X2) = X0
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ) ),
    inference(rectify,[],[f3488]) ).

fof(f3488,plain,
    ! [X0] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
        | ! [X1] : c_Nat_OSuc(X1) != X0 )
      & ( ? [X1] : c_Nat_OSuc(X1) = X0
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ) ),
    inference(nnf_transformation,[],[f1348]) ).

fof(f1348,plain,
    ! [X0] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
    <=> ? [X1] : c_Nat_OSuc(X1) = X0 ),
    inference(rectify,[],[f380]) ).

fof(f380,axiom,
    ! [X11] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X11)
    <=> ? [X24] : c_Nat_OSuc(X24) = X11 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr0__conv__Suc) ).

fof(f9667,plain,
    spl38_553,
    inference(avatar_split_clause,[],[f5125,f9665]) ).

fof(f9665,plain,
    ( spl38_553
  <=> ! [X0,X3,X2,X1] :
        ( c_Orderings_Oord__class_Oless(X2,X1,X0)
        | c_Orderings_Oord__class_Oless(X2,X0,X1)
        | ~ sP13(X0,X1,X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_553])]) ).

fof(f5125,plain,
    ! [X2,X3,X0,X1] :
      ( c_Orderings_Oord__class_Oless(X2,X1,X0)
      | c_Orderings_Oord__class_Oless(X2,X0,X1)
      | ~ sP13(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f3793]) ).

fof(f9663,plain,
    spl38_552,
    inference(avatar_split_clause,[],[f5116,f9661]) ).

fof(f9661,plain,
    ( spl38_552
  <=> ! [X0,X3,X2,X1] :
        ( c_Orderings_Oord__class_Oless(X2,X1,X0)
        | c_Orderings_Oord__class_Oless(X2,X0,X1)
        | ~ sP11(X0,X1,X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_552])]) ).

fof(f5116,plain,
    ! [X2,X3,X0,X1] :
      ( c_Orderings_Oord__class_Oless(X2,X1,X0)
      | c_Orderings_Oord__class_Oless(X2,X0,X1)
      | ~ sP11(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f3788]) ).

fof(f9659,plain,
    spl38_551,
    inference(avatar_split_clause,[],[f5078,f9657]) ).

fof(f9657,plain,
    ( spl38_551
  <=> ! [X0,X3,X2,X1] :
        ( X0 = X2
        | ~ c_Polynomial_Opdivmod__rel(X3,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X1,X0)
        | ~ class_Fields_Ofield(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_551])]) ).

fof(f5078,plain,
    ! [X2,X3,X0,X1] :
      ( X0 = X2
      | ~ c_Polynomial_Opdivmod__rel(X3,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X1,X0)
      | ~ class_Fields_Ofield(X3) ),
    inference(cnf_transformation,[],[f3770]) ).

fof(f3770,plain,
    ! [X0,X1,X2,X3] :
      ( ( ( c_Polynomial_Opdivmod__rel(X3,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X1,X0)
          | X0 != X2
          | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) != X1 )
        & ( ( X0 = X2
            & c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X1 )
          | ~ c_Polynomial_Opdivmod__rel(X3,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X1,X0) ) )
      | ~ class_Fields_Ofield(X3) ),
    inference(flattening,[],[f3769]) ).

fof(f3769,plain,
    ! [X0,X1,X2,X3] :
      ( ( ( c_Polynomial_Opdivmod__rel(X3,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X1,X0)
          | X0 != X2
          | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) != X1 )
        & ( ( X0 = X2
            & c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X1 )
          | ~ c_Polynomial_Opdivmod__rel(X3,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X1,X0) ) )
      | ~ class_Fields_Ofield(X3) ),
    inference(nnf_transformation,[],[f3083]) ).

fof(f3083,plain,
    ! [X0,X1,X2,X3] :
      ( ( c_Polynomial_Opdivmod__rel(X3,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X1,X0)
      <=> ( X0 = X2
          & c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X1 ) )
      | ~ class_Fields_Ofield(X3) ),
    inference(ennf_transformation,[],[f2012]) ).

fof(f2012,plain,
    ! [X0,X1,X2,X3] :
      ( class_Fields_Ofield(X3)
     => ( c_Polynomial_Opdivmod__rel(X3,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X1,X0)
      <=> ( X0 = X2
          & c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X1 ) ) ),
    inference(rectify,[],[f674]) ).

fof(f674,axiom,
    ! [X63,X15,X3,X4] :
      ( class_Fields_Ofield(X4)
     => ( c_Polynomial_Opdivmod__rel(X4,X3,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X15,X63)
      <=> ( X3 = X63
          & c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X15 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__rel__by__0__iff) ).

fof(f9655,plain,
    spl38_550,
    inference(avatar_split_clause,[],[f4888,f9653]) ).

fof(f9653,plain,
    ( spl38_550
  <=> ! [X2,X0,X1] :
        ( X0 = X1
        | ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
        | ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
        | ~ class_Orderings_Oorder(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_550])]) ).

fof(f4888,plain,
    ! [X2,X0,X1] :
      ( X0 = X1
      | ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
      | ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
      | ~ class_Orderings_Oorder(X2) ),
    inference(cnf_transformation,[],[f2930]) ).

fof(f2930,plain,
    ! [X0,X1,X2] :
      ( X0 = X1
      | ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
      | ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
      | ~ class_Orderings_Oorder(X2) ),
    inference(flattening,[],[f2929]) ).

fof(f2929,plain,
    ! [X0,X1,X2] :
      ( X0 = X1
      | ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
      | ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
      | ~ class_Orderings_Oorder(X2) ),
    inference(ennf_transformation,[],[f1892]) ).

fof(f1892,plain,
    ! [X0,X1,X2] :
      ( class_Orderings_Oorder(X2)
     => ( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
       => ( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
         => X0 = X1 ) ) ),
    inference(rectify,[],[f561]) ).

fof(f561,axiom,
    ! [X13,X28,X4] :
      ( class_Orderings_Oorder(X4)
     => ( c_Orderings_Oord__class_Oless__eq(X4,X28,X13)
       => ( c_Orderings_Oord__class_Oless__eq(X4,X13,X28)
         => X13 = X28 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I5_J) ).

fof(f9651,plain,
    spl38_549,
    inference(avatar_split_clause,[],[f4883,f9649]) ).

fof(f9649,plain,
    ( spl38_549
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless(X2,X1,X0)
        | ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
        | X0 = X1
        | ~ class_Orderings_Oorder(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_549])]) ).

fof(f4883,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless(X2,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
      | X0 = X1
      | ~ class_Orderings_Oorder(X2) ),
    inference(cnf_transformation,[],[f2920]) ).

fof(f2920,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(X2,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
      | X0 = X1
      | ~ class_Orderings_Oorder(X2) ),
    inference(flattening,[],[f2919]) ).

fof(f2919,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(X2,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
      | X0 = X1
      | ~ class_Orderings_Oorder(X2) ),
    inference(ennf_transformation,[],[f1887]) ).

fof(f1887,plain,
    ! [X0,X1,X2] :
      ( class_Orderings_Oorder(X2)
     => ( X0 != X1
       => ( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
         => c_Orderings_Oord__class_Oless(X2,X1,X0) ) ) ),
    inference(rectify,[],[f616]) ).

fof(f616,axiom,
    ! [X27,X18,X4] :
      ( class_Orderings_Oorder(X4)
     => ( X18 != X27
       => ( c_Orderings_Oord__class_Oless__eq(X4,X18,X27)
         => c_Orderings_Oord__class_Oless(X4,X18,X27) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__neq__le__trans) ).

fof(f9647,plain,
    spl38_548,
    inference(avatar_split_clause,[],[f4850,f9645]) ).

fof(f9645,plain,
    ( spl38_548
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,c_Polynomial_Osmult(X2,X1,X0)),c_Polynomial_Odegree(X2,X0))
        | ~ class_Rings_Ocomm__semiring__0(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_548])]) ).

fof(f4850,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,c_Polynomial_Osmult(X2,X1,X0)),c_Polynomial_Odegree(X2,X0))
      | ~ class_Rings_Ocomm__semiring__0(X2) ),
    inference(cnf_transformation,[],[f2884]) ).

fof(f2884,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,c_Polynomial_Osmult(X2,X1,X0)),c_Polynomial_Odegree(X2,X0))
      | ~ class_Rings_Ocomm__semiring__0(X2) ),
    inference(ennf_transformation,[],[f1859]) ).

fof(f1859,plain,
    ! [X0,X1,X2] :
      ( class_Rings_Ocomm__semiring__0(X2)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,c_Polynomial_Osmult(X2,X1,X0)),c_Polynomial_Odegree(X2,X0)) ),
    inference(rectify,[],[f212]) ).

fof(f212,axiom,
    ! [X14,X18,X4] :
      ( class_Rings_Ocomm__semiring__0(X4)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X4,c_Polynomial_Osmult(X4,X18,X14)),c_Polynomial_Odegree(X4,X14)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__smult__le) ).

fof(f9643,plain,
    spl38_547,
    inference(avatar_split_clause,[],[f4824,f9641]) ).

fof(f9641,plain,
    ( spl38_547
  <=> ! [X2,X0,X1] :
        ( hAPP(c_Polynomial_Ocoeff(X2,c_Polynomial_OpCons(X2,X1,X0)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
        | ~ class_Groups_Ozero(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_547])]) ).

fof(f4824,plain,
    ! [X2,X0,X1] :
      ( hAPP(c_Polynomial_Ocoeff(X2,c_Polynomial_OpCons(X2,X1,X0)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
      | ~ class_Groups_Ozero(X2) ),
    inference(cnf_transformation,[],[f2859]) ).

fof(f2859,plain,
    ! [X0,X1,X2] :
      ( hAPP(c_Polynomial_Ocoeff(X2,c_Polynomial_OpCons(X2,X1,X0)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
      | ~ class_Groups_Ozero(X2) ),
    inference(ennf_transformation,[],[f1841]) ).

fof(f1841,plain,
    ! [X0,X1,X2] :
      ( class_Groups_Ozero(X2)
     => hAPP(c_Polynomial_Ocoeff(X2,c_Polynomial_OpCons(X2,X1,X0)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 ),
    inference(rectify,[],[f47]) ).

fof(f47,axiom,
    ! [X14,X18,X4] :
      ( class_Groups_Ozero(X4)
     => hAPP(c_Polynomial_Ocoeff(X4,c_Polynomial_OpCons(X4,X18,X14)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X18 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__pCons__0) ).

fof(f9639,plain,
    spl38_546,
    inference(avatar_split_clause,[],[f4753,f9637]) ).

fof(f9637,plain,
    ( spl38_546
  <=> ! [X2,X0,X1] :
        ( c_Groups_Oplus__class_Oplus(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Oplus__class_Oplus(X2,X1,X0)) = X0
        | ~ class_Groups_Ogroup__add(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_546])]) ).

fof(f4753,plain,
    ! [X2,X0,X1] :
      ( c_Groups_Oplus__class_Oplus(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Oplus__class_Oplus(X2,X1,X0)) = X0
      | ~ class_Groups_Ogroup__add(X2) ),
    inference(cnf_transformation,[],[f2784]) ).

fof(f2784,plain,
    ! [X0,X1,X2] :
      ( c_Groups_Oplus__class_Oplus(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Oplus__class_Oplus(X2,X1,X0)) = X0
      | ~ class_Groups_Ogroup__add(X2) ),
    inference(ennf_transformation,[],[f1790]) ).

fof(f1790,plain,
    ! [X0,X1,X2] :
      ( class_Groups_Ogroup__add(X2)
     => c_Groups_Oplus__class_Oplus(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Oplus__class_Oplus(X2,X1,X0)) = X0 ),
    inference(rectify,[],[f494]) ).

fof(f494,axiom,
    ! [X27,X18,X4] :
      ( class_Groups_Ogroup__add(X4)
     => c_Groups_Oplus__class_Oplus(X4,c_Groups_Ouminus__class_Ouminus(X4,X18),c_Groups_Oplus__class_Oplus(X4,X18,X27)) = X27 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__add__cancel) ).

fof(f9635,plain,
    spl38_545,
    inference(avatar_split_clause,[],[f4752,f9633]) ).

fof(f9633,plain,
    ( spl38_545
  <=> ! [X2,X0,X1] :
        ( c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Oplus__class_Oplus(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)) = X0
        | ~ class_Groups_Ogroup__add(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_545])]) ).

fof(f4752,plain,
    ! [X2,X0,X1] :
      ( c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Oplus__class_Oplus(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)) = X0
      | ~ class_Groups_Ogroup__add(X2) ),
    inference(cnf_transformation,[],[f2783]) ).

fof(f2783,plain,
    ! [X0,X1,X2] :
      ( c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Oplus__class_Oplus(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)) = X0
      | ~ class_Groups_Ogroup__add(X2) ),
    inference(ennf_transformation,[],[f1789]) ).

fof(f1789,plain,
    ! [X0,X1,X2] :
      ( class_Groups_Ogroup__add(X2)
     => c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Oplus__class_Oplus(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)) = X0 ),
    inference(rectify,[],[f495]) ).

fof(f495,axiom,
    ! [X27,X18,X4] :
      ( class_Groups_Ogroup__add(X4)
     => c_Groups_Oplus__class_Oplus(X4,X18,c_Groups_Oplus__class_Oplus(X4,c_Groups_Ouminus__class_Ouminus(X4,X18),X27)) = X27 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__minus__cancel) ).

fof(f9631,plain,
    spl38_544,
    inference(avatar_split_clause,[],[f4724,f9629]) ).

fof(f9629,plain,
    ( spl38_544
  <=> ! [X2,X0,X1] :
        ( X0 = X1
        | ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
        | c_Orderings_Oord__class_Oless(X2,X1,X0)
        | ~ class_Orderings_Olinorder(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_544])]) ).

fof(f4724,plain,
    ! [X2,X0,X1] :
      ( X0 = X1
      | ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
      | c_Orderings_Oord__class_Oless(X2,X1,X0)
      | ~ class_Orderings_Olinorder(X2) ),
    inference(cnf_transformation,[],[f3662]) ).

fof(f3662,plain,
    ! [X0,X1,X2] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
          | X0 != X1 )
        & ( X0 = X1
          | ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ) )
      | c_Orderings_Oord__class_Oless(X2,X1,X0)
      | ~ class_Orderings_Olinorder(X2) ),
    inference(nnf_transformation,[],[f2756]) ).

fof(f2756,plain,
    ! [X0,X1,X2] :
      ( ( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
      <=> X0 = X1 )
      | c_Orderings_Oord__class_Oless(X2,X1,X0)
      | ~ class_Orderings_Olinorder(X2) ),
    inference(flattening,[],[f2755]) ).

fof(f2755,plain,
    ! [X0,X1,X2] :
      ( ( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
      <=> X0 = X1 )
      | c_Orderings_Oord__class_Oless(X2,X1,X0)
      | ~ class_Orderings_Olinorder(X2) ),
    inference(ennf_transformation,[],[f1770]) ).

fof(f1770,plain,
    ! [X0,X1,X2] :
      ( class_Orderings_Olinorder(X2)
     => ( ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
       => ( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
        <=> X0 = X1 ) ) ),
    inference(rectify,[],[f617]) ).

fof(f617,axiom,
    ! [X17,X3,X4] :
      ( class_Orderings_Olinorder(X4)
     => ( ~ c_Orderings_Oord__class_Oless(X4,X3,X17)
       => ( c_Orderings_Oord__class_Oless__eq(X4,X3,X17)
        <=> X3 = X17 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv1) ).

fof(f9627,plain,
    spl38_543,
    inference(avatar_split_clause,[],[f4716,f9625]) ).

fof(f9625,plain,
    ( spl38_543
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless(X2,X0,X1)
        | X0 = X1
        | c_Orderings_Oord__class_Oless(X2,X1,X0)
        | ~ class_Orderings_Olinorder(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_543])]) ).

fof(f4716,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless(X2,X0,X1)
      | X0 = X1
      | c_Orderings_Oord__class_Oless(X2,X1,X0)
      | ~ class_Orderings_Olinorder(X2) ),
    inference(cnf_transformation,[],[f2742]) ).

fof(f2742,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(X2,X0,X1)
      | X0 = X1
      | c_Orderings_Oord__class_Oless(X2,X1,X0)
      | ~ class_Orderings_Olinorder(X2) ),
    inference(flattening,[],[f2741]) ).

fof(f2741,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(X2,X0,X1)
      | X0 = X1
      | c_Orderings_Oord__class_Oless(X2,X1,X0)
      | ~ class_Orderings_Olinorder(X2) ),
    inference(ennf_transformation,[],[f1763]) ).

fof(f1763,plain,
    ! [X0,X1,X2] :
      ( class_Orderings_Olinorder(X2)
     => ( c_Orderings_Oord__class_Oless(X2,X0,X1)
        | X0 = X1
        | c_Orderings_Oord__class_Oless(X2,X1,X0) ) ),
    inference(rectify,[],[f591]) ).

fof(f591,axiom,
    ! [X28,X13,X4] :
      ( class_Orderings_Olinorder(X4)
     => ( c_Orderings_Oord__class_Oless(X4,X28,X13)
        | X13 = X28
        | c_Orderings_Oord__class_Oless(X4,X13,X28) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__less__linear) ).

fof(f9623,plain,
    spl38_542,
    inference(avatar_split_clause,[],[f4671,f9621]) ).

fof(f9621,plain,
    ( spl38_542
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless(X2,X0,X1)
        | c_Orderings_Oord__class_Oless(X2,X1,X0)
        | X0 = X1
        | ~ class_Rings_Olinordered__idom(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_542])]) ).

fof(f4671,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless(X2,X0,X1)
      | c_Orderings_Oord__class_Oless(X2,X1,X0)
      | X0 = X1
      | ~ class_Rings_Olinordered__idom(X2) ),
    inference(cnf_transformation,[],[f2685]) ).

fof(f2685,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(X2,X0,X1)
      | c_Orderings_Oord__class_Oless(X2,X1,X0)
      | X0 = X1
      | ~ class_Rings_Olinordered__idom(X2) ),
    inference(flattening,[],[f2684]) ).

fof(f2684,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(X2,X0,X1)
      | c_Orderings_Oord__class_Oless(X2,X1,X0)
      | X0 = X1
      | ~ class_Rings_Olinordered__idom(X2) ),
    inference(ennf_transformation,[],[f1728]) ).

fof(f1728,plain,
    ! [X0,X1,X2] :
      ( class_Rings_Olinordered__idom(X2)
     => ( X0 != X1
       => ( ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
         => c_Orderings_Oord__class_Oless(X2,X0,X1) ) ) ),
    inference(rectify,[],[f130]) ).

fof(f130,axiom,
    ! [X28,X13,X4] :
      ( class_Rings_Olinordered__idom(X4)
     => ( X13 != X28
       => ( ~ c_Orderings_Oord__class_Oless(X4,X13,X28)
         => c_Orderings_Oord__class_Oless(X4,X28,X13) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE__linordered__idom) ).

fof(f9619,plain,
    spl38_541,
    inference(avatar_split_clause,[],[f4598,f9617]) ).

fof(f9617,plain,
    ( spl38_541
  <=> ! [X2,X0,X1] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),c_Polynomial_Opoly__gcd(X2,X1,X0)),X1))
        | ~ class_Fields_Ofield(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_541])]) ).

fof(f4598,plain,
    ! [X2,X0,X1] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),c_Polynomial_Opoly__gcd(X2,X1,X0)),X1))
      | ~ class_Fields_Ofield(X2) ),
    inference(cnf_transformation,[],[f2639]) ).

fof(f2639,plain,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),c_Polynomial_Opoly__gcd(X2,X1,X0)),X1))
      | ~ class_Fields_Ofield(X2) ),
    inference(ennf_transformation,[],[f1693]) ).

fof(f1693,plain,
    ! [X0,X1,X2] :
      ( class_Fields_Ofield(X2)
     => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),c_Polynomial_Opoly__gcd(X2,X1,X0)),X1)) ),
    inference(rectify,[],[f788]) ).

fof(f788,axiom,
    ! [X28,X13,X4] :
      ( class_Fields_Ofield(X4)
     => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4)),c_Polynomial_Opoly__gcd(X4,X13,X28)),X13)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__gcd__dvd1) ).

fof(f9615,plain,
    spl38_540,
    inference(avatar_split_clause,[],[f4597,f9613]) ).

fof(f9613,plain,
    ( spl38_540
  <=> ! [X2,X0,X1] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),c_Polynomial_Opoly__gcd(X2,X1,X0)),X0))
        | ~ class_Fields_Ofield(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_540])]) ).

fof(f4597,plain,
    ! [X2,X0,X1] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),c_Polynomial_Opoly__gcd(X2,X1,X0)),X0))
      | ~ class_Fields_Ofield(X2) ),
    inference(cnf_transformation,[],[f2638]) ).

fof(f2638,plain,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),c_Polynomial_Opoly__gcd(X2,X1,X0)),X0))
      | ~ class_Fields_Ofield(X2) ),
    inference(ennf_transformation,[],[f1692]) ).

fof(f1692,plain,
    ! [X0,X1,X2] :
      ( class_Fields_Ofield(X2)
     => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),c_Polynomial_Opoly__gcd(X2,X1,X0)),X0)) ),
    inference(rectify,[],[f789]) ).

fof(f789,axiom,
    ! [X28,X13,X4] :
      ( class_Fields_Ofield(X4)
     => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4)),c_Polynomial_Opoly__gcd(X4,X13,X28)),X28)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__gcd__dvd2) ).

fof(f9611,plain,
    spl38_539,
    inference(avatar_split_clause,[],[f4527,f9609]) ).

fof(f9609,plain,
    ( spl38_539
  <=> ! [X0,X1] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_539])]) ).

fof(f4527,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
      | c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) ),
    inference(cnf_transformation,[],[f3604]) ).

fof(f3604,plain,
    ! [X0,X1] :
      ( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != X0
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != X1 )
      & ( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
          & c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1 )
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) ) ),
    inference(flattening,[],[f3603]) ).

fof(f3603,plain,
    ! [X0,X1] :
      ( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != X0
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != X1 )
      & ( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
          & c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1 )
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) ) ),
    inference(nnf_transformation,[],[f1634]) ).

fof(f1634,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)
    <=> ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
        & c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1 ) ),
    inference(rectify,[],[f423]) ).

fof(f423,axiom,
    ! [X11,X34] :
      ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X34),X11)
    <=> ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X11
        & c_Groups_Oone__class_Oone(tc_Nat_Onat) = X34 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__1__iff) ).

fof(f9607,plain,
    spl38_538,
    inference(avatar_split_clause,[],[f4526,f9605]) ).

fof(f9605,plain,
    ( spl38_538
  <=> ! [X0,X1] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_538])]) ).

fof(f4526,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
      | c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) ),
    inference(cnf_transformation,[],[f3604]) ).

fof(f9603,plain,
    spl38_537,
    inference(avatar_split_clause,[],[f4350,f9601]) ).

fof(f9601,plain,
    ( spl38_537
  <=> ! [X0,X1] :
        ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) = X0
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_537])]) ).

fof(f4350,plain,
    ! [X0,X1] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) = X0
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
    inference(cnf_transformation,[],[f2511]) ).

fof(f2511,plain,
    ! [X0,X1] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) = X0
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
    inference(ennf_transformation,[],[f1531]) ).

fof(f1531,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
     => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) = X0 ),
    inference(rectify,[],[f992]) ).

fof(f992,axiom,
    ! [X19,X10] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X10,X19)
     => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X10)) = X19 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__diff__inverse) ).

fof(f9599,plain,
    spl38_536,
    inference(avatar_split_clause,[],[f4349,f9597]) ).

fof(f9597,plain,
    ( spl38_536
  <=> ! [X0,X1] :
        ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) = X1
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_536])]) ).

fof(f4349,plain,
    ! [X0,X1] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) = X1
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
    inference(cnf_transformation,[],[f2510]) ).

fof(f2510,plain,
    ! [X0,X1] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) = X1
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
    inference(ennf_transformation,[],[f1530]) ).

fof(f1530,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
     => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) = X1 ),
    inference(rectify,[],[f983]) ).

fof(f983,axiom,
    ! [X10,X38] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X38,X10)
     => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X10,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X10,X38)) = X38 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__diff__cancel) ).

fof(f9595,plain,
    spl38_535,
    inference(avatar_split_clause,[],[f4340,f9593]) ).

fof(f9593,plain,
    ( spl38_535
  <=> ! [X0,X1] :
        ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) = X1
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_535])]) ).

fof(f4340,plain,
    ! [X0,X1] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) = X1
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
    inference(cnf_transformation,[],[f2500]) ).

fof(f2500,plain,
    ! [X0,X1] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) = X1
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
    inference(ennf_transformation,[],[f1522]) ).

fof(f1522,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
     => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) = X1 ),
    inference(rectify,[],[f990]) ).

fof(f990,axiom,
    ! [X10,X19] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X10)
     => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X10)) = X19 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__inverse) ).

fof(f9591,plain,
    spl38_534,
    inference(avatar_split_clause,[],[f4299,f9589]) ).

fof(f9589,plain,
    ( spl38_534
  <=> ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X0
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X0)
        | ~ class_Groups_Ozero(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_534])]) ).

fof(f4299,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X0
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X0)
      | ~ class_Groups_Ozero(X1) ),
    inference(cnf_transformation,[],[f3522]) ).

fof(f3522,plain,
    ! [X0,X1] :
      ( ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X0)
          | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) != X0 )
        & ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X0
          | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X0) ) )
      | ~ class_Groups_Ozero(X1) ),
    inference(nnf_transformation,[],[f2460]) ).

fof(f2460,plain,
    ! [X0,X1] :
      ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X0)
      <=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X0 )
      | ~ class_Groups_Ozero(X1) ),
    inference(ennf_transformation,[],[f1485]) ).

fof(f1485,plain,
    ! [X0,X1] :
      ( class_Groups_Ozero(X1)
     => ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X0)
      <=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X0 ) ),
    inference(rectify,[],[f29]) ).

fof(f29,axiom,
    ! [X7,X4] :
      ( class_Groups_Ozero(X4)
     => ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X4,X7)
      <=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X7 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psize__eq__0__iff) ).

fof(f9587,plain,
    spl38_533,
    inference(avatar_split_clause,[],[f4292,f9585]) ).

fof(f4292,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X1,c_Polynomial_OpCons(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))))
      | ~ class_Groups_Ozero(X1) ),
    inference(cnf_transformation,[],[f2454]) ).

fof(f2454,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X1,c_Polynomial_OpCons(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))))
      | ~ class_Groups_Ozero(X1) ),
    inference(ennf_transformation,[],[f1480]) ).

fof(f1480,plain,
    ! [X0,X1] :
      ( class_Groups_Ozero(X1)
     => c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X1,c_Polynomial_OpCons(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))) ),
    inference(rectify,[],[f40]) ).

fof(f40,axiom,
    ! [X18,X4] :
      ( class_Groups_Ozero(X4)
     => c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X4,c_Polynomial_OpCons(X4,X18,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__pCons__0) ).

fof(f9583,plain,
    spl38_532,
    inference(avatar_split_clause,[],[f4249,f9581]) ).

fof(f9581,plain,
    ( spl38_532
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0))
        | ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
        | ~ class_Rings_Olinordered__idom(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_532])]) ).

fof(f4249,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0))
      | ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
      | ~ class_Rings_Olinordered__idom(X1) ),
    inference(cnf_transformation,[],[f3514]) ).

fof(f3514,plain,
    ! [X0,X1] :
      ( ( ( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0))
          | ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1)) )
        & ( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
          | ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0)) ) )
      | ~ class_Rings_Olinordered__idom(X1) ),
    inference(nnf_transformation,[],[f2417]) ).

fof(f2417,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0))
      <=> c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1)) )
      | ~ class_Rings_Olinordered__idom(X1) ),
    inference(ennf_transformation,[],[f1443]) ).

fof(f1443,plain,
    ! [X0,X1] :
      ( class_Rings_Olinordered__idom(X1)
     => ( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0))
      <=> c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ) ),
    inference(rectify,[],[f78]) ).

fof(f78,axiom,
    ! [X12,X4] :
      ( class_Rings_Olinordered__idom(X4)
     => ( c_Orderings_Oord__class_Oless(X4,X12,c_Groups_Ouminus__class_Ouminus(X4,X12))
      <=> c_Orderings_Oord__class_Oless(X4,X12,c_Groups_Ozero__class_Ozero(X4)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__minus__self__iff) ).

fof(f9579,plain,
    spl38_531,
    inference(avatar_split_clause,[],[f4248,f9577]) ).

fof(f9577,plain,
    ( spl38_531
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
        | ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0))
        | ~ class_Rings_Olinordered__idom(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_531])]) ).

fof(f4248,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
      | ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0))
      | ~ class_Rings_Olinordered__idom(X1) ),
    inference(cnf_transformation,[],[f3514]) ).

fof(f9575,plain,
    spl38_530,
    inference(avatar_split_clause,[],[f4225,f9573]) ).

fof(f9573,plain,
    ( spl38_530
  <=> ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(X1) = X0
        | c_Groups_Ozero__class_Ozero(X1) != c_Groups_Oplus__class_Oplus(X1,X0,X0)
        | ~ class_Groups_Olinordered__ab__group__add(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_530])]) ).

fof(f4225,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X1) = X0
      | c_Groups_Ozero__class_Ozero(X1) != c_Groups_Oplus__class_Oplus(X1,X0,X0)
      | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(cnf_transformation,[],[f3503]) ).

fof(f3503,plain,
    ! [X0,X1] :
      ( ( ( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oplus__class_Oplus(X1,X0,X0)
          | c_Groups_Ozero__class_Ozero(X1) != X0 )
        & ( c_Groups_Ozero__class_Ozero(X1) = X0
          | c_Groups_Ozero__class_Ozero(X1) != c_Groups_Oplus__class_Oplus(X1,X0,X0) ) )
      | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(nnf_transformation,[],[f2404]) ).

fof(f2404,plain,
    ! [X0,X1] :
      ( ( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oplus__class_Oplus(X1,X0,X0)
      <=> c_Groups_Ozero__class_Ozero(X1) = X0 )
      | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(ennf_transformation,[],[f1431]) ).

fof(f1431,plain,
    ! [X0,X1] :
      ( class_Groups_Olinordered__ab__group__add(X1)
     => ( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oplus__class_Oplus(X1,X0,X0)
      <=> c_Groups_Ozero__class_Ozero(X1) = X0 ) ),
    inference(rectify,[],[f701]) ).

fof(f701,axiom,
    ! [X12,X4] :
      ( class_Groups_Olinordered__ab__group__add(X4)
     => ( c_Groups_Ozero__class_Ozero(X4) = c_Groups_Oplus__class_Oplus(X4,X12,X12)
      <=> c_Groups_Ozero__class_Ozero(X4) = X12 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__eq__0__iff) ).

fof(f9571,plain,
    spl38_529,
    inference(avatar_split_clause,[],[f4224,f9569]) ).

fof(f9569,plain,
    ( spl38_529
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
        | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
        | ~ class_Groups_Olinordered__ab__group__add(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_529])]) ).

fof(f4224,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
      | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
      | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(cnf_transformation,[],[f3502]) ).

fof(f3502,plain,
    ! [X0,X1] :
      ( ( ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
          | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
        & ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
          | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0) ) )
      | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(nnf_transformation,[],[f2403]) ).

fof(f2403,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
      <=> c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
      | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(ennf_transformation,[],[f1430]) ).

fof(f1430,plain,
    ! [X0,X1] :
      ( class_Groups_Olinordered__ab__group__add(X1)
     => ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
      <=> c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) ) ),
    inference(rectify,[],[f151]) ).

fof(f151,axiom,
    ! [X12,X4] :
      ( class_Groups_Olinordered__ab__group__add(X4)
     => ( c_Orderings_Oord__class_Oless(X4,c_Groups_Ouminus__class_Ouminus(X4,X12),X12)
      <=> c_Orderings_Oord__class_Oless(X4,c_Groups_Ozero__class_Ozero(X4),X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__less__nonneg) ).

fof(f9567,plain,
    spl38_528,
    inference(avatar_split_clause,[],[f4223,f9565]) ).

fof(f9565,plain,
    ( spl38_528
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
        | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
        | ~ class_Groups_Olinordered__ab__group__add(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_528])]) ).

fof(f4223,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
      | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
      | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(cnf_transformation,[],[f3502]) ).

fof(f9563,plain,
    spl38_527,
    inference(avatar_split_clause,[],[f4222,f9561]) ).

fof(f9561,plain,
    ( spl38_527
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
        | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
        | ~ class_Groups_Olinordered__ab__group__add(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_527])]) ).

fof(f4222,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
      | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
      | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(cnf_transformation,[],[f3501]) ).

fof(f3501,plain,
    ! [X0,X1] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
          | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
        & ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
          | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0) ) )
      | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(nnf_transformation,[],[f2402]) ).

fof(f2402,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
      <=> c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
      | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(ennf_transformation,[],[f1429]) ).

fof(f1429,plain,
    ! [X0,X1] :
      ( class_Groups_Olinordered__ab__group__add(X1)
     => ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
      <=> c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0) ) ),
    inference(rectify,[],[f155]) ).

fof(f155,axiom,
    ! [X12,X4] :
      ( class_Groups_Olinordered__ab__group__add(X4)
     => ( c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ouminus__class_Ouminus(X4,X12),X12)
      <=> c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__le__self__iff) ).

fof(f9559,plain,
    spl38_526,
    inference(avatar_split_clause,[],[f4221,f9557]) ).

fof(f9557,plain,
    ( spl38_526
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
        | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
        | ~ class_Groups_Olinordered__ab__group__add(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_526])]) ).

fof(f4221,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
      | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
      | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(cnf_transformation,[],[f3501]) ).

fof(f9555,plain,
    spl38_525,
    inference(avatar_split_clause,[],[f4220,f9553]) ).

fof(f9553,plain,
    ( spl38_525
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0))
        | ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
        | ~ class_Groups_Olinordered__ab__group__add(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_525])]) ).

fof(f4220,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0))
      | ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
      | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(cnf_transformation,[],[f3500]) ).

fof(f3500,plain,
    ! [X0,X1] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0))
          | ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1)) )
        & ( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
          | ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0)) ) )
      | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(nnf_transformation,[],[f2401]) ).

fof(f2401,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0))
      <=> c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1)) )
      | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(ennf_transformation,[],[f1428]) ).

fof(f1428,plain,
    ! [X0,X1] :
      ( class_Groups_Olinordered__ab__group__add(X1)
     => ( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0))
      <=> c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ) ),
    inference(rectify,[],[f153]) ).

fof(f153,axiom,
    ! [X12,X4] :
      ( class_Groups_Olinordered__ab__group__add(X4)
     => ( c_Orderings_Oord__class_Oless__eq(X4,X12,c_Groups_Ouminus__class_Ouminus(X4,X12))
      <=> c_Orderings_Oord__class_Oless__eq(X4,X12,c_Groups_Ozero__class_Ozero(X4)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__minus__self__iff) ).

fof(f9551,plain,
    spl38_524,
    inference(avatar_split_clause,[],[f4219,f9549]) ).

fof(f9549,plain,
    ( spl38_524
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
        | ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0))
        | ~ class_Groups_Olinordered__ab__group__add(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_524])]) ).

fof(f4219,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
      | ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0))
      | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(cnf_transformation,[],[f3500]) ).

fof(f9547,plain,
    spl38_523,
    inference(avatar_split_clause,[],[f4196,f9545]) ).

fof(f9545,plain,
    ( spl38_523
  <=> ! [X0,X1] :
        ( c_Rings_Oinverse__class_Oinverse(X1,c_Rings_Oinverse__class_Oinverse(X1,X0)) = X0
        | c_Groups_Ozero__class_Ozero(X1) = X0
        | ~ class_Rings_Odivision__ring(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_523])]) ).

fof(f4196,plain,
    ! [X0,X1] :
      ( c_Rings_Oinverse__class_Oinverse(X1,c_Rings_Oinverse__class_Oinverse(X1,X0)) = X0
      | c_Groups_Ozero__class_Ozero(X1) = X0
      | ~ class_Rings_Odivision__ring(X1) ),
    inference(cnf_transformation,[],[f2375]) ).

fof(f2375,plain,
    ! [X0,X1] :
      ( c_Rings_Oinverse__class_Oinverse(X1,c_Rings_Oinverse__class_Oinverse(X1,X0)) = X0
      | c_Groups_Ozero__class_Ozero(X1) = X0
      | ~ class_Rings_Odivision__ring(X1) ),
    inference(flattening,[],[f2374]) ).

fof(f2374,plain,
    ! [X0,X1] :
      ( c_Rings_Oinverse__class_Oinverse(X1,c_Rings_Oinverse__class_Oinverse(X1,X0)) = X0
      | c_Groups_Ozero__class_Ozero(X1) = X0
      | ~ class_Rings_Odivision__ring(X1) ),
    inference(ennf_transformation,[],[f1407]) ).

fof(f1407,plain,
    ! [X0,X1] :
      ( class_Rings_Odivision__ring(X1)
     => ( c_Groups_Ozero__class_Ozero(X1) != X0
       => c_Rings_Oinverse__class_Oinverse(X1,c_Rings_Oinverse__class_Oinverse(X1,X0)) = X0 ) ),
    inference(rectify,[],[f812]) ).

fof(f812,axiom,
    ! [X18,X4] :
      ( class_Rings_Odivision__ring(X4)
     => ( c_Groups_Ozero__class_Ozero(X4) != X18
       => c_Rings_Oinverse__class_Oinverse(X4,c_Rings_Oinverse__class_Oinverse(X4,X18)) = X18 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__inverse__inverse__eq) ).

fof(f9543,plain,
    spl38_522,
    inference(avatar_split_clause,[],[f4192,f9541]) ).

fof(f9541,plain,
    ( spl38_522
  <=> ! [X0,X1] :
        ( c_Rings_Oinverse__class_Oinverse(X1,c_Groups_Ouminus__class_Ouminus(X1,X0)) = c_Groups_Ouminus__class_Ouminus(X1,c_Rings_Oinverse__class_Oinverse(X1,X0))
        | ~ class_Rings_Odivision__ring__inverse__zero(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_522])]) ).

fof(f4192,plain,
    ! [X0,X1] :
      ( c_Rings_Oinverse__class_Oinverse(X1,c_Groups_Ouminus__class_Ouminus(X1,X0)) = c_Groups_Ouminus__class_Ouminus(X1,c_Rings_Oinverse__class_Oinverse(X1,X0))
      | ~ class_Rings_Odivision__ring__inverse__zero(X1) ),
    inference(cnf_transformation,[],[f2370]) ).

fof(f2370,plain,
    ! [X0,X1] :
      ( c_Rings_Oinverse__class_Oinverse(X1,c_Groups_Ouminus__class_Ouminus(X1,X0)) = c_Groups_Ouminus__class_Ouminus(X1,c_Rings_Oinverse__class_Oinverse(X1,X0))
      | ~ class_Rings_Odivision__ring__inverse__zero(X1) ),
    inference(ennf_transformation,[],[f1404]) ).

fof(f1404,plain,
    ! [X0,X1] :
      ( class_Rings_Odivision__ring__inverse__zero(X1)
     => c_Rings_Oinverse__class_Oinverse(X1,c_Groups_Ouminus__class_Ouminus(X1,X0)) = c_Groups_Ouminus__class_Ouminus(X1,c_Rings_Oinverse__class_Oinverse(X1,X0)) ),
    inference(rectify,[],[f806]) ).

fof(f806,axiom,
    ! [X18,X4] :
      ( class_Rings_Odivision__ring__inverse__zero(X4)
     => c_Rings_Oinverse__class_Oinverse(X4,c_Groups_Ouminus__class_Ouminus(X4,X18)) = c_Groups_Ouminus__class_Ouminus(X4,c_Rings_Oinverse__class_Oinverse(X4,X18)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__minus__eq) ).

fof(f9539,plain,
    spl38_521,
    inference(avatar_split_clause,[],[f4170,f9537]) ).

fof(f9537,plain,
    ( spl38_521
  <=> ! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_521])]) ).

fof(f4170,plain,
    ! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1),
    inference(cnf_transformation,[],[f1369]) ).

fof(f1369,plain,
    ! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1),
    inference(rectify,[],[f422]) ).

fof(f422,axiom,
    ! [X10,X19] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),X10) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X10),X19),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__commute) ).

fof(f9535,plain,
    spl38_520,
    inference(avatar_split_clause,[],[f4169,f9533]) ).

fof(f9533,plain,
    ( spl38_520
  <=> ! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_520])]) ).

fof(f4169,plain,
    ! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X1),
    inference(cnf_transformation,[],[f1368]) ).

fof(f1368,plain,
    ! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X1),
    inference(rectify,[],[f739]) ).

fof(f739,axiom,
    ! [X74,X33] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X33),X74) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X74),X33),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__commute) ).

fof(f9531,plain,
    spl38_519,
    inference(avatar_split_clause,[],[f4130,f9529]) ).

fof(f4130,plain,
    ! [X0] :
      ( c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))
      | ~ class_Rings_Ocomm__semiring__1(X0) ),
    inference(cnf_transformation,[],[f2357]) ).

fof(f2357,plain,
    ! [X0] :
      ( c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))
      | ~ class_Rings_Ocomm__semiring__1(X0) ),
    inference(ennf_transformation,[],[f1338]) ).

fof(f1338,plain,
    ! [X0] :
      ( class_Rings_Ocomm__semiring__1(X0)
     => c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) ),
    inference(rectify,[],[f186]) ).

fof(f186,axiom,
    ! [X4] :
      ( class_Rings_Ocomm__semiring__1(X4)
     => c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X4)) = c_Polynomial_OpCons(X4,c_Groups_Oone__class_Oone(X4),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__poly__def) ).

fof(f9527,plain,
    spl38_518,
    inference(avatar_split_clause,[],[f4115,f9525]) ).

fof(f4115,plain,
    ! [X0] :
      ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))
      | ~ class_Groups_Ozero(X0) ),
    inference(cnf_transformation,[],[f2342]) ).

fof(f2342,plain,
    ! [X0] :
      ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))
      | ~ class_Groups_Ozero(X0) ),
    inference(ennf_transformation,[],[f1323]) ).

fof(f1323,plain,
    ! [X0] :
      ( class_Groups_Ozero(X0)
     => c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) ),
    inference(rectify,[],[f44]) ).

fof(f44,axiom,
    ! [X4] :
      ( class_Groups_Ozero(X4)
     => c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = c_Polynomial_OpCons(X4,c_Groups_Ozero__class_Ozero(X4),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pCons__0__0) ).

fof(f9399,plain,
    ( spl38_517
    | ~ spl38_3
    | ~ spl38_125
    | ~ spl38_465 ),
    inference(avatar_split_clause,[],[f9046,f8745,f6516,f5906,f9397]) ).

fof(f9397,plain,
    ( spl38_517
  <=> ! [X0] : v_s____ = c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,v_s____) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_517])]) ).

fof(f8745,plain,
    ( spl38_465
  <=> ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Osmult(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
        | ~ class_Rings_Ocomm__semiring__0(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_465])]) ).

fof(f9046,plain,
    ( ! [X0] : v_s____ = c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,v_s____)
    | ~ spl38_3
    | ~ spl38_125
    | ~ spl38_465 ),
    inference(forward_demodulation,[],[f9042,f5908]) ).

fof(f9042,plain,
    ( ! [X0] : c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
    | ~ spl38_125
    | ~ spl38_465 ),
    inference(resolution,[],[f8746,f6518]) ).

fof(f8746,plain,
    ( ! [X0,X1] :
        ( ~ class_Rings_Ocomm__semiring__0(X1)
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Osmult(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) )
    | ~ spl38_465 ),
    inference(avatar_component_clause,[],[f8745]) ).

fof(f9280,plain,
    ( spl38_516
    | ~ spl38_3
    | ~ spl38_125
    | ~ spl38_464 ),
    inference(avatar_split_clause,[],[f9041,f8741,f6516,f5906,f9278]) ).

fof(f9278,plain,
    ( spl38_516
  <=> ! [X0] : v_s____ = c_Polynomial_Osynthetic__div(tc_Complex_Ocomplex,v_s____,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_516])]) ).

fof(f8741,plain,
    ( spl38_464
  <=> ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Osynthetic__div(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0)
        | ~ class_Rings_Ocomm__semiring__0(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_464])]) ).

fof(f9041,plain,
    ( ! [X0] : v_s____ = c_Polynomial_Osynthetic__div(tc_Complex_Ocomplex,v_s____,X0)
    | ~ spl38_3
    | ~ spl38_125
    | ~ spl38_464 ),
    inference(forward_demodulation,[],[f9037,f5908]) ).

fof(f9037,plain,
    ( ! [X0] : c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_Osynthetic__div(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0)
    | ~ spl38_125
    | ~ spl38_464 ),
    inference(resolution,[],[f8742,f6518]) ).

fof(f8742,plain,
    ( ! [X0,X1] :
        ( ~ class_Rings_Ocomm__semiring__0(X1)
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Osynthetic__div(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0) )
    | ~ spl38_464 ),
    inference(avatar_component_clause,[],[f8741]) ).

fof(f9180,plain,
    ( spl38_515
    | ~ spl38_3
    | ~ spl38_125
    | ~ spl38_463 ),
    inference(avatar_split_clause,[],[f9036,f8737,f6516,f5906,f9178]) ).

fof(f9178,plain,
    ( spl38_515
  <=> ! [X0] : v_s____ = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Complex_Ocomplex,v_s____,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_515])]) ).

fof(f8737,plain,
    ( spl38_463
  <=> ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0)
        | ~ class_Rings_Ocomm__semiring__0(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_463])]) ).

fof(f9036,plain,
    ( ! [X0] : v_s____ = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Complex_Ocomplex,v_s____,X0)
    | ~ spl38_3
    | ~ spl38_125
    | ~ spl38_463 ),
    inference(forward_demodulation,[],[f9032,f5908]) ).

fof(f9032,plain,
    ( ! [X0] : c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0)
    | ~ spl38_125
    | ~ spl38_463 ),
    inference(resolution,[],[f8738,f6518]) ).

fof(f8738,plain,
    ( ! [X0,X1] :
        ( ~ class_Rings_Ocomm__semiring__0(X1)
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0) )
    | ~ spl38_463 ),
    inference(avatar_component_clause,[],[f8737]) ).

fof(f9066,plain,
    ( spl38_514
    | ~ spl38_3
    | ~ spl38_125
    | ~ spl38_462 ),
    inference(avatar_split_clause,[],[f9031,f8733,f6516,f5906,f9064]) ).

fof(f9064,plain,
    ( spl38_514
  <=> ! [X0] : v_s____ = c_Polynomial_Opcompose(tc_Complex_Ocomplex,v_s____,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_514])]) ).

fof(f8733,plain,
    ( spl38_462
  <=> ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Opcompose(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0)
        | ~ class_Rings_Ocomm__semiring__0(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_462])]) ).

fof(f9031,plain,
    ( ! [X0] : v_s____ = c_Polynomial_Opcompose(tc_Complex_Ocomplex,v_s____,X0)
    | ~ spl38_3
    | ~ spl38_125
    | ~ spl38_462 ),
    inference(forward_demodulation,[],[f9027,f5908]) ).

fof(f9027,plain,
    ( ! [X0] : c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_Opcompose(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0)
    | ~ spl38_125
    | ~ spl38_462 ),
    inference(resolution,[],[f8734,f6518]) ).

fof(f8734,plain,
    ( ! [X0,X1] :
        ( ~ class_Rings_Ocomm__semiring__0(X1)
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Opcompose(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0) )
    | ~ spl38_462 ),
    inference(avatar_component_clause,[],[f8733]) ).

fof(f8965,plain,
    ( spl38_513
    | ~ spl38_3
    | ~ spl38_55
    | ~ spl38_441 ),
    inference(avatar_split_clause,[],[f8942,f8648,f6166,f5906,f8962]) ).

fof(f8962,plain,
    ( spl38_513
  <=> v_s____ = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),v_s____) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_513])]) ).

fof(f6166,plain,
    ( spl38_55
  <=> class_Groups_Oab__group__add(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_55])]) ).

fof(f8648,plain,
    ( spl38_441
  <=> ! [X0] :
        ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))
        | ~ class_Groups_Oab__group__add(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_441])]) ).

fof(f8942,plain,
    ( v_s____ = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),v_s____)
    | ~ spl38_3
    | ~ spl38_55
    | ~ spl38_441 ),
    inference(forward_demodulation,[],[f8939,f5908]) ).

fof(f8939,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
    | ~ spl38_55
    | ~ spl38_441 ),
    inference(resolution,[],[f8649,f6168]) ).

fof(f6168,plain,
    ( class_Groups_Oab__group__add(tc_Complex_Ocomplex)
    | ~ spl38_55 ),
    inference(avatar_component_clause,[],[f6166]) ).

fof(f8649,plain,
    ( ! [X0] :
        ( ~ class_Groups_Oab__group__add(X0)
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) )
    | ~ spl38_441 ),
    inference(avatar_component_clause,[],[f8648]) ).

fof(f8938,plain,
    spl38_512,
    inference(avatar_split_clause,[],[f5722,f8936]) ).

fof(f8936,plain,
    ( spl38_512
  <=> ! [X2,X0,X3] :
        ( hAPP(c_Polynomial_Ocoeff(X3,c_Polynomial_Omonom(X3,X0,X2)),X2) = X0
        | ~ class_Groups_Ozero(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_512])]) ).

fof(f5722,plain,
    ! [X2,X3,X0] :
      ( hAPP(c_Polynomial_Ocoeff(X3,c_Polynomial_Omonom(X3,X0,X2)),X2) = X0
      | ~ class_Groups_Ozero(X3) ),
    inference(equality_resolution,[],[f5229]) ).

fof(f5229,plain,
    ! [X2,X3,X0,X1] :
      ( hAPP(c_Polynomial_Ocoeff(X3,c_Polynomial_Omonom(X3,X0,X2)),X1) = X0
      | X1 != X2
      | ~ class_Groups_Ozero(X3) ),
    inference(cnf_transformation,[],[f3247]) ).

fof(f3247,plain,
    ! [X0,X1,X2,X3] :
      ( ( ( c_Groups_Ozero__class_Ozero(X3) = hAPP(c_Polynomial_Ocoeff(X3,c_Polynomial_Omonom(X3,X0,X2)),X1)
          | X1 = X2 )
        & ( hAPP(c_Polynomial_Ocoeff(X3,c_Polynomial_Omonom(X3,X0,X2)),X1) = X0
          | X1 != X2 ) )
      | ~ class_Groups_Ozero(X3) ),
    inference(ennf_transformation,[],[f2116]) ).

fof(f2116,plain,
    ! [X0,X1,X2,X3] :
      ( class_Groups_Ozero(X3)
     => ( ( X1 != X2
         => c_Groups_Ozero__class_Ozero(X3) = hAPP(c_Polynomial_Ocoeff(X3,c_Polynomial_Omonom(X3,X0,X2)),X1) )
        & ( X1 = X2
         => hAPP(c_Polynomial_Ocoeff(X3,c_Polynomial_Omonom(X3,X0,X2)),X1) = X0 ) ) ),
    inference(rectify,[],[f22]) ).

fof(f22,axiom,
    ! [X18,X10,X19,X4] :
      ( class_Groups_Ozero(X4)
     => ( ( X10 != X19
         => c_Groups_Ozero__class_Ozero(X4) = hAPP(c_Polynomial_Ocoeff(X4,c_Polynomial_Omonom(X4,X18,X19)),X10) )
        & ( X10 = X19
         => hAPP(c_Polynomial_Ocoeff(X4,c_Polynomial_Omonom(X4,X18,X19)),X10) = X18 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__monom) ).

fof(f8934,plain,
    spl38_511,
    inference(avatar_split_clause,[],[f5660,f8932]) ).

fof(f8932,plain,
    ( spl38_511
  <=> ! [X2,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_Osmult(X2,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)))
        | ~ class_Rings_Oidom(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_511])]) ).

fof(f5660,plain,
    ! [X2,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_Osmult(X2,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)))
      | ~ class_Rings_Oidom(X2) ),
    inference(equality_resolution,[],[f4785]) ).

fof(f4785,plain,
    ! [X2,X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_Osmult(X2,X1,X0)
      | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X0
      | ~ class_Rings_Oidom(X2) ),
    inference(cnf_transformation,[],[f3681]) ).

fof(f3681,plain,
    ! [X0,X1,X2] :
      ( ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_Osmult(X2,X1,X0)
          | ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X0
            & c_Groups_Ozero__class_Ozero(X2) != X1 ) )
        & ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
          | c_Groups_Ozero__class_Ozero(X2) = X1
          | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != c_Polynomial_Osmult(X2,X1,X0) ) )
      | ~ class_Rings_Oidom(X2) ),
    inference(flattening,[],[f3680]) ).

fof(f3680,plain,
    ! [X0,X1,X2] :
      ( ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_Osmult(X2,X1,X0)
          | ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X0
            & c_Groups_Ozero__class_Ozero(X2) != X1 ) )
        & ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
          | c_Groups_Ozero__class_Ozero(X2) = X1
          | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != c_Polynomial_Osmult(X2,X1,X0) ) )
      | ~ class_Rings_Oidom(X2) ),
    inference(nnf_transformation,[],[f2810]) ).

fof(f2810,plain,
    ! [X0,X1,X2] :
      ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_Osmult(X2,X1,X0)
      <=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
          | c_Groups_Ozero__class_Ozero(X2) = X1 ) )
      | ~ class_Rings_Oidom(X2) ),
    inference(ennf_transformation,[],[f1809]) ).

fof(f1809,plain,
    ! [X0,X1,X2] :
      ( class_Rings_Oidom(X2)
     => ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_Osmult(X2,X1,X0)
      <=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
          | c_Groups_Ozero__class_Ozero(X2) = X1 ) ) ),
    inference(rectify,[],[f14]) ).

fof(f14,axiom,
    ! [X7,X12,X4] :
      ( class_Rings_Oidom(X4)
     => ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = c_Polynomial_Osmult(X4,X12,X7)
      <=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X7
          | c_Groups_Ozero__class_Ozero(X4) = X12 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__eq__0__iff) ).

fof(f8930,plain,
    spl38_510,
    inference(avatar_split_clause,[],[f5659,f8928]) ).

fof(f8928,plain,
    ( spl38_510
  <=> ! [X2,X0] :
        ( c_Groups_Ozero__class_Ozero(X2) = hAPP(c_Polynomial_Opoly(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))),X0)
        | ~ class_Rings_Oidom(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_510])]) ).

fof(f5659,plain,
    ! [X2,X0] :
      ( c_Groups_Ozero__class_Ozero(X2) = hAPP(c_Polynomial_Opoly(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))),X0)
      | ~ class_Rings_Oidom(X2) ),
    inference(equality_resolution,[],[f4781]) ).

fof(f4781,plain,
    ! [X2,X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X2) = hAPP(c_Polynomial_Opoly(X2,X1),X0)
      | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X1
      | ~ class_Rings_Oidom(X2) ),
    inference(cnf_transformation,[],[f3679]) ).

fof(f3679,plain,
    ! [X0,X1,X2] :
      ( ( ( c_Groups_Ozero__class_Ozero(X2) = hAPP(c_Polynomial_Opoly(X2,X1),X0)
          | ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Oorder(X2,X0,X1)
            & c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X1 ) )
        & ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Polynomial_Oorder(X2,X0,X1)
          | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
          | c_Groups_Ozero__class_Ozero(X2) != hAPP(c_Polynomial_Opoly(X2,X1),X0) ) )
      | ~ class_Rings_Oidom(X2) ),
    inference(flattening,[],[f3678]) ).

fof(f3678,plain,
    ! [X0,X1,X2] :
      ( ( ( c_Groups_Ozero__class_Ozero(X2) = hAPP(c_Polynomial_Opoly(X2,X1),X0)
          | ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Oorder(X2,X0,X1)
            & c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X1 ) )
        & ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Polynomial_Oorder(X2,X0,X1)
          | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
          | c_Groups_Ozero__class_Ozero(X2) != hAPP(c_Polynomial_Opoly(X2,X1),X0) ) )
      | ~ class_Rings_Oidom(X2) ),
    inference(nnf_transformation,[],[f2809]) ).

fof(f2809,plain,
    ! [X0,X1,X2] :
      ( ( c_Groups_Ozero__class_Ozero(X2) = hAPP(c_Polynomial_Opoly(X2,X1),X0)
      <=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Polynomial_Oorder(X2,X0,X1)
          | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1 ) )
      | ~ class_Rings_Oidom(X2) ),
    inference(ennf_transformation,[],[f1808]) ).

fof(f1808,plain,
    ! [X0,X1,X2] :
      ( class_Rings_Oidom(X2)
     => ( c_Groups_Ozero__class_Ozero(X2) = hAPP(c_Polynomial_Opoly(X2,X1),X0)
      <=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Polynomial_Oorder(X2,X0,X1)
          | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1 ) ) ),
    inference(rectify,[],[f27]) ).

fof(f27,axiom,
    ! [X12,X7,X4] :
      ( class_Rings_Oidom(X4)
     => ( c_Groups_Ozero__class_Ozero(X4) = hAPP(c_Polynomial_Opoly(X4,X7),X12)
      <=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Polynomial_Oorder(X4,X12,X7)
          | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X7 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__root) ).

fof(f8926,plain,
    spl38_509,
    inference(avatar_split_clause,[],[f5658,f8924]) ).

fof(f8924,plain,
    ( spl38_509
  <=> ! [X2,X0] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X2,c_Polynomial_Osmult(X2,c_Groups_Ozero__class_Ozero(X2),X0))
        | ~ class_Rings_Oidom(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_509])]) ).

fof(f5658,plain,
    ! [X2,X0] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X2,c_Polynomial_Osmult(X2,c_Groups_Ozero__class_Ozero(X2),X0))
      | ~ class_Rings_Oidom(X2) ),
    inference(equality_resolution,[],[f4769]) ).

fof(f4769,plain,
    ! [X2,X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X2,c_Polynomial_Osmult(X2,X1,X0))
      | c_Groups_Ozero__class_Ozero(X2) != X1
      | ~ class_Rings_Oidom(X2) ),
    inference(cnf_transformation,[],[f2795]) ).

fof(f2795,plain,
    ! [X0,X1,X2] :
      ( ( ( c_Polynomial_Odegree(X2,X0) = c_Polynomial_Odegree(X2,c_Polynomial_Osmult(X2,X1,X0))
          | c_Groups_Ozero__class_Ozero(X2) = X1 )
        & ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X2,c_Polynomial_Osmult(X2,X1,X0))
          | c_Groups_Ozero__class_Ozero(X2) != X1 ) )
      | ~ class_Rings_Oidom(X2) ),
    inference(ennf_transformation,[],[f1800]) ).

fof(f1800,plain,
    ! [X0,X1,X2] :
      ( class_Rings_Oidom(X2)
     => ( ( c_Groups_Ozero__class_Ozero(X2) != X1
         => c_Polynomial_Odegree(X2,X0) = c_Polynomial_Odegree(X2,c_Polynomial_Osmult(X2,X1,X0)) )
        & ( c_Groups_Ozero__class_Ozero(X2) = X1
         => c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X2,c_Polynomial_Osmult(X2,X1,X0)) ) ) ),
    inference(rectify,[],[f37]) ).

fof(f37,axiom,
    ! [X14,X18,X4] :
      ( class_Rings_Oidom(X4)
     => ( ( c_Groups_Ozero__class_Ozero(X4) != X18
         => c_Polynomial_Odegree(X4,X14) = c_Polynomial_Odegree(X4,c_Polynomial_Osmult(X4,X18,X14)) )
        & ( c_Groups_Ozero__class_Ozero(X4) = X18
         => c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X4,c_Polynomial_Osmult(X4,X18,X14)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__smult__eq) ).

fof(f8922,plain,
    spl38_508,
    inference(avatar_split_clause,[],[f5640,f8920]) ).

fof(f8920,plain,
    ( spl38_508
  <=> ! [X2,X0] :
        ( c_Groups_Ozero__class_Ozero(X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ozero__class_Ozero(X2)),X0)
        | ~ class_Rings_Oring__no__zero__divisors(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_508])]) ).

fof(f5640,plain,
    ! [X2,X0] :
      ( c_Groups_Ozero__class_Ozero(X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ozero__class_Ozero(X2)),X0)
      | ~ class_Rings_Oring__no__zero__divisors(X2) ),
    inference(equality_resolution,[],[f4682]) ).

fof(f4682,plain,
    ! [X2,X0,X1] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) = c_Groups_Ozero__class_Ozero(X2)
      | c_Groups_Ozero__class_Ozero(X2) != X1
      | ~ class_Rings_Oring__no__zero__divisors(X2) ),
    inference(cnf_transformation,[],[f3656]) ).

fof(f3656,plain,
    ! [X0,X1,X2] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) = c_Groups_Ozero__class_Ozero(X2)
          | ( c_Groups_Ozero__class_Ozero(X2) != X0
            & c_Groups_Ozero__class_Ozero(X2) != X1 ) )
        & ( c_Groups_Ozero__class_Ozero(X2) = X0
          | c_Groups_Ozero__class_Ozero(X2) = X1
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) != c_Groups_Ozero__class_Ozero(X2) ) )
      | ~ class_Rings_Oring__no__zero__divisors(X2) ),
    inference(flattening,[],[f3655]) ).

fof(f3655,plain,
    ! [X0,X1,X2] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) = c_Groups_Ozero__class_Ozero(X2)
          | ( c_Groups_Ozero__class_Ozero(X2) != X0
            & c_Groups_Ozero__class_Ozero(X2) != X1 ) )
        & ( c_Groups_Ozero__class_Ozero(X2) = X0
          | c_Groups_Ozero__class_Ozero(X2) = X1
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) != c_Groups_Ozero__class_Ozero(X2) ) )
      | ~ class_Rings_Oring__no__zero__divisors(X2) ),
    inference(nnf_transformation,[],[f2696]) ).

fof(f2696,plain,
    ! [X0,X1,X2] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) = c_Groups_Ozero__class_Ozero(X2)
      <=> ( c_Groups_Ozero__class_Ozero(X2) = X0
          | c_Groups_Ozero__class_Ozero(X2) = X1 ) )
      | ~ class_Rings_Oring__no__zero__divisors(X2) ),
    inference(ennf_transformation,[],[f1735]) ).

fof(f1735,plain,
    ! [X0,X1,X2] :
      ( class_Rings_Oring__no__zero__divisors(X2)
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) = c_Groups_Ozero__class_Ozero(X2)
      <=> ( c_Groups_Ozero__class_Ozero(X2) = X0
          | c_Groups_Ozero__class_Ozero(X2) = X1 ) ) ),
    inference(rectify,[],[f165]) ).

fof(f165,axiom,
    ! [X20,X12,X4] :
      ( class_Rings_Oring__no__zero__divisors(X4)
     => ( c_Groups_Ozero__class_Ozero(X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X20)
      <=> ( c_Groups_Ozero__class_Ozero(X4) = X20
          | c_Groups_Ozero__class_Ozero(X4) = X12 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__0__iff) ).

fof(f8918,plain,
    spl38_507,
    inference(avatar_split_clause,[],[f5639,f8916]) ).

fof(f8916,plain,
    ( spl38_507
  <=> ! [X2,X1] :
        ( c_Groups_Ozero__class_Ozero(X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),c_Groups_Ozero__class_Ozero(X2))
        | ~ class_Rings_Oring__no__zero__divisors(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_507])]) ).

fof(f5639,plain,
    ! [X2,X1] :
      ( c_Groups_Ozero__class_Ozero(X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),c_Groups_Ozero__class_Ozero(X2))
      | ~ class_Rings_Oring__no__zero__divisors(X2) ),
    inference(equality_resolution,[],[f4683]) ).

fof(f4683,plain,
    ! [X2,X0,X1] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) = c_Groups_Ozero__class_Ozero(X2)
      | c_Groups_Ozero__class_Ozero(X2) != X0
      | ~ class_Rings_Oring__no__zero__divisors(X2) ),
    inference(cnf_transformation,[],[f3656]) ).

fof(f8914,plain,
    spl38_506,
    inference(avatar_split_clause,[],[f5599,f8912]) ).

fof(f8912,plain,
    ( spl38_506
  <=> ! [X2,X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_506])]) ).

fof(f5599,plain,
    ! [X2,X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2),X0),
    inference(equality_resolution,[],[f4486]) ).

fof(f4486,plain,
    ! [X2,X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2) != X1 ),
    inference(cnf_transformation,[],[f3583]) ).

fof(f3583,plain,
    ! [X0,X1] :
      ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0)
        | ! [X2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2) != X1 )
      & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),sK29(X0,X1)) = X1
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK29])],[f3581,f3582]) ).

fof(f3582,plain,
    ! [X0,X1] :
      ( ? [X3] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3) = X1
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),sK29(X0,X1)) = X1 ),
    introduced(choice_axiom,[]) ).

fof(f3581,plain,
    ! [X0,X1] :
      ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0)
        | ! [X2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2) != X1 )
      & ( ? [X3] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3) = X1
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0) ) ),
    inference(rectify,[],[f3580]) ).

fof(f3580,plain,
    ! [X0,X1] :
      ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0)
        | ! [X2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2) != X1 )
      & ( ? [X2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2) = X1
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0) ) ),
    inference(nnf_transformation,[],[f1622]) ).

fof(f1622,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0)
    <=> ? [X2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2) = X1 ),
    inference(rectify,[],[f913]) ).

fof(f913,axiom,
    ! [X56,X34] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X34,X56)
    <=> ? [X26] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X56),X26) = X34 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__eq__0__iff) ).

fof(f8910,plain,
    spl38_505,
    inference(avatar_split_clause,[],[f5598,f8908]) ).

fof(f8908,plain,
    ( spl38_505
  <=> ! [X2,X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_505])]) ).

fof(f5598,plain,
    ! [X2,X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2),X0),
    inference(equality_resolution,[],[f4482]) ).

fof(f4482,plain,
    ! [X2,X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2) != X1 ),
    inference(cnf_transformation,[],[f3578]) ).

fof(f3578,plain,
    ! [X0,X1] :
      ( ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0)
        | ! [X2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2) != X1 )
      & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),sK28(X0,X1)) = X1
        | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK28])],[f3576,f3577]) ).

fof(f3577,plain,
    ! [X0,X1] :
      ( ? [X3] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3) = X1
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),sK28(X0,X1)) = X1 ),
    introduced(choice_axiom,[]) ).

fof(f3576,plain,
    ! [X0,X1] :
      ( ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0)
        | ! [X2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2) != X1 )
      & ( ? [X3] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3) = X1
        | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0) ) ),
    inference(rectify,[],[f3575]) ).

fof(f3575,plain,
    ! [X0,X1] :
      ( ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0)
        | ! [X2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2) != X1 )
      & ( ? [X2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2) = X1
        | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0) ) ),
    inference(nnf_transformation,[],[f1620]) ).

fof(f1620,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0)
    <=> ? [X2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2) = X1 ),
    inference(rectify,[],[f925]) ).

fof(f925,axiom,
    ! [X56,X34] :
      ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X34,X56)
    <=> ? [X26] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X56),X26) = X34 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__eq__0__iff) ).

fof(f8906,plain,
    spl38_504,
    inference(avatar_split_clause,[],[f5473,f8904]) ).

fof(f8904,plain,
    ( spl38_504
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_504])]) ).

fof(f5473,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(definition_unfolding,[],[f4468,f4035]) ).

fof(f4468,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) ),
    inference(cnf_transformation,[],[f3565]) ).

fof(f3565,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) ) ),
    inference(nnf_transformation,[],[f1615]) ).

fof(f1615,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
    inference(rectify,[],[f390]) ).

fof(f390,axiom,
    ! [X11,X34] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X34,c_Nat_OSuc(X11))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq__le) ).

fof(f8902,plain,
    spl38_503,
    inference(avatar_split_clause,[],[f5460,f8900]) ).

fof(f8900,plain,
    ( spl38_503
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_503])]) ).

fof(f5460,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
    inference(definition_unfolding,[],[f4442,f4035]) ).

fof(f4442,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1))
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
    inference(cnf_transformation,[],[f3541]) ).

fof(f3541,plain,
    ! [X0,X1] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1)) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
    inference(nnf_transformation,[],[f1604]) ).

fof(f1604,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1)) ),
    inference(rectify,[],[f351]) ).

fof(f351,axiom,
    ! [X11,X34] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X34,X11)
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X11,c_Nat_OSuc(X34)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__eq) ).

fof(f8898,plain,
    spl38_502,
    inference(avatar_split_clause,[],[f5459,f8896]) ).

fof(f8896,plain,
    ( spl38_502
  <=> ! [X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_502])]) ).

fof(f5459,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(definition_unfolding,[],[f4443,f4035]) ).

fof(f4443,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1)) ),
    inference(cnf_transformation,[],[f3541]) ).

fof(f8894,plain,
    spl38_501,
    inference(avatar_split_clause,[],[f5458,f8892]) ).

fof(f8892,plain,
    ( spl38_501
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_501])]) ).

fof(f5458,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
    inference(definition_unfolding,[],[f4440,f4035]) ).

fof(f4440,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X0),X1)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
    inference(cnf_transformation,[],[f3540]) ).

fof(f3540,plain,
    ! [X0,X1] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X0),X1) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X0),X1)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
    inference(nnf_transformation,[],[f1603]) ).

fof(f1603,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X0),X1) ),
    inference(rectify,[],[f359]) ).

fof(f359,axiom,
    ! [X11,X34] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X11)
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X11),X34) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__eq__eq) ).

fof(f8890,plain,
    ( spl38_500
    | ~ spl38_363
    | ~ spl38_421 ),
    inference(avatar_split_clause,[],[f8846,f8126,f7695,f8888]) ).

fof(f8888,plain,
    ( spl38_500
  <=> ! [X0] : ~ sP6(v_s____,X0,c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_500])]) ).

fof(f7695,plain,
    ( spl38_363
  <=> ! [X2,X0,X1] :
        ( ~ hBOOL(hAPP(hAPP(X2,X1),X0))
        | ~ sP6(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_363])]) ).

fof(f8126,plain,
    ( spl38_421
  <=> ! [X0] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0),v_s____)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_421])]) ).

fof(f8846,plain,
    ( ! [X0] : ~ sP6(v_s____,X0,c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
    | ~ spl38_363
    | ~ spl38_421 ),
    inference(resolution,[],[f8127,f7696]) ).

fof(f7696,plain,
    ( ! [X2,X0,X1] :
        ( ~ hBOOL(hAPP(hAPP(X2,X1),X0))
        | ~ sP6(X0,X1,X2) )
    | ~ spl38_363 ),
    inference(avatar_component_clause,[],[f7695]) ).

fof(f8127,plain,
    ( ! [X0] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0),v_s____))
    | ~ spl38_421 ),
    inference(avatar_component_clause,[],[f8126]) ).

fof(f8886,plain,
    spl38_499,
    inference(avatar_split_clause,[],[f5457,f8884]) ).

fof(f8884,plain,
    ( spl38_499
  <=> ! [X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_499])]) ).

fof(f5457,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) ),
    inference(definition_unfolding,[],[f4441,f4035]) ).

fof(f4441,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X0),X1) ),
    inference(cnf_transformation,[],[f3540]) ).

fof(f8882,plain,
    spl38_498,
    inference(avatar_split_clause,[],[f5448,f8880]) ).

fof(f8880,plain,
    ( spl38_498
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_498])]) ).

fof(f5448,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) ),
    inference(definition_unfolding,[],[f4387,f4035]) ).

fof(f4387,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X0) ),
    inference(cnf_transformation,[],[f2553]) ).

fof(f2553,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X0) ),
    inference(ennf_transformation,[],[f1563]) ).

fof(f1563,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X0)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
    inference(rectify,[],[f385]) ).

fof(f385,axiom,
    ! [X10,X19] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X19),X10)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__lessD) ).

fof(f8878,plain,
    spl38_497,
    inference(avatar_split_clause,[],[f5441,f8876]) ).

fof(f8876,plain,
    ( spl38_497
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_497])]) ).

fof(f5441,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
    inference(definition_unfolding,[],[f4364,f4035]) ).

fof(f4364,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
    inference(cnf_transformation,[],[f2526]) ).

fof(f2526,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
    inference(ennf_transformation,[],[f1544]) ).

fof(f1544,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X0) ),
    inference(rectify,[],[f387]) ).

fof(f387,axiom,
    ! [X10,X19] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X10)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X19),X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__leI) ).

fof(f8874,plain,
    spl38_496,
    inference(avatar_split_clause,[],[f5437,f8872]) ).

fof(f8872,plain,
    ( spl38_496
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_496])]) ).

fof(f5437,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
    inference(definition_unfolding,[],[f4347,f4035]) ).

fof(f4347,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
    inference(cnf_transformation,[],[f2508]) ).

fof(f2508,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
    inference(ennf_transformation,[],[f1528]) ).

fof(f1528,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) ),
    inference(rectify,[],[f388]) ).

fof(f388,axiom,
    ! [X10,X19] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X10)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,c_Nat_OSuc(X10)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__less__Suc) ).

fof(f8870,plain,
    spl38_495,
    inference(avatar_split_clause,[],[f5321,f8868]) ).

fof(f8868,plain,
    ( spl38_495
  <=> ! [X2,X0,X1] :
        ( sP15(X0,X1,X2)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X1,X2),c_Polynomial_Odegree(X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_495])]) ).

fof(f5321,plain,
    ! [X2,X0,X1] :
      ( sP15(X0,X1,X2)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X1,X2),c_Polynomial_Odegree(X1,X0)) ),
    inference(cnf_transformation,[],[f3822]) ).

fof(f3822,plain,
    ! [X0,X1,X2] :
      ( ( sP15(X0,X1,X2)
        | ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X1,X2),c_Polynomial_Odegree(X1,X0))
          & c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) != X2
          & c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) != X0 ) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X1,X2),c_Polynomial_Odegree(X1,X0))
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X2
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X0
        | ~ sP15(X0,X1,X2) ) ),
    inference(rectify,[],[f3821]) ).

fof(f3821,plain,
    ! [X2,X4,X0] :
      ( ( sP15(X2,X4,X0)
        | ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X4,X0),c_Polynomial_Odegree(X4,X2))
          & c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) != X0
          & c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) != X2 ) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X4,X0),c_Polynomial_Odegree(X4,X2))
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X0
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X2
        | ~ sP15(X2,X4,X0) ) ),
    inference(flattening,[],[f3820]) ).

fof(f3820,plain,
    ! [X2,X4,X0] :
      ( ( sP15(X2,X4,X0)
        | ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X4,X0),c_Polynomial_Odegree(X4,X2))
          & c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) != X0
          & c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) != X2 ) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X4,X0),c_Polynomial_Odegree(X4,X2))
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X0
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X2
        | ~ sP15(X2,X4,X0) ) ),
    inference(nnf_transformation,[],[f3475]) ).

fof(f3475,plain,
    ! [X2,X4,X0] :
      ( sP15(X2,X4,X0)
    <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X4,X0),c_Polynomial_Odegree(X4,X2))
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X0
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X2 ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP15])]) ).

fof(f8866,plain,
    spl38_494,
    inference(avatar_split_clause,[],[f5011,f8864]) ).

fof(f8864,plain,
    ( spl38_494
  <=> ! [X2,X0,X1] :
        ( X0 = X1
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_494])]) ).

fof(f5011,plain,
    ! [X2,X0,X1] :
      ( X0 = X1
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) ),
    inference(cnf_transformation,[],[f3739]) ).

fof(f3739,plain,
    ! [X0,X1,X2] :
      ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)
        | X0 != X1 )
      & ( X0 = X1
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) ) ),
    inference(nnf_transformation,[],[f1977]) ).

fof(f1977,plain,
    ! [X0,X1,X2] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)
    <=> X0 = X1 ),
    inference(rectify,[],[f722]) ).

fof(f722,axiom,
    ! [X11,X34,X35] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X35,X34) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X35,X11)
    <=> X11 = X34 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel) ).

fof(f8862,plain,
    spl38_493,
    inference(avatar_split_clause,[],[f5009,f8860]) ).

fof(f8860,plain,
    ( spl38_493
  <=> ! [X2,X0,X1] :
        ( X0 = X2
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_493])]) ).

fof(f5009,plain,
    ! [X2,X0,X1] :
      ( X0 = X2
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) ),
    inference(cnf_transformation,[],[f3738]) ).

fof(f3738,plain,
    ! [X0,X1,X2] :
      ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)
        | X0 != X2 )
      & ( X0 = X2
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) ) ),
    inference(nnf_transformation,[],[f1976]) ).

fof(f1976,plain,
    ! [X0,X1,X2] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)
    <=> X0 = X2 ),
    inference(rectify,[],[f723]) ).

fof(f723,axiom,
    ! [X11,X35,X34] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X11,X35) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X34,X35)
    <=> X11 = X34 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__right__cancel) ).

fof(f8858,plain,
    spl38_492,
    inference(avatar_split_clause,[],[f4928,f8856]) ).

fof(f8856,plain,
    ( spl38_492
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_492])]) ).

fof(f4928,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    inference(cnf_transformation,[],[f2969]) ).

fof(f2969,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    inference(flattening,[],[f2968]) ).

fof(f2968,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    inference(ennf_transformation,[],[f1921]) ).

fof(f1921,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
       => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0) ) ),
    inference(rectify,[],[f317]) ).

fof(f317,axiom,
    ! [X30,X37,X38] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X38,X37)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X37,X30)
       => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X38,X30) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__trans) ).

fof(f8854,plain,
    spl38_491,
    inference(avatar_split_clause,[],[f4915,f8852]) ).

fof(f8852,plain,
    ( spl38_491
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X0)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_491])]) ).

fof(f4915,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1) ),
    inference(cnf_transformation,[],[f2955]) ).

fof(f2955,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1) ),
    inference(flattening,[],[f2954]) ).

fof(f2954,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1) ),
    inference(ennf_transformation,[],[f1908]) ).

fof(f1908,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
       => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X0) ) ),
    inference(rectify,[],[f735]) ).

fof(f735,axiom,
    ! [X30,X37,X38] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X38,X37)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X37,X30)
       => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X38,X30) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__trans) ).

fof(f8850,plain,
    spl38_490,
    inference(avatar_split_clause,[],[f4849,f8848]) ).

fof(f8848,plain,
    ( spl38_490
  <=> ! [X2,X0,X1] :
        ( c_Polynomial_Odegree(X2,X1) = c_Polynomial_Odegree(X2,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,X1,X0))
        | ~ class_Rings_Ocomm__semiring__0(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_490])]) ).

fof(f4849,plain,
    ! [X2,X0,X1] :
      ( c_Polynomial_Odegree(X2,X1) = c_Polynomial_Odegree(X2,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,X1,X0))
      | ~ class_Rings_Ocomm__semiring__0(X2) ),
    inference(cnf_transformation,[],[f2883]) ).

fof(f2883,plain,
    ! [X0,X1,X2] :
      ( c_Polynomial_Odegree(X2,X1) = c_Polynomial_Odegree(X2,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,X1,X0))
      | ~ class_Rings_Ocomm__semiring__0(X2) ),
    inference(ennf_transformation,[],[f1858]) ).

fof(f1858,plain,
    ! [X0,X1,X2] :
      ( class_Rings_Ocomm__semiring__0(X2)
     => c_Polynomial_Odegree(X2,X1) = c_Polynomial_Odegree(X2,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,X1,X0)) ),
    inference(rectify,[],[f43]) ).

fof(f43,axiom,
    ! [X5,X14,X4] :
      ( class_Rings_Ocomm__semiring__0(X4)
     => c_Polynomial_Odegree(X4,X14) = c_Polynomial_Odegree(X4,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X4,X14,X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__offset__poly) ).

fof(f8845,plain,
    spl38_489,
    inference(avatar_split_clause,[],[f4842,f8843]) ).

fof(f8843,plain,
    ( spl38_489
  <=> ! [X2,X0,X1] :
        ( X0 = X1
        | c_Polynomial_Ocoeff(X2,X0) != c_Polynomial_Ocoeff(X2,X1)
        | ~ class_Groups_Ozero(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_489])]) ).

fof(f4842,plain,
    ! [X2,X0,X1] :
      ( X0 = X1
      | c_Polynomial_Ocoeff(X2,X0) != c_Polynomial_Ocoeff(X2,X1)
      | ~ class_Groups_Ozero(X2) ),
    inference(cnf_transformation,[],[f3697]) ).

fof(f3697,plain,
    ! [X0,X1,X2] :
      ( ( ( c_Polynomial_Ocoeff(X2,X0) = c_Polynomial_Ocoeff(X2,X1)
          | X0 != X1 )
        & ( X0 = X1
          | c_Polynomial_Ocoeff(X2,X0) != c_Polynomial_Ocoeff(X2,X1) ) )
      | ~ class_Groups_Ozero(X2) ),
    inference(nnf_transformation,[],[f2880]) ).

fof(f2880,plain,
    ! [X0,X1,X2] :
      ( ( c_Polynomial_Ocoeff(X2,X0) = c_Polynomial_Ocoeff(X2,X1)
      <=> X0 = X1 )
      | ~ class_Groups_Ozero(X2) ),
    inference(ennf_transformation,[],[f1855]) ).

fof(f1855,plain,
    ! [X0,X1,X2] :
      ( class_Groups_Ozero(X2)
     => ( c_Polynomial_Ocoeff(X2,X0) = c_Polynomial_Ocoeff(X2,X1)
      <=> X0 = X1 ) ),
    inference(rectify,[],[f21]) ).

fof(f21,axiom,
    ! [X17,X3,X4] :
      ( class_Groups_Ozero(X4)
     => ( c_Polynomial_Ocoeff(X4,X3) = c_Polynomial_Ocoeff(X4,X17)
      <=> X3 = X17 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__inject) ).

fof(f8841,plain,
    spl38_488,
    inference(avatar_split_clause,[],[f4815,f8839]) ).

fof(f8839,plain,
    ( spl38_488
  <=> ! [X2,X0,X1] :
        ( c_Groups_Ozero__class_Ozero(X2) = X0
        | c_Groups_Oplus__class_Oplus(X2,X1,X0) != X1
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_488])]) ).

fof(f4815,plain,
    ! [X2,X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X2) = X0
      | c_Groups_Oplus__class_Oplus(X2,X1,X0) != X1
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ),
    inference(cnf_transformation,[],[f3688]) ).

fof(f3688,plain,
    ! [X0,X1,X2] :
      ( ( ( c_Groups_Oplus__class_Oplus(X2,X1,X0) = X1
          | c_Groups_Ozero__class_Ozero(X2) != X0 )
        & ( c_Groups_Ozero__class_Ozero(X2) = X0
          | c_Groups_Oplus__class_Oplus(X2,X1,X0) != X1 ) )
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ),
    inference(nnf_transformation,[],[f2848]) ).

fof(f2848,plain,
    ! [X0,X1,X2] :
      ( ( c_Groups_Oplus__class_Oplus(X2,X1,X0) = X1
      <=> c_Groups_Ozero__class_Ozero(X2) = X0 )
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ),
    inference(ennf_transformation,[],[f1833]) ).

fof(f1833,plain,
    ! [X0,X1,X2] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2)
     => ( c_Groups_Oplus__class_Oplus(X2,X1,X0) = X1
      <=> c_Groups_Ozero__class_Ozero(X2) = X0 ) ),
    inference(rectify,[],[f461]) ).

fof(f461,axiom,
    ! [X12,X20,X4] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4)
     => ( c_Groups_Oplus__class_Oplus(X4,X20,X12) = X20
      <=> c_Groups_Ozero__class_Ozero(X4) = X12 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__iff) ).

fof(f8837,plain,
    spl38_487,
    inference(avatar_split_clause,[],[f4766,f8835]) ).

fof(f8835,plain,
    ( spl38_487
  <=> ! [X2,X0,X1] :
        ( X0 = X1
        | c_Groups_Ouminus__class_Ouminus(X2,X0) != c_Groups_Ouminus__class_Ouminus(X2,X1)
        | ~ class_Groups_Ogroup__add(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_487])]) ).

fof(f4766,plain,
    ! [X2,X0,X1] :
      ( X0 = X1
      | c_Groups_Ouminus__class_Ouminus(X2,X0) != c_Groups_Ouminus__class_Ouminus(X2,X1)
      | ~ class_Groups_Ogroup__add(X2) ),
    inference(cnf_transformation,[],[f3676]) ).

fof(f3676,plain,
    ! [X0,X1,X2] :
      ( ( ( c_Groups_Ouminus__class_Ouminus(X2,X0) = c_Groups_Ouminus__class_Ouminus(X2,X1)
          | X0 != X1 )
        & ( X0 = X1
          | c_Groups_Ouminus__class_Ouminus(X2,X0) != c_Groups_Ouminus__class_Ouminus(X2,X1) ) )
      | ~ class_Groups_Ogroup__add(X2) ),
    inference(nnf_transformation,[],[f2793]) ).

fof(f2793,plain,
    ! [X0,X1,X2] :
      ( ( c_Groups_Ouminus__class_Ouminus(X2,X0) = c_Groups_Ouminus__class_Ouminus(X2,X1)
      <=> X0 = X1 )
      | ~ class_Groups_Ogroup__add(X2) ),
    inference(ennf_transformation,[],[f1798]) ).

fof(f1798,plain,
    ! [X0,X1,X2] :
      ( class_Groups_Ogroup__add(X2)
     => ( c_Groups_Ouminus__class_Ouminus(X2,X0) = c_Groups_Ouminus__class_Ouminus(X2,X1)
      <=> X0 = X1 ) ),
    inference(rectify,[],[f136]) ).

fof(f136,axiom,
    ! [X20,X12,X4] :
      ( class_Groups_Ogroup__add(X4)
     => ( c_Groups_Ouminus__class_Ouminus(X4,X12) = c_Groups_Ouminus__class_Ouminus(X4,X20)
      <=> X12 = X20 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__equal__iff__equal) ).

fof(f8833,plain,
    spl38_486,
    inference(avatar_split_clause,[],[f4762,f8831]) ).

fof(f8831,plain,
    ( spl38_486
  <=> ! [X2,X0,X1] :
        ( X0 = X1
        | c_Groups_Ozero__class_Ozero(X2) != c_Groups_Ominus__class_Ominus(X2,X1,X0)
        | ~ class_Groups_Ogroup__add(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_486])]) ).

fof(f4762,plain,
    ! [X2,X0,X1] :
      ( X0 = X1
      | c_Groups_Ozero__class_Ozero(X2) != c_Groups_Ominus__class_Ominus(X2,X1,X0)
      | ~ class_Groups_Ogroup__add(X2) ),
    inference(cnf_transformation,[],[f3674]) ).

fof(f3674,plain,
    ! [X0,X1,X2] :
      ( ( ( c_Groups_Ozero__class_Ozero(X2) = c_Groups_Ominus__class_Ominus(X2,X1,X0)
          | X0 != X1 )
        & ( X0 = X1
          | c_Groups_Ozero__class_Ozero(X2) != c_Groups_Ominus__class_Ominus(X2,X1,X0) ) )
      | ~ class_Groups_Ogroup__add(X2) ),
    inference(nnf_transformation,[],[f2791]) ).

fof(f2791,plain,
    ! [X0,X1,X2] :
      ( ( c_Groups_Ozero__class_Ozero(X2) = c_Groups_Ominus__class_Ominus(X2,X1,X0)
      <=> X0 = X1 )
      | ~ class_Groups_Ogroup__add(X2) ),
    inference(ennf_transformation,[],[f1796]) ).

fof(f1796,plain,
    ! [X0,X1,X2] :
      ( class_Groups_Ogroup__add(X2)
     => ( c_Groups_Ozero__class_Ozero(X2) = c_Groups_Ominus__class_Ominus(X2,X1,X0)
      <=> X0 = X1 ) ),
    inference(rectify,[],[f972]) ).

fof(f972,axiom,
    ! [X20,X12,X4] :
      ( class_Groups_Ogroup__add(X4)
     => ( c_Groups_Ozero__class_Ozero(X4) = c_Groups_Ominus__class_Ominus(X4,X12,X20)
      <=> X12 = X20 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__minus__eq) ).

fof(f8829,plain,
    spl38_485,
    inference(avatar_split_clause,[],[f4751,f8827]) ).

fof(f8827,plain,
    ( spl38_485
  <=> ! [X2,X0,X1] :
        ( X0 = X1
        | c_Groups_Ozero__class_Ozero(X2) != c_Groups_Ominus__class_Ominus(X2,X1,X0)
        | ~ class_Groups_Oab__group__add(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_485])]) ).

fof(f4751,plain,
    ! [X2,X0,X1] :
      ( X0 = X1
      | c_Groups_Ozero__class_Ozero(X2) != c_Groups_Ominus__class_Ominus(X2,X1,X0)
      | ~ class_Groups_Oab__group__add(X2) ),
    inference(cnf_transformation,[],[f3670]) ).

fof(f3670,plain,
    ! [X0,X1,X2] :
      ( ( ( X0 = X1
          | c_Groups_Ozero__class_Ozero(X2) != c_Groups_Ominus__class_Ominus(X2,X1,X0) )
        & ( c_Groups_Ozero__class_Ozero(X2) = c_Groups_Ominus__class_Ominus(X2,X1,X0)
          | X0 != X1 ) )
      | ~ class_Groups_Oab__group__add(X2) ),
    inference(nnf_transformation,[],[f2782]) ).

fof(f2782,plain,
    ! [X0,X1,X2] :
      ( ( X0 = X1
      <=> c_Groups_Ozero__class_Ozero(X2) = c_Groups_Ominus__class_Ominus(X2,X1,X0) )
      | ~ class_Groups_Oab__group__add(X2) ),
    inference(ennf_transformation,[],[f1788]) ).

fof(f1788,plain,
    ! [X0,X1,X2] :
      ( class_Groups_Oab__group__add(X2)
     => ( X0 = X1
      <=> c_Groups_Ozero__class_Ozero(X2) = c_Groups_Ominus__class_Ominus(X2,X1,X0) ) ),
    inference(rectify,[],[f971]) ).

fof(f971,axiom,
    ! [X20,X12,X4] :
      ( class_Groups_Oab__group__add(X4)
     => ( X12 = X20
      <=> c_Groups_Ozero__class_Ozero(X4) = c_Groups_Ominus__class_Ominus(X4,X12,X20) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__iff__diff__eq__0) ).

fof(f8825,plain,
    spl38_484,
    inference(avatar_split_clause,[],[f4618,f8823]) ).

fof(f8823,plain,
    ( spl38_484
  <=> ! [X2,X0,X1] :
        ( X0 = X1
        | c_Groups_Ouminus__class_Ouminus(X2,X0) != c_Groups_Ouminus__class_Ouminus(X2,X1)
        | ~ class_Lattices_Oboolean__algebra(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_484])]) ).

fof(f4618,plain,
    ! [X2,X0,X1] :
      ( X0 = X1
      | c_Groups_Ouminus__class_Ouminus(X2,X0) != c_Groups_Ouminus__class_Ouminus(X2,X1)
      | ~ class_Lattices_Oboolean__algebra(X2) ),
    inference(cnf_transformation,[],[f3627]) ).

fof(f3627,plain,
    ! [X0,X1,X2] :
      ( ( ( c_Groups_Ouminus__class_Ouminus(X2,X0) = c_Groups_Ouminus__class_Ouminus(X2,X1)
          | X0 != X1 )
        & ( X0 = X1
          | c_Groups_Ouminus__class_Ouminus(X2,X0) != c_Groups_Ouminus__class_Ouminus(X2,X1) ) )
      | ~ class_Lattices_Oboolean__algebra(X2) ),
    inference(nnf_transformation,[],[f2660]) ).

fof(f2660,plain,
    ! [X0,X1,X2] :
      ( ( c_Groups_Ouminus__class_Ouminus(X2,X0) = c_Groups_Ouminus__class_Ouminus(X2,X1)
      <=> X0 = X1 )
      | ~ class_Lattices_Oboolean__algebra(X2) ),
    inference(ennf_transformation,[],[f1708]) ).

fof(f1708,plain,
    ! [X0,X1,X2] :
      ( class_Lattices_Oboolean__algebra(X2)
     => ( c_Groups_Ouminus__class_Ouminus(X2,X0) = c_Groups_Ouminus__class_Ouminus(X2,X1)
      <=> X0 = X1 ) ),
    inference(rectify,[],[f782]) ).

fof(f782,axiom,
    ! [X17,X3,X4] :
      ( class_Lattices_Oboolean__algebra(X4)
     => ( c_Groups_Ouminus__class_Ouminus(X4,X17) = c_Groups_Ouminus__class_Ouminus(X4,X3)
      <=> X3 = X17 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__eq__compl__iff) ).

fof(f8821,plain,
    spl38_483,
    inference(avatar_split_clause,[],[f4584,f8819]) ).

fof(f8819,plain,
    ( spl38_483
  <=> ! [X2,X0,X1] :
        ( X0 = X1
        | c_Rings_Oinverse__class_Oinverse(X2,X0) != c_Rings_Oinverse__class_Oinverse(X2,X1)
        | ~ class_Rings_Odivision__ring__inverse__zero(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_483])]) ).

fof(f4584,plain,
    ! [X2,X0,X1] :
      ( X0 = X1
      | c_Rings_Oinverse__class_Oinverse(X2,X0) != c_Rings_Oinverse__class_Oinverse(X2,X1)
      | ~ class_Rings_Odivision__ring__inverse__zero(X2) ),
    inference(cnf_transformation,[],[f2621]) ).

fof(f2621,plain,
    ! [X0,X1,X2] :
      ( X0 = X1
      | c_Rings_Oinverse__class_Oinverse(X2,X0) != c_Rings_Oinverse__class_Oinverse(X2,X1)
      | ~ class_Rings_Odivision__ring__inverse__zero(X2) ),
    inference(flattening,[],[f2620]) ).

fof(f2620,plain,
    ! [X0,X1,X2] :
      ( X0 = X1
      | c_Rings_Oinverse__class_Oinverse(X2,X0) != c_Rings_Oinverse__class_Oinverse(X2,X1)
      | ~ class_Rings_Odivision__ring__inverse__zero(X2) ),
    inference(ennf_transformation,[],[f1680]) ).

fof(f1680,plain,
    ! [X0,X1,X2] :
      ( class_Rings_Odivision__ring__inverse__zero(X2)
     => ( c_Rings_Oinverse__class_Oinverse(X2,X0) = c_Rings_Oinverse__class_Oinverse(X2,X1)
       => X0 = X1 ) ),
    inference(rectify,[],[f817]) ).

fof(f817,axiom,
    ! [X27,X18,X4] :
      ( class_Rings_Odivision__ring__inverse__zero(X4)
     => ( c_Rings_Oinverse__class_Oinverse(X4,X18) = c_Rings_Oinverse__class_Oinverse(X4,X27)
       => X18 = X27 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__eq__imp__eq) ).

fof(f8817,plain,
    spl38_482,
    inference(avatar_split_clause,[],[f4522,f8815]) ).

fof(f8815,plain,
    ( spl38_482
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_482])]) ).

fof(f4522,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
    inference(cnf_transformation,[],[f3600]) ).

fof(f3600,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) ) ),
    inference(nnf_transformation,[],[f1632]) ).

fof(f1632,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
    inference(rectify,[],[f955]) ).

fof(f955,axiom,
    ! [X34,X11] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X11,X34))
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X34,X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__diff) ).

fof(f8813,plain,
    spl38_481,
    inference(avatar_split_clause,[],[f4521,f8811]) ).

fof(f8811,plain,
    ( spl38_481
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_481])]) ).

fof(f4521,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) ),
    inference(cnf_transformation,[],[f3600]) ).

fof(f8809,plain,
    spl38_480,
    inference(avatar_split_clause,[],[f4519,f8807]) ).

fof(f8807,plain,
    ( spl38_480
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_480])]) ).

fof(f4519,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
    inference(cnf_transformation,[],[f3599]) ).

fof(f3599,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | ( X0 != X1
          & ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ) )
      & ( X0 = X1
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(flattening,[],[f3598]) ).

fof(f3598,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | ( X0 != X1
          & ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ) )
      & ( X0 = X1
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(nnf_transformation,[],[f1631]) ).

fof(f1631,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
    <=> ( X0 = X1
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ) ),
    inference(rectify,[],[f709]) ).

fof(f709,axiom,
    ! [X8,X55] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X55,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X8,c_Groups_Oone__class_Oone(tc_Int_Oint)))
    <=> ( X8 = X55
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X55,X8) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__add1__eq) ).

fof(f8805,plain,
    spl38_479,
    inference(avatar_split_clause,[],[f4517,f8803]) ).

fof(f8803,plain,
    ( spl38_479
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_479])]) ).

fof(f4517,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ),
    inference(cnf_transformation,[],[f3597]) ).

fof(f3597,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(nnf_transformation,[],[f1630]) ).

fof(f1630,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ),
    inference(rectify,[],[f708]) ).

fof(f708,axiom,
    ! [X8,X55] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X55,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X8,c_Groups_Oone__class_Oone(tc_Int_Oint)))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X55,X8) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__add1__eq__le) ).

fof(f8801,plain,
    spl38_478,
    inference(avatar_split_clause,[],[f4516,f8799]) ).

fof(f8799,plain,
    ( spl38_478
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_478])]) ).

fof(f4516,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(cnf_transformation,[],[f3597]) ).

fof(f8797,plain,
    spl38_477,
    inference(avatar_split_clause,[],[f4514,f8795]) ).

fof(f8795,plain,
    ( spl38_477
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_477])]) ).

fof(f4514,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X0) ),
    inference(cnf_transformation,[],[f3596]) ).

fof(f3596,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X0) ) ),
    inference(nnf_transformation,[],[f1629]) ).

fof(f1629,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X0)
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
    inference(rectify,[],[f711]) ).

fof(f711,axiom,
    ! [X8,X55] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X55,c_Groups_Oone__class_Oone(tc_Int_Oint)),X8)
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X55,X8) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add1__zle__eq) ).

fof(f8793,plain,
    spl38_476,
    inference(avatar_split_clause,[],[f4449,f8791]) ).

fof(f8791,plain,
    ( spl38_476
  <=> ! [X0,X1] :
        ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK25(X0,X1)) = X0
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_476])]) ).

fof(f4449,plain,
    ! [X0,X1] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK25(X0,X1)) = X0
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
    inference(cnf_transformation,[],[f3551]) ).

fof(f3551,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
        | ! [X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != X0 )
      & ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK25(X0,X1)) = X0
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK25])],[f3549,f3550]) ).

fof(f3550,plain,
    ! [X0,X1] :
      ( ? [X3] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3) = X0
     => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK25(X0,X1)) = X0 ),
    introduced(choice_axiom,[]) ).

fof(f3549,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
        | ! [X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != X0 )
      & ( ? [X3] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3) = X0
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
    inference(rectify,[],[f3548]) ).

fof(f3548,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
        | ! [X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != X0 )
      & ( ? [X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = X0
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
    inference(nnf_transformation,[],[f1607]) ).

fof(f1607,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
    <=> ? [X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = X0 ),
    inference(rectify,[],[f655]) ).

fof(f655,axiom,
    ! [X11,X34] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X11)
    <=> ? [X65] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X34,X65) = X11 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__iff__add) ).

fof(f8789,plain,
    spl38_475,
    inference(avatar_split_clause,[],[f4447,f8787]) ).

fof(f8787,plain,
    ( spl38_475
  <=> ! [X0,X1] :
        ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK24(X0,X1)) = X0
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_475])]) ).

fof(f4447,plain,
    ! [X0,X1] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK24(X0,X1)) = X0
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
    inference(cnf_transformation,[],[f3547]) ).

fof(f3547,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
        | ! [X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != X0 )
      & ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK24(X0,X1)) = X0
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK24])],[f3545,f3546]) ).

fof(f3546,plain,
    ! [X0,X1] :
      ( ? [X3] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3) = X0
     => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK24(X0,X1)) = X0 ),
    introduced(choice_axiom,[]) ).

fof(f3545,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
        | ! [X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != X0 )
      & ( ? [X3] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3) = X0
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
    inference(rectify,[],[f3544]) ).

fof(f3544,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
        | ! [X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != X0 )
      & ( ? [X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = X0
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
    inference(nnf_transformation,[],[f1606]) ).

fof(f1606,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
    <=> ? [X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = X0 ),
    inference(rectify,[],[f775]) ).

fof(f775,axiom,
    ! [X62,X35] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X35,X62)
    <=> ? [X16] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X35,X16) = X62 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__Suc__ex__iff) ).

fof(f8785,plain,
    spl38_474,
    inference(avatar_split_clause,[],[f4389,f8783]) ).

fof(f8783,plain,
    ( spl38_474
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,X1),X1)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_474])]) ).

fof(f4389,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,X1),X1)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(cnf_transformation,[],[f2556]) ).

fof(f2556,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,X1),X1)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(ennf_transformation,[],[f1565]) ).

fof(f1565,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,X1),X1) ),
    inference(rectify,[],[f912]) ).

fof(f912,axiom,
    ! [X19,X10] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X10)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X10),X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__less__divisor) ).

fof(f8781,plain,
    spl38_473,
    inference(avatar_split_clause,[],[f4380,f8779]) ).

fof(f8779,plain,
    ( spl38_473
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X1),X1)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_473])]) ).

fof(f4380,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X1),X1)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(cnf_transformation,[],[f2546]) ).

fof(f2546,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X1),X1)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(ennf_transformation,[],[f1558]) ).

fof(f1558,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
     => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X1),X1) ),
    inference(rectify,[],[f914]) ).

fof(f914,axiom,
    ! [X18,X27] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X27)
     => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X18,X27),X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__mod__bound) ).

fof(f8777,plain,
    spl38_472,
    inference(avatar_split_clause,[],[f4379,f8775]) ).

fof(f8775,plain,
    ( spl38_472
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X1))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_472])]) ).

fof(f4379,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X1))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(cnf_transformation,[],[f2545]) ).

fof(f2545,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X1))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(ennf_transformation,[],[f1557]) ).

fof(f1557,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
     => c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X1)) ),
    inference(rectify,[],[f915]) ).

fof(f915,axiom,
    ! [X18,X27] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X27,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
     => c_Orderings_Oord__class_Oless(tc_Int_Oint,X27,c_Divides_Odiv__class_Omod(tc_Int_Oint,X18,X27)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__mod__bound) ).

fof(f8773,plain,
    spl38_471,
    inference(avatar_split_clause,[],[f4373,f8771]) ).

fof(f8771,plain,
    ( spl38_471
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0),X1)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_471])]) ).

fof(f4373,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0),X1)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(cnf_transformation,[],[f2535]) ).

fof(f2535,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0),X1)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(ennf_transformation,[],[f1551]) ).

fof(f1551,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
     => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0),X1) ),
    inference(rectify,[],[f929]) ).

fof(f929,axiom,
    ! [X30,X19] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X19)
     => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X19,X30),X19) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__le__nonneg__dividend) ).

fof(f8769,plain,
    spl38_470,
    inference(avatar_split_clause,[],[f4358,f8767]) ).

fof(f8767,plain,
    ( spl38_470
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_470])]) ).

fof(f4358,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
    inference(cnf_transformation,[],[f2520]) ).

fof(f2520,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
    inference(ennf_transformation,[],[f1538]) ).

fof(f1538,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
     => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X0) ),
    inference(rectify,[],[f713]) ).

fof(f713,axiom,
    ! [X33,X74] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X74,X33)
     => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X74,c_Groups_Oone__class_Oone(tc_Int_Oint)),X33) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__imp__add1__zle) ).

fof(f8763,plain,
    spl38_469,
    inference(avatar_split_clause,[],[f4323,f8761]) ).

fof(f8761,plain,
    ( spl38_469
  <=> ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X0)
        | ~ class_Rings_Ocomm__semiring__1(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_469])]) ).

fof(f4323,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X0)
      | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(cnf_transformation,[],[f2482]) ).

fof(f2482,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X0)
      | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(ennf_transformation,[],[f1507]) ).

fof(f1507,plain,
    ! [X0,X1] :
      ( class_Rings_Ocomm__semiring__1(X1)
     => c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X0) ),
    inference(rectify,[],[f440]) ).

fof(f440,axiom,
    ! [X18,X4] :
      ( class_Rings_Ocomm__semiring__1(X4)
     => c_Groups_Ozero__class_Ozero(X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Groups_Ozero__class_Ozero(X4)),X18) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).

fof(f8759,plain,
    spl38_468,
    inference(avatar_split_clause,[],[f4322,f8757]) ).

fof(f4322,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Ozero__class_Ozero(X1))
      | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(cnf_transformation,[],[f2481]) ).

fof(f2481,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Ozero__class_Ozero(X1))
      | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(ennf_transformation,[],[f1506]) ).

fof(f1506,plain,
    ! [X0,X1] :
      ( class_Rings_Ocomm__semiring__1(X1)
     => c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(rectify,[],[f439]) ).

fof(f439,axiom,
    ! [X18,X4] :
      ( class_Rings_Ocomm__semiring__1(X4)
     => c_Groups_Ozero__class_Ozero(X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X18),c_Groups_Ozero__class_Ozero(X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).

fof(f8755,plain,
    spl38_467,
    inference(avatar_split_clause,[],[f4321,f8753]) ).

fof(f8753,plain,
    ( spl38_467
  <=> ! [X0,X1] :
        ( c_Groups_Oone__class_Oone(X1) = hAPP(c_Polynomial_Opoly(X1,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1))),X0)
        | ~ class_Rings_Ocomm__semiring__1(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_467])]) ).

fof(f4321,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(X1) = hAPP(c_Polynomial_Opoly(X1,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1))),X0)
      | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(cnf_transformation,[],[f2480]) ).

fof(f2480,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(X1) = hAPP(c_Polynomial_Opoly(X1,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1))),X0)
      | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(ennf_transformation,[],[f1505]) ).

fof(f1505,plain,
    ! [X0,X1] :
      ( class_Rings_Ocomm__semiring__1(X1)
     => c_Groups_Oone__class_Oone(X1) = hAPP(c_Polynomial_Opoly(X1,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1))),X0) ),
    inference(rectify,[],[f173]) ).

fof(f173,axiom,
    ! [X13,X4] :
      ( class_Rings_Ocomm__semiring__1(X4)
     => c_Groups_Oone__class_Oone(X4) = hAPP(c_Polynomial_Opoly(X4,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X4))),X13) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__1) ).

fof(f8751,plain,
    spl38_466,
    inference(avatar_split_clause,[],[f4320,f8749]) ).

fof(f8749,plain,
    ( spl38_466
  <=> ! [X0,X1] :
        ( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ class_Rings_Ocomm__semiring__1(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_466])]) ).

fof(f4320,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(cnf_transformation,[],[f2479]) ).

fof(f2479,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(ennf_transformation,[],[f1504]) ).

fof(f1504,plain,
    ! [X0,X1] :
      ( class_Rings_Ocomm__semiring__1(X1)
     => c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(rectify,[],[f418]) ).

fof(f418,axiom,
    ! [X13,X4] :
      ( class_Rings_Ocomm__semiring__1(X4)
     => c_Groups_Oone__class_Oone(X4) = hAPP(hAPP(c_Power_Opower__class_Opower(X4),X13),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).

fof(f8747,plain,
    spl38_465,
    inference(avatar_split_clause,[],[f4308,f8745]) ).

fof(f4308,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Osmult(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
      | ~ class_Rings_Ocomm__semiring__0(X1) ),
    inference(cnf_transformation,[],[f2467]) ).

fof(f2467,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Osmult(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
      | ~ class_Rings_Ocomm__semiring__0(X1) ),
    inference(ennf_transformation,[],[f1492]) ).

fof(f1492,plain,
    ! [X0,X1] :
      ( class_Rings_Ocomm__semiring__0(X1)
     => c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Osmult(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) ),
    inference(rectify,[],[f24]) ).

fof(f24,axiom,
    ! [X18,X4] :
      ( class_Rings_Ocomm__semiring__0(X4)
     => c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = c_Polynomial_Osmult(X4,X18,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__0__right) ).

fof(f8743,plain,
    spl38_464,
    inference(avatar_split_clause,[],[f4307,f8741]) ).

fof(f4307,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Osynthetic__div(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0)
      | ~ class_Rings_Ocomm__semiring__0(X1) ),
    inference(cnf_transformation,[],[f2466]) ).

fof(f2466,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Osynthetic__div(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0)
      | ~ class_Rings_Ocomm__semiring__0(X1) ),
    inference(ennf_transformation,[],[f1491]) ).

fof(f1491,plain,
    ! [X0,X1] :
      ( class_Rings_Ocomm__semiring__0(X1)
     => c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Osynthetic__div(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0) ),
    inference(rectify,[],[f207]) ).

fof(f207,axiom,
    ! [X22,X4] :
      ( class_Rings_Ocomm__semiring__0(X4)
     => c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = c_Polynomial_Osynthetic__div(X4,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X22) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_synthetic__div__0) ).

fof(f8739,plain,
    spl38_463,
    inference(avatar_split_clause,[],[f4306,f8737]) ).

fof(f4306,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0)
      | ~ class_Rings_Ocomm__semiring__0(X1) ),
    inference(cnf_transformation,[],[f2465]) ).

fof(f2465,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0)
      | ~ class_Rings_Ocomm__semiring__0(X1) ),
    inference(ennf_transformation,[],[f1490]) ).

fof(f1490,plain,
    ! [X0,X1] :
      ( class_Rings_Ocomm__semiring__0(X1)
     => c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0) ),
    inference(rectify,[],[f5]) ).

fof(f5,axiom,
    ! [X5,X4] :
      ( class_Rings_Ocomm__semiring__0(X4)
     => c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X4,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_offset__poly__0) ).

fof(f8735,plain,
    spl38_462,
    inference(avatar_split_clause,[],[f4305,f8733]) ).

fof(f4305,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Opcompose(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0)
      | ~ class_Rings_Ocomm__semiring__0(X1) ),
    inference(cnf_transformation,[],[f2464]) ).

fof(f2464,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Opcompose(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0)
      | ~ class_Rings_Ocomm__semiring__0(X1) ),
    inference(ennf_transformation,[],[f1489]) ).

fof(f1489,plain,
    ! [X0,X1] :
      ( class_Rings_Ocomm__semiring__0(X1)
     => c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Opcompose(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0) ),
    inference(rectify,[],[f55]) ).

fof(f55,axiom,
    ! [X21,X4] :
      ( class_Rings_Ocomm__semiring__0(X4)
     => c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = c_Polynomial_Opcompose(X4,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X21) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pcompose__0) ).

fof(f8731,plain,
    spl38_461,
    inference(avatar_split_clause,[],[f4304,f8729]) ).

fof(f4304,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X0)
      | ~ class_Rings_Ocomm__semiring__0(X1) ),
    inference(cnf_transformation,[],[f2463]) ).

fof(f2463,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X0)
      | ~ class_Rings_Ocomm__semiring__0(X1) ),
    inference(ennf_transformation,[],[f1488]) ).

fof(f1488,plain,
    ! [X0,X1] :
      ( class_Rings_Ocomm__semiring__0(X1)
     => c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X0) ),
    inference(rectify,[],[f11]) ).

fof(f11,axiom,
    ! [X13,X4] :
      ( class_Rings_Ocomm__semiring__0(X4)
     => c_Groups_Ozero__class_Ozero(X4) = hAPP(c_Polynomial_Opoly(X4,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))),X13) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__0) ).

fof(f8727,plain,
    spl38_460,
    inference(avatar_split_clause,[],[f4291,f8725]) ).

fof(f4291,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Polynomial_Ocoeff(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X0)
      | ~ class_Groups_Ozero(X1) ),
    inference(cnf_transformation,[],[f2453]) ).

fof(f2453,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Polynomial_Ocoeff(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X0)
      | ~ class_Groups_Ozero(X1) ),
    inference(ennf_transformation,[],[f1479]) ).

fof(f1479,plain,
    ! [X0,X1] :
      ( class_Groups_Ozero(X1)
     => c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Polynomial_Ocoeff(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X0) ),
    inference(rectify,[],[f12]) ).

fof(f12,axiom,
    ! [X10,X4] :
      ( class_Groups_Ozero(X4)
     => c_Groups_Ozero__class_Ozero(X4) = hAPP(c_Polynomial_Ocoeff(X4,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))),X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__0) ).

fof(f8722,plain,
    spl38_459,
    inference(avatar_split_clause,[],[f4284,f8720]) ).

fof(f8720,plain,
    ( spl38_459
  <=> ! [X0,X1] :
        ( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oone__class_Oone(X1)),X0)
        | ~ class_Groups_Omonoid__mult(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_459])]) ).

fof(f4284,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oone__class_Oone(X1)),X0)
      | ~ class_Groups_Omonoid__mult(X1) ),
    inference(cnf_transformation,[],[f2446]) ).

fof(f2446,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oone__class_Oone(X1)),X0)
      | ~ class_Groups_Omonoid__mult(X1) ),
    inference(ennf_transformation,[],[f1472]) ).

fof(f1472,plain,
    ! [X0,X1] :
      ( class_Groups_Omonoid__mult(X1)
     => c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oone__class_Oone(X1)),X0) ),
    inference(rectify,[],[f326]) ).

fof(f326,axiom,
    ! [X10,X4] :
      ( class_Groups_Omonoid__mult(X4)
     => c_Groups_Oone__class_Oone(X4) = hAPP(hAPP(c_Power_Opower__class_Opower(X4),c_Groups_Oone__class_Oone(X4)),X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__one) ).

fof(f8718,plain,
    spl38_458,
    inference(avatar_split_clause,[],[f4280,f8716]) ).

fof(f8716,plain,
    ( spl38_458
  <=> ! [X0,X1] :
        ( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ class_Power_Opower(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_458])]) ).

fof(f4280,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      | ~ class_Power_Opower(X1) ),
    inference(cnf_transformation,[],[f2442]) ).

fof(f2442,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      | ~ class_Power_Opower(X1) ),
    inference(ennf_transformation,[],[f1468]) ).

fof(f1468,plain,
    ! [X0,X1] :
      ( class_Power_Opower(X1)
     => c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(rectify,[],[f377]) ).

fof(f377,axiom,
    ! [X18,X4] :
      ( class_Power_Opower(X4)
     => c_Groups_Oone__class_Oone(X4) = hAPP(hAPP(c_Power_Opower__class_Opower(X4),X18),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__0) ).

fof(f8714,plain,
    spl38_457,
    inference(avatar_split_clause,[],[f4279,f8712]) ).

fof(f8712,plain,
    ( spl38_457
  <=> ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X0)
        | ~ class_Rings_Omult__zero(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_457])]) ).

fof(f4279,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X0)
      | ~ class_Rings_Omult__zero(X1) ),
    inference(cnf_transformation,[],[f2441]) ).

fof(f2441,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X0)
      | ~ class_Rings_Omult__zero(X1) ),
    inference(ennf_transformation,[],[f1467]) ).

fof(f1467,plain,
    ! [X0,X1] :
      ( class_Rings_Omult__zero(X1)
     => c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X0) ),
    inference(rectify,[],[f167]) ).

fof(f167,axiom,
    ! [X18,X4] :
      ( class_Rings_Omult__zero(X4)
     => c_Groups_Ozero__class_Ozero(X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Groups_Ozero__class_Ozero(X4)),X18) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__zero__left) ).

fof(f8710,plain,
    spl38_456,
    inference(avatar_split_clause,[],[f4278,f8708]) ).

fof(f8708,plain,
    ( spl38_456
  <=> ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Ozero__class_Ozero(X1))
        | ~ class_Rings_Omult__zero(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_456])]) ).

fof(f4278,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Ozero__class_Ozero(X1))
      | ~ class_Rings_Omult__zero(X1) ),
    inference(cnf_transformation,[],[f2440]) ).

fof(f2440,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Ozero__class_Ozero(X1))
      | ~ class_Rings_Omult__zero(X1) ),
    inference(ennf_transformation,[],[f1466]) ).

fof(f1466,plain,
    ! [X0,X1] :
      ( class_Rings_Omult__zero(X1)
     => c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(rectify,[],[f166]) ).

fof(f166,axiom,
    ! [X18,X4] :
      ( class_Rings_Omult__zero(X4)
     => c_Groups_Ozero__class_Ozero(X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X18),c_Groups_Ozero__class_Ozero(X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__zero__right) ).

fof(f8706,plain,
    spl38_455,
    inference(avatar_split_clause,[],[f4263,f8704]) ).

fof(f8704,plain,
    ( spl38_455
  <=> ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(X1) = X0
        | c_Groups_Ozero__class_Ozero(X1) != c_Groups_Ouminus__class_Ouminus(X1,X0)
        | ~ class_Groups_Ogroup__add(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_455])]) ).

fof(f4263,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X1) = X0
      | c_Groups_Ozero__class_Ozero(X1) != c_Groups_Ouminus__class_Ouminus(X1,X0)
      | ~ class_Groups_Ogroup__add(X1) ),
    inference(cnf_transformation,[],[f3518]) ).

fof(f3518,plain,
    ! [X0,X1] :
      ( ( ( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ouminus__class_Ouminus(X1,X0)
          | c_Groups_Ozero__class_Ozero(X1) != X0 )
        & ( c_Groups_Ozero__class_Ozero(X1) = X0
          | c_Groups_Ozero__class_Ozero(X1) != c_Groups_Ouminus__class_Ouminus(X1,X0) ) )
      | ~ class_Groups_Ogroup__add(X1) ),
    inference(nnf_transformation,[],[f2428]) ).

fof(f2428,plain,
    ! [X0,X1] :
      ( ( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ouminus__class_Ouminus(X1,X0)
      <=> c_Groups_Ozero__class_Ozero(X1) = X0 )
      | ~ class_Groups_Ogroup__add(X1) ),
    inference(ennf_transformation,[],[f1454]) ).

fof(f1454,plain,
    ! [X0,X1] :
      ( class_Groups_Ogroup__add(X1)
     => ( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ouminus__class_Ouminus(X1,X0)
      <=> c_Groups_Ozero__class_Ozero(X1) = X0 ) ),
    inference(rectify,[],[f188]) ).

fof(f188,axiom,
    ! [X12,X4] :
      ( class_Groups_Ogroup__add(X4)
     => ( c_Groups_Ozero__class_Ozero(X4) = c_Groups_Ouminus__class_Ouminus(X4,X12)
      <=> c_Groups_Ozero__class_Ozero(X4) = X12 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__equal__0__iff__equal) ).

fof(f8702,plain,
    spl38_454,
    inference(avatar_split_clause,[],[f4257,f8700]) ).

fof(f8700,plain,
    ( spl38_454
  <=> ! [X0,X1] :
        ( c_Polynomial_Odegree(X1,X0) = c_Polynomial_Odegree(X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X0))
        | ~ class_Groups_Oab__group__add(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_454])]) ).

fof(f4257,plain,
    ! [X0,X1] :
      ( c_Polynomial_Odegree(X1,X0) = c_Polynomial_Odegree(X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X0))
      | ~ class_Groups_Oab__group__add(X1) ),
    inference(cnf_transformation,[],[f2422]) ).

fof(f2422,plain,
    ! [X0,X1] :
      ( c_Polynomial_Odegree(X1,X0) = c_Polynomial_Odegree(X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X0))
      | ~ class_Groups_Oab__group__add(X1) ),
    inference(ennf_transformation,[],[f1448]) ).

fof(f1448,plain,
    ! [X0,X1] :
      ( class_Groups_Oab__group__add(X1)
     => c_Polynomial_Odegree(X1,X0) = c_Polynomial_Odegree(X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X0)) ),
    inference(rectify,[],[f281]) ).

fof(f281,axiom,
    ! [X14,X4] :
      ( class_Groups_Oab__group__add(X4)
     => c_Polynomial_Odegree(X4,X14) = c_Polynomial_Odegree(X4,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4),X14)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__minus) ).

fof(f8698,plain,
    spl38_453,
    inference(avatar_split_clause,[],[f4212,f8696]) ).

fof(f8696,plain,
    ( spl38_453
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0))
        | ~ class_Rings_Olinordered__ring(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_453])]) ).

fof(f4212,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0))
      | ~ class_Rings_Olinordered__ring(X1) ),
    inference(cnf_transformation,[],[f2396]) ).

fof(f2396,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0))
      | ~ class_Rings_Olinordered__ring(X1) ),
    inference(ennf_transformation,[],[f1423]) ).

fof(f1423,plain,
    ! [X0,X1] :
      ( class_Rings_Olinordered__ring(X1)
     => c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0)) ),
    inference(rectify,[],[f76]) ).

fof(f76,axiom,
    ! [X18,X4] :
      ( class_Rings_Olinordered__ring(X4)
     => c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X18),X18)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__square) ).

fof(f8694,plain,
    spl38_452,
    inference(avatar_split_clause,[],[f4211,f8692]) ).

fof(f8692,plain,
    ( spl38_452
  <=> ! [X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0),c_Groups_Ozero__class_Ozero(X1))
        | ~ class_Rings_Olinordered__ring(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_452])]) ).

fof(f4211,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0),c_Groups_Ozero__class_Ozero(X1))
      | ~ class_Rings_Olinordered__ring(X1) ),
    inference(cnf_transformation,[],[f2395]) ).

fof(f2395,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0),c_Groups_Ozero__class_Ozero(X1))
      | ~ class_Rings_Olinordered__ring(X1) ),
    inference(ennf_transformation,[],[f1422]) ).

fof(f1422,plain,
    ! [X0,X1] :
      ( class_Rings_Olinordered__ring(X1)
     => ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(rectify,[],[f73]) ).

fof(f73,axiom,
    ! [X18,X4] :
      ( class_Rings_Olinordered__ring(X4)
     => ~ c_Orderings_Oord__class_Oless(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X18),X18),c_Groups_Ozero__class_Ozero(X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__square__less__zero) ).

fof(f8690,plain,
    spl38_451,
    inference(avatar_split_clause,[],[f4207,f8688]) ).

fof(f4207,plain,
    ! [X0,X1] :
      ( c_Polynomial_Opdivmod__rel(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0)
      | ~ class_Fields_Ofield(X1) ),
    inference(cnf_transformation,[],[f2390]) ).

fof(f2390,plain,
    ! [X0,X1] :
      ( c_Polynomial_Opdivmod__rel(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0)
      | ~ class_Fields_Ofield(X1) ),
    inference(ennf_transformation,[],[f1418]) ).

fof(f1418,plain,
    ! [X0,X1] :
      ( class_Fields_Ofield(X1)
     => c_Polynomial_Opdivmod__rel(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0) ),
    inference(rectify,[],[f672]) ).

fof(f672,axiom,
    ! [X13,X4] :
      ( class_Fields_Ofield(X4)
     => c_Polynomial_Opdivmod__rel(X4,X13,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X13) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__rel__by__0) ).

fof(f8686,plain,
    spl38_450,
    inference(avatar_split_clause,[],[f4206,f8684]) ).

fof(f8684,plain,
    ( spl38_450
  <=> ! [X0,X1] :
        ( c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1)) = c_Polynomial_Opoly__gcd(X1,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1)),X0)
        | ~ class_Fields_Ofield(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_450])]) ).

fof(f4206,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1)) = c_Polynomial_Opoly__gcd(X1,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1)),X0)
      | ~ class_Fields_Ofield(X1) ),
    inference(cnf_transformation,[],[f2389]) ).

fof(f2389,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1)) = c_Polynomial_Opoly__gcd(X1,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1)),X0)
      | ~ class_Fields_Ofield(X1) ),
    inference(ennf_transformation,[],[f1417]) ).

fof(f1417,plain,
    ! [X0,X1] :
      ( class_Fields_Ofield(X1)
     => c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1)) = c_Polynomial_Opoly__gcd(X1,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1)),X0) ),
    inference(rectify,[],[f799]) ).

fof(f799,axiom,
    ! [X28,X4] :
      ( class_Fields_Ofield(X4)
     => c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X4)) = c_Polynomial_Opoly__gcd(X4,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X4)),X28) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__gcd__1__left) ).

fof(f8682,plain,
    spl38_449,
    inference(avatar_split_clause,[],[f4205,f8680]) ).

fof(f8680,plain,
    ( spl38_449
  <=> ! [X0,X1] :
        ( c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1)) = c_Polynomial_Opoly__gcd(X1,X0,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1)))
        | ~ class_Fields_Ofield(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_449])]) ).

fof(f4205,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1)) = c_Polynomial_Opoly__gcd(X1,X0,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1)))
      | ~ class_Fields_Ofield(X1) ),
    inference(cnf_transformation,[],[f2388]) ).

fof(f2388,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1)) = c_Polynomial_Opoly__gcd(X1,X0,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1)))
      | ~ class_Fields_Ofield(X1) ),
    inference(ennf_transformation,[],[f1416]) ).

fof(f1416,plain,
    ! [X0,X1] :
      ( class_Fields_Ofield(X1)
     => c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1)) = c_Polynomial_Opoly__gcd(X1,X0,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1))) ),
    inference(rectify,[],[f800]) ).

fof(f800,axiom,
    ! [X13,X4] :
      ( class_Fields_Ofield(X4)
     => c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X4)) = c_Polynomial_Opoly__gcd(X4,X13,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X4))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__gcd__1__right) ).

fof(f8678,plain,
    spl38_448,
    inference(avatar_split_clause,[],[f4203,f8676]) ).

fof(f8676,plain,
    ( spl38_448
  <=> ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X0)
        | ~ class_RealVector_Oreal__normed__algebra(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_448])]) ).

fof(f4203,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X0)
      | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(cnf_transformation,[],[f2386]) ).

fof(f2386,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X0)
      | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(ennf_transformation,[],[f1414]) ).

fof(f1414,plain,
    ! [X0,X1] :
      ( class_RealVector_Oreal__normed__algebra(X1)
     => c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X0) ),
    inference(rectify,[],[f752]) ).

fof(f752,axiom,
    ! [X28,X4] :
      ( class_RealVector_Oreal__normed__algebra(X4)
     => c_Groups_Ozero__class_Ozero(X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Groups_Ozero__class_Ozero(X4)),X28) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Ozero) ).

fof(f8674,plain,
    spl38_447,
    inference(avatar_split_clause,[],[f4201,f8672]) ).

fof(f8672,plain,
    ( spl38_447
  <=> ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Ozero__class_Ozero(X1))
        | ~ class_RealVector_Oreal__normed__algebra(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_447])]) ).

fof(f4201,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Ozero__class_Ozero(X1))
      | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(cnf_transformation,[],[f2384]) ).

fof(f2384,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Ozero__class_Ozero(X1))
      | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(ennf_transformation,[],[f1412]) ).

fof(f1412,plain,
    ! [X0,X1] :
      ( class_RealVector_Oreal__normed__algebra(X1)
     => c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(rectify,[],[f753]) ).

fof(f753,axiom,
    ! [X18,X4] :
      ( class_RealVector_Oreal__normed__algebra(X4)
     => c_Groups_Ozero__class_Ozero(X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X18),c_Groups_Ozero__class_Ozero(X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ozero__right) ).

fof(f8670,plain,
    spl38_446,
    inference(avatar_split_clause,[],[f4195,f8668]) ).

fof(f8668,plain,
    ( spl38_446
  <=> ! [X0,X1] :
        ( c_Rings_Oinverse__class_Oinverse(X1,X0) != c_Groups_Ozero__class_Ozero(X1)
        | c_Groups_Ozero__class_Ozero(X1) = X0
        | ~ class_Rings_Odivision__ring(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_446])]) ).

fof(f4195,plain,
    ! [X0,X1] :
      ( c_Rings_Oinverse__class_Oinverse(X1,X0) != c_Groups_Ozero__class_Ozero(X1)
      | c_Groups_Ozero__class_Ozero(X1) = X0
      | ~ class_Rings_Odivision__ring(X1) ),
    inference(cnf_transformation,[],[f2373]) ).

fof(f2373,plain,
    ! [X0,X1] :
      ( c_Rings_Oinverse__class_Oinverse(X1,X0) != c_Groups_Ozero__class_Ozero(X1)
      | c_Groups_Ozero__class_Ozero(X1) = X0
      | ~ class_Rings_Odivision__ring(X1) ),
    inference(flattening,[],[f2372]) ).

fof(f2372,plain,
    ! [X0,X1] :
      ( c_Rings_Oinverse__class_Oinverse(X1,X0) != c_Groups_Ozero__class_Ozero(X1)
      | c_Groups_Ozero__class_Ozero(X1) = X0
      | ~ class_Rings_Odivision__ring(X1) ),
    inference(ennf_transformation,[],[f1406]) ).

fof(f1406,plain,
    ! [X0,X1] :
      ( class_Rings_Odivision__ring(X1)
     => ( c_Groups_Ozero__class_Ozero(X1) != X0
       => c_Rings_Oinverse__class_Oinverse(X1,X0) != c_Groups_Ozero__class_Ozero(X1) ) ),
    inference(rectify,[],[f813]) ).

fof(f813,axiom,
    ! [X18,X4] :
      ( class_Rings_Odivision__ring(X4)
     => ( c_Groups_Ozero__class_Ozero(X4) != X18
       => c_Groups_Ozero__class_Ozero(X4) != c_Rings_Oinverse__class_Oinverse(X4,X18) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__imp__inverse__nonzero) ).

fof(f8666,plain,
    spl38_445,
    inference(avatar_split_clause,[],[f4193,f8664]) ).

fof(f8664,plain,
    ( spl38_445
  <=> ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(X1) = X0
        | c_Rings_Oinverse__class_Oinverse(X1,X0) != c_Groups_Ozero__class_Ozero(X1)
        | ~ class_Rings_Odivision__ring__inverse__zero(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_445])]) ).

fof(f4193,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X1) = X0
      | c_Rings_Oinverse__class_Oinverse(X1,X0) != c_Groups_Ozero__class_Ozero(X1)
      | ~ class_Rings_Odivision__ring__inverse__zero(X1) ),
    inference(cnf_transformation,[],[f3497]) ).

fof(f3497,plain,
    ! [X0,X1] :
      ( ( ( c_Rings_Oinverse__class_Oinverse(X1,X0) = c_Groups_Ozero__class_Ozero(X1)
          | c_Groups_Ozero__class_Ozero(X1) != X0 )
        & ( c_Groups_Ozero__class_Ozero(X1) = X0
          | c_Rings_Oinverse__class_Oinverse(X1,X0) != c_Groups_Ozero__class_Ozero(X1) ) )
      | ~ class_Rings_Odivision__ring__inverse__zero(X1) ),
    inference(nnf_transformation,[],[f2371]) ).

fof(f2371,plain,
    ! [X0,X1] :
      ( ( c_Rings_Oinverse__class_Oinverse(X1,X0) = c_Groups_Ozero__class_Ozero(X1)
      <=> c_Groups_Ozero__class_Ozero(X1) = X0 )
      | ~ class_Rings_Odivision__ring__inverse__zero(X1) ),
    inference(ennf_transformation,[],[f1405]) ).

fof(f1405,plain,
    ! [X0,X1] :
      ( class_Rings_Odivision__ring__inverse__zero(X1)
     => ( c_Rings_Oinverse__class_Oinverse(X1,X0) = c_Groups_Ozero__class_Ozero(X1)
      <=> c_Groups_Ozero__class_Ozero(X1) = X0 ) ),
    inference(rectify,[],[f814]) ).

fof(f814,axiom,
    ! [X12,X4] :
      ( class_Rings_Odivision__ring__inverse__zero(X4)
     => ( c_Groups_Ozero__class_Ozero(X4) = c_Rings_Oinverse__class_Oinverse(X4,X12)
      <=> c_Groups_Ozero__class_Ozero(X4) = X12 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__nonzero__iff__nonzero) ).

fof(f8662,plain,
    spl38_444,
    inference(avatar_split_clause,[],[f4189,f8660]) ).

fof(f8660,plain,
    ( spl38_444
  <=> ! [X0,X1] :
        ( c_Groups_Oone__class_Oone(X1) = X0
        | c_Groups_Oone__class_Oone(X1) != c_Rings_Oinverse__class_Oinverse(X1,X0)
        | ~ class_Fields_Ofield__inverse__zero(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_444])]) ).

fof(f4189,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(X1) = X0
      | c_Groups_Oone__class_Oone(X1) != c_Rings_Oinverse__class_Oinverse(X1,X0)
      | ~ class_Fields_Ofield__inverse__zero(X1) ),
    inference(cnf_transformation,[],[f3496]) ).

fof(f3496,plain,
    ! [X0,X1] :
      ( ( ( c_Groups_Oone__class_Oone(X1) = c_Rings_Oinverse__class_Oinverse(X1,X0)
          | c_Groups_Oone__class_Oone(X1) != X0 )
        & ( c_Groups_Oone__class_Oone(X1) = X0
          | c_Groups_Oone__class_Oone(X1) != c_Rings_Oinverse__class_Oinverse(X1,X0) ) )
      | ~ class_Fields_Ofield__inverse__zero(X1) ),
    inference(nnf_transformation,[],[f2368]) ).

fof(f2368,plain,
    ! [X0,X1] :
      ( ( c_Groups_Oone__class_Oone(X1) = c_Rings_Oinverse__class_Oinverse(X1,X0)
      <=> c_Groups_Oone__class_Oone(X1) = X0 )
      | ~ class_Fields_Ofield__inverse__zero(X1) ),
    inference(ennf_transformation,[],[f1402]) ).

fof(f1402,plain,
    ! [X0,X1] :
      ( class_Fields_Ofield__inverse__zero(X1)
     => ( c_Groups_Oone__class_Oone(X1) = c_Rings_Oinverse__class_Oinverse(X1,X0)
      <=> c_Groups_Oone__class_Oone(X1) = X0 ) ),
    inference(rectify,[],[f830]) ).

fof(f830,axiom,
    ! [X3,X4] :
      ( class_Fields_Ofield__inverse__zero(X4)
     => ( c_Groups_Oone__class_Oone(X4) = c_Rings_Oinverse__class_Oinverse(X4,X3)
      <=> c_Groups_Oone__class_Oone(X4) = X3 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__eq__1__iff) ).

fof(f8658,plain,
    spl38_443,
    inference(avatar_split_clause,[],[f4148,f8656]) ).

fof(f8656,plain,
    ( spl38_443
  <=> ! [X0] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_443])]) ).

fof(f4148,plain,
    ! [X0] :
      ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(cnf_transformation,[],[f3493]) ).

fof(f3493,plain,
    ! [X0] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != X0 )
      & ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
    inference(nnf_transformation,[],[f1350]) ).

fof(f1350,plain,
    ! [X0] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    <=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0 ),
    inference(rectify,[],[f263]) ).

fof(f263,axiom,
    ! [X34] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    <=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = X34 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__dvd__1__iff__1) ).

fof(f8654,plain,
    spl38_442,
    inference(avatar_split_clause,[],[f4103,f8652]) ).

fof(f8652,plain,
    ( spl38_442
  <=> ! [X0] :
        ( c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oplus__class_Oplus(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Oone__class_Oone(X0)))
        | ~ class_Rings_Olinordered__semidom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_442])]) ).

fof(f4103,plain,
    ! [X0] :
      ( c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oplus__class_Oplus(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Oone__class_Oone(X0)))
      | ~ class_Rings_Olinordered__semidom(X0) ),
    inference(cnf_transformation,[],[f2330]) ).

fof(f2330,plain,
    ! [X0] :
      ( c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oplus__class_Oplus(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Oone__class_Oone(X0)))
      | ~ class_Rings_Olinordered__semidom(X0) ),
    inference(ennf_transformation,[],[f1311]) ).

fof(f1311,plain,
    ! [X0] :
      ( class_Rings_Olinordered__semidom(X0)
     => c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oplus__class_Oplus(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Oone__class_Oone(X0))) ),
    inference(rectify,[],[f555]) ).

fof(f555,axiom,
    ! [X4] :
      ( class_Rings_Olinordered__semidom(X4)
     => c_Orderings_Oord__class_Oless(X4,c_Groups_Ozero__class_Ozero(X4),c_Groups_Oplus__class_Oplus(X4,c_Groups_Oone__class_Oone(X4),c_Groups_Oone__class_Oone(X4))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__two) ).

fof(f8650,plain,
    spl38_441,
    inference(avatar_split_clause,[],[f4092,f8648]) ).

fof(f4092,plain,
    ! [X0] :
      ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))
      | ~ class_Groups_Oab__group__add(X0) ),
    inference(cnf_transformation,[],[f2319]) ).

fof(f2319,plain,
    ! [X0] :
      ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))
      | ~ class_Groups_Oab__group__add(X0) ),
    inference(ennf_transformation,[],[f1300]) ).

fof(f1300,plain,
    ! [X0] :
      ( class_Groups_Oab__group__add(X0)
     => c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) ),
    inference(rectify,[],[f280]) ).

fof(f280,axiom,
    ! [X4] :
      ( class_Groups_Oab__group__add(X4)
     => c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__poly__code_I1_J) ).

fof(f8644,plain,
    ( spl38_440
    | ~ spl38_3
    | ~ spl38_125
    | ~ spl38_394 ),
    inference(avatar_split_clause,[],[f8289,f8016,f6516,f5906,f8642]) ).

fof(f8642,plain,
    ( spl38_440
  <=> ! [X0] : v_s____ = c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_440])]) ).

fof(f8016,plain,
    ( spl38_394
  <=> ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Osmult(X1,c_Groups_Ozero__class_Ozero(X1),X0)
        | ~ class_Rings_Ocomm__semiring__0(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_394])]) ).

fof(f8289,plain,
    ( ! [X0] : v_s____ = c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X0)
    | ~ spl38_3
    | ~ spl38_125
    | ~ spl38_394 ),
    inference(forward_demodulation,[],[f8285,f5908]) ).

fof(f8285,plain,
    ( ! [X0] : c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X0)
    | ~ spl38_125
    | ~ spl38_394 ),
    inference(resolution,[],[f8017,f6518]) ).

fof(f8017,plain,
    ( ! [X0,X1] :
        ( ~ class_Rings_Ocomm__semiring__0(X1)
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Osmult(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
    | ~ spl38_394 ),
    inference(avatar_component_clause,[],[f8016]) ).

fof(f8592,plain,
    ( spl38_439
    | ~ spl38_3
    | ~ spl38_122
    | ~ spl38_393 ),
    inference(avatar_split_clause,[],[f8278,f8012,f6501,f5906,f8590]) ).

fof(f8590,plain,
    ( spl38_439
  <=> ! [X0] : v_s____ = c_Polynomial_Omonom(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_439])]) ).

fof(f8012,plain,
    ( spl38_393
  <=> ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Omonom(X1,c_Groups_Ozero__class_Ozero(X1),X0)
        | ~ class_Groups_Ozero(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_393])]) ).

fof(f8278,plain,
    ( ! [X0] : v_s____ = c_Polynomial_Omonom(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X0)
    | ~ spl38_3
    | ~ spl38_122
    | ~ spl38_393 ),
    inference(forward_demodulation,[],[f8274,f5908]) ).

fof(f8274,plain,
    ( ! [X0] : c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_Omonom(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X0)
    | ~ spl38_122
    | ~ spl38_393 ),
    inference(resolution,[],[f8013,f6503]) ).

fof(f8013,plain,
    ( ! [X0,X1] :
        ( ~ class_Groups_Ozero(X1)
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Omonom(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
    | ~ spl38_393 ),
    inference(avatar_component_clause,[],[f8012]) ).

fof(f8448,plain,
    ( spl38_438
    | ~ spl38_3
    | ~ spl38_119
    | ~ spl38_392 ),
    inference(avatar_split_clause,[],[f8273,f8008,f6486,f5906,f8446]) ).

fof(f8446,plain,
    ( spl38_438
  <=> ! [X0] : c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),v_s____,X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_438])]) ).

fof(f6486,plain,
    ( spl38_119
  <=> class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_119])]) ).

fof(f8008,plain,
    ( spl38_392
  <=> ! [X0,X1] :
        ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0) = X0
        | ~ class_Groups_Ocomm__monoid__add(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_392])]) ).

fof(f8273,plain,
    ( ! [X0] : c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),v_s____,X0) = X0
    | ~ spl38_3
    | ~ spl38_119
    | ~ spl38_392 ),
    inference(forward_demodulation,[],[f8269,f5908]) ).

fof(f8269,plain,
    ( ! [X0] : c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0) = X0
    | ~ spl38_119
    | ~ spl38_392 ),
    inference(resolution,[],[f8009,f6488]) ).

fof(f6488,plain,
    ( class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex)
    | ~ spl38_119 ),
    inference(avatar_component_clause,[],[f6486]) ).

fof(f8009,plain,
    ( ! [X0,X1] :
        ( ~ class_Groups_Ocomm__monoid__add(X1)
        | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0) = X0 )
    | ~ spl38_392 ),
    inference(avatar_component_clause,[],[f8008]) ).

fof(f8408,plain,
    ( spl38_437
    | ~ spl38_3
    | ~ spl38_119
    | ~ spl38_391 ),
    inference(avatar_split_clause,[],[f8268,f8004,f6486,f5906,f8406]) ).

fof(f8406,plain,
    ( spl38_437
  <=> ! [X0] : c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),X0,v_s____) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_437])]) ).

fof(f8004,plain,
    ( spl38_391
  <=> ! [X0,X1] :
        ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = X0
        | ~ class_Groups_Ocomm__monoid__add(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_391])]) ).

fof(f8268,plain,
    ( ! [X0] : c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),X0,v_s____) = X0
    | ~ spl38_3
    | ~ spl38_119
    | ~ spl38_391 ),
    inference(forward_demodulation,[],[f8264,f5908]) ).

fof(f8264,plain,
    ( ! [X0] : c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = X0
    | ~ spl38_119
    | ~ spl38_391 ),
    inference(resolution,[],[f8005,f6488]) ).

fof(f8005,plain,
    ( ! [X0,X1] :
        ( ~ class_Groups_Ocomm__monoid__add(X1)
        | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = X0 )
    | ~ spl38_391 ),
    inference(avatar_component_clause,[],[f8004]) ).

fof(f8237,plain,
    ( ~ spl38_128
    | ~ spl38_220
    | spl38_420 ),
    inference(avatar_split_clause,[],[f8169,f8122,f6926,f6531]) ).

fof(f6926,plain,
    ( spl38_220
  <=> ! [X0] :
        ( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Ocomm__semiring__1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_220])]) ).

fof(f8169,plain,
    ( ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)
    | ~ spl38_220
    | spl38_420 ),
    inference(resolution,[],[f8124,f6927]) ).

fof(f6927,plain,
    ( ! [X0] :
        ( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Ocomm__semiring__1(X0) )
    | ~ spl38_220 ),
    inference(avatar_component_clause,[],[f6926]) ).

fof(f8124,plain,
    ( ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | spl38_420 ),
    inference(avatar_component_clause,[],[f8122]) ).

fof(f8189,plain,
    spl38_436,
    inference(avatar_split_clause,[],[f5838,f8187]) ).

fof(f8187,plain,
    ( spl38_436
  <=> ! [X0,X1] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
        | ~ sP1(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_436])]) ).

fof(f5838,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
      | ~ sP1(X0,X1) ),
    inference(forward_demodulation,[],[f5837,f4029]) ).

fof(f4029,plain,
    ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
    inference(cnf_transformation,[],[f1237]) ).

fof(f1237,plain,
    ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
    inference(rectify,[],[f637]) ).

fof(f637,axiom,
    ! [X19] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X19,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).

fof(f5837,plain,
    ! [X0,X1] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
      | ~ sP1(X0,X1) ),
    inference(forward_demodulation,[],[f5496,f4164]) ).

fof(f4164,plain,
    ! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),
    inference(cnf_transformation,[],[f1363]) ).

fof(f1363,plain,
    ! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),
    inference(rectify,[],[f719]) ).

fof(f719,axiom,
    ! [X10,X19] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X10) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X19),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__commute) ).

fof(f5496,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1
      | ~ sP1(X0,X1) ),
    inference(definition_unfolding,[],[f4506,f4035]) ).

fof(f4506,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
      | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
      | ~ sP1(X0,X1) ),
    inference(cnf_transformation,[],[f3594]) ).

fof(f3594,plain,
    ! [X0,X1] :
      ( ( sP1(X0,X1)
        | ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0
            | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 )
          & ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
            | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ) ) )
      & ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
          & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
        | ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
          & c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 )
        | ~ sP1(X0,X1) ) ),
    inference(flattening,[],[f3593]) ).

fof(f3593,plain,
    ! [X0,X1] :
      ( ( sP1(X0,X1)
        | ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0
            | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 )
          & ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
            | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ) ) )
      & ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
          & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
        | ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
          & c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 )
        | ~ sP1(X0,X1) ) ),
    inference(nnf_transformation,[],[f3453]) ).

fof(f3453,plain,
    ! [X0,X1] :
      ( sP1(X0,X1)
    <=> ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
          & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
        | ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
          & c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

fof(f8185,plain,
    spl38_435,
    inference(avatar_split_clause,[],[f5836,f8183]) ).

fof(f8183,plain,
    ( spl38_435
  <=> ! [X0,X1] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
        | ~ sP1(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_435])]) ).

fof(f5836,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
      | c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
      | ~ sP1(X0,X1) ),
    inference(forward_demodulation,[],[f5835,f4029]) ).

fof(f5835,plain,
    ! [X0,X1] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
      | c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
      | ~ sP1(X0,X1) ),
    inference(forward_demodulation,[],[f5834,f4164]) ).

fof(f5834,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1
      | ~ sP1(X0,X1) ),
    inference(forward_demodulation,[],[f5833,f4029]) ).

fof(f5833,plain,
    ! [X0,X1] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1
      | ~ sP1(X0,X1) ),
    inference(forward_demodulation,[],[f5495,f4164]) ).

fof(f5495,plain,
    ! [X0,X1] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1
      | ~ sP1(X0,X1) ),
    inference(definition_unfolding,[],[f4508,f4035,f4035]) ).

fof(f4508,plain,
    ! [X0,X1] :
      ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
      | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
      | ~ sP1(X0,X1) ),
    inference(cnf_transformation,[],[f3594]) ).

fof(f8181,plain,
    spl38_434,
    inference(avatar_split_clause,[],[f5832,f8179]) ).

fof(f8179,plain,
    ( spl38_434
  <=> ! [X0,X1] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
        | ~ sP1(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_434])]) ).

fof(f5832,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
      | ~ sP1(X0,X1) ),
    inference(forward_demodulation,[],[f5831,f4029]) ).

fof(f5831,plain,
    ! [X0,X1] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
      | ~ sP1(X0,X1) ),
    inference(forward_demodulation,[],[f5494,f4164]) ).

fof(f5494,plain,
    ! [X0,X1] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
      | ~ sP1(X0,X1) ),
    inference(definition_unfolding,[],[f4509,f4035]) ).

fof(f4509,plain,
    ! [X0,X1] :
      ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
      | ~ sP1(X0,X1) ),
    inference(cnf_transformation,[],[f3594]) ).

fof(f8177,plain,
    spl38_433,
    inference(avatar_split_clause,[],[f5822,f8175]) ).

fof(f8175,plain,
    ( spl38_433
  <=> ! [X0,X1] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
        | ~ sP0(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_433])]) ).

fof(f5822,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
      | ~ sP0(X0,X1) ),
    inference(forward_demodulation,[],[f5821,f4029]) ).

fof(f5821,plain,
    ! [X0,X1] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
      | ~ sP0(X0,X1) ),
    inference(forward_demodulation,[],[f5489,f4164]) ).

fof(f5489,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1
      | ~ sP0(X0,X1) ),
    inference(definition_unfolding,[],[f4498,f4035]) ).

fof(f4498,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
      | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f3591]) ).

fof(f3591,plain,
    ! [X0,X1] :
      ( ( sP0(X0,X1)
        | ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0
            | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 )
          & ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
            | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ) ) )
      & ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
          & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
        | ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
          & c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 )
        | ~ sP0(X0,X1) ) ),
    inference(flattening,[],[f3590]) ).

fof(f3590,plain,
    ! [X0,X1] :
      ( ( sP0(X0,X1)
        | ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0
            | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 )
          & ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
            | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ) ) )
      & ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
          & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
        | ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
          & c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 )
        | ~ sP0(X0,X1) ) ),
    inference(nnf_transformation,[],[f3451]) ).

fof(f3451,plain,
    ! [X0,X1] :
      ( sP0(X0,X1)
    <=> ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
          & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
        | ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
          & c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f8173,plain,
    spl38_432,
    inference(avatar_split_clause,[],[f5820,f8171]) ).

fof(f8171,plain,
    ( spl38_432
  <=> ! [X0,X1] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
        | ~ sP0(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_432])]) ).

fof(f5820,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
      | c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
      | ~ sP0(X0,X1) ),
    inference(forward_demodulation,[],[f5819,f4029]) ).

fof(f5819,plain,
    ! [X0,X1] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
      | c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
      | ~ sP0(X0,X1) ),
    inference(forward_demodulation,[],[f5818,f4164]) ).

fof(f5818,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1
      | ~ sP0(X0,X1) ),
    inference(forward_demodulation,[],[f5817,f4029]) ).

fof(f5817,plain,
    ! [X0,X1] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1
      | ~ sP0(X0,X1) ),
    inference(forward_demodulation,[],[f5488,f4164]) ).

fof(f5488,plain,
    ! [X0,X1] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1
      | ~ sP0(X0,X1) ),
    inference(definition_unfolding,[],[f4500,f4035,f4035]) ).

fof(f4500,plain,
    ! [X0,X1] :
      ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
      | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f3591]) ).

fof(f8168,plain,
    spl38_431,
    inference(avatar_split_clause,[],[f5816,f8166]) ).

fof(f8166,plain,
    ( spl38_431
  <=> ! [X0,X1] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
        | ~ sP0(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_431])]) ).

fof(f5816,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
      | ~ sP0(X0,X1) ),
    inference(forward_demodulation,[],[f5815,f4029]) ).

fof(f5815,plain,
    ! [X0,X1] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
      | ~ sP0(X0,X1) ),
    inference(forward_demodulation,[],[f5487,f4164]) ).

fof(f5487,plain,
    ! [X0,X1] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
      | ~ sP0(X0,X1) ),
    inference(definition_unfolding,[],[f4501,f4035]) ).

fof(f4501,plain,
    ! [X0,X1] :
      ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f3591]) ).

fof(f8164,plain,
    spl38_430,
    inference(avatar_split_clause,[],[f5781,f8162]) ).

fof(f8162,plain,
    ( spl38_430
  <=> ! [X0,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_430])]) ).

fof(f5781,plain,
    ! [X0,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))),
    inference(forward_demodulation,[],[f5420,f5407]) ).

fof(f5407,plain,
    ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),
    inference(definition_unfolding,[],[f4036,f4035]) ).

fof(f4036,plain,
    ! [X0] : c_Nat_OSuc(X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),
    inference(cnf_transformation,[],[f1244]) ).

fof(f1244,plain,
    ! [X0] : c_Nat_OSuc(X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),
    inference(rectify,[],[f687]) ).

fof(f687,axiom,
    ! [X10] : c_Nat_OSuc(X10) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X10),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).

fof(f5420,plain,
    ! [X0,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
    inference(definition_unfolding,[],[f4161,f4035]) ).

fof(f4161,plain,
    ! [X0,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))),
    inference(cnf_transformation,[],[f1360]) ).

fof(f1360,plain,
    ! [X0,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))),
    inference(rectify,[],[f682]) ).

fof(f682,axiom,
    ! [X19,X38] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X38,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X38,X19))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__Suc1) ).

fof(f8160,plain,
    spl38_429,
    inference(avatar_split_clause,[],[f5780,f8158]) ).

fof(f8158,plain,
    ( spl38_429
  <=> ! [X0,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_429])]) ).

fof(f5780,plain,
    ! [X0,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))),
    inference(forward_demodulation,[],[f5419,f5407]) ).

fof(f5419,plain,
    ! [X0,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
    inference(definition_unfolding,[],[f4160,f4035]) ).

fof(f4160,plain,
    ! [X0,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))),
    inference(cnf_transformation,[],[f1359]) ).

fof(f1359,plain,
    ! [X0,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))),
    inference(rectify,[],[f683]) ).

fof(f683,axiom,
    ! [X19,X38] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X38,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X38))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__Suc2) ).

fof(f8156,plain,
    spl38_428,
    inference(avatar_split_clause,[],[f5715,f8154]) ).

fof(f8154,plain,
    ( spl38_428
  <=> ! [X2,X0,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
        | ~ sP9(X0,X1,X2,c_Groups_Ozero__class_Ozero(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_428])]) ).

fof(f5715,plain,
    ! [X2,X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
      | ~ sP9(X0,X1,X2,c_Groups_Ozero__class_Ozero(X2)) ),
    inference(equality_resolution,[],[f5088]) ).

fof(f5088,plain,
    ! [X2,X3,X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
      | c_Groups_Ozero__class_Ozero(X2) != X3
      | ~ sP9(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f3779]) ).

fof(f3779,plain,
    ! [X0,X1,X2,X3] :
      ( ( sP9(X0,X1,X2,X3)
        | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),X1),X0))
          & c_Groups_Ozero__class_Ozero(X2) != X3 )
        | ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X0
          & c_Groups_Ozero__class_Ozero(X2) = X3 ) )
      & ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),X1),X0))
            | c_Groups_Ozero__class_Ozero(X2) = X3 )
          & ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
            | c_Groups_Ozero__class_Ozero(X2) != X3 ) )
        | ~ sP9(X0,X1,X2,X3) ) ),
    inference(rectify,[],[f3778]) ).

fof(f3778,plain,
    ! [X0,X1,X3,X2] :
      ( ( sP9(X0,X1,X3,X2)
        | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X1),X0))
          & c_Groups_Ozero__class_Ozero(X3) != X2 )
        | ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) != X0
          & c_Groups_Ozero__class_Ozero(X3) = X2 ) )
      & ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X1),X0))
            | c_Groups_Ozero__class_Ozero(X3) = X2 )
          & ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X0
            | c_Groups_Ozero__class_Ozero(X3) != X2 ) )
        | ~ sP9(X0,X1,X3,X2) ) ),
    inference(flattening,[],[f3777]) ).

fof(f3777,plain,
    ! [X0,X1,X3,X2] :
      ( ( sP9(X0,X1,X3,X2)
        | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X1),X0))
          & c_Groups_Ozero__class_Ozero(X3) != X2 )
        | ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) != X0
          & c_Groups_Ozero__class_Ozero(X3) = X2 ) )
      & ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X1),X0))
            | c_Groups_Ozero__class_Ozero(X3) = X2 )
          & ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X0
            | c_Groups_Ozero__class_Ozero(X3) != X2 ) )
        | ~ sP9(X0,X1,X3,X2) ) ),
    inference(nnf_transformation,[],[f3466]) ).

fof(f3466,plain,
    ! [X0,X1,X3,X2] :
      ( sP9(X0,X1,X3,X2)
    <=> ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X1),X0))
          | c_Groups_Ozero__class_Ozero(X3) = X2 )
        & ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X0
          | c_Groups_Ozero__class_Ozero(X3) != X2 ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP9])]) ).

fof(f8152,plain,
    spl38_427,
    inference(avatar_split_clause,[],[f5661,f8150]) ).

fof(f8150,plain,
    ( spl38_427
  <=> ! [X2,X0] :
        ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_Osmult(X2,c_Groups_Ozero__class_Ozero(X2),X0)
        | ~ class_Rings_Oidom(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_427])]) ).

fof(f5661,plain,
    ! [X2,X0] :
      ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_Osmult(X2,c_Groups_Ozero__class_Ozero(X2),X0)
      | ~ class_Rings_Oidom(X2) ),
    inference(equality_resolution,[],[f4784]) ).

fof(f4784,plain,
    ! [X2,X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_Osmult(X2,X1,X0)
      | c_Groups_Ozero__class_Ozero(X2) != X1
      | ~ class_Rings_Oidom(X2) ),
    inference(cnf_transformation,[],[f3681]) ).

fof(f8148,plain,
    spl38_426,
    inference(avatar_split_clause,[],[f5551,f8146]) ).

fof(f8146,plain,
    ( spl38_426
  <=> ! [X1] :
        ( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ozero__class_Ozero(X1))
        | ~ class_Groups_Olinordered__ab__group__add(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_426])]) ).

fof(f5551,plain,
    ! [X1] :
      ( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ozero__class_Ozero(X1))
      | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(equality_resolution,[],[f4226]) ).

fof(f4226,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oplus__class_Oplus(X1,X0,X0)
      | c_Groups_Ozero__class_Ozero(X1) != X0
      | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(cnf_transformation,[],[f3503]) ).

fof(f8144,plain,
    spl38_425,
    inference(avatar_split_clause,[],[f5421,f8142]) ).

fof(f8142,plain,
    ( spl38_425
  <=> ! [X0,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_425])]) ).

fof(f5421,plain,
    ! [X0,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
    inference(definition_unfolding,[],[f4162,f4035]) ).

fof(f4162,plain,
    ! [X0,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0),c_Nat_OSuc(X1)),
    inference(cnf_transformation,[],[f1361]) ).

fof(f1361,plain,
    ! [X0,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0),c_Nat_OSuc(X1)),
    inference(rectify,[],[f954]) ).

fof(f954,axiom,
    ! [X10,X19] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X10),c_Nat_OSuc(X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less__Suc) ).

fof(f8140,plain,
    spl38_424,
    inference(avatar_split_clause,[],[f5408,f8138]) ).

fof(f8138,plain,
    ( spl38_424
  <=> ! [X0] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_424])]) ).

fof(f5408,plain,
    ! [X0] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0,
    inference(definition_unfolding,[],[f4037,f4035]) ).

fof(f4037,plain,
    ! [X0] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0,
    inference(cnf_transformation,[],[f1245]) ).

fof(f1245,plain,
    ! [X0] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0,
    inference(rectify,[],[f935]) ).

fof(f935,axiom,
    ! [X10] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X10),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X10,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__1) ).

fof(f8136,plain,
    spl38_423,
    inference(avatar_split_clause,[],[f5050,f8134]) ).

fof(f8134,plain,
    ( spl38_423
  <=> ! [X2,X0,X1,X3] : hAPP(hAPP(c_Power_Opower_Opower(X3,X2,X1),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_423])]) ).

fof(f5050,plain,
    ! [X2,X3,X0,X1] : hAPP(hAPP(c_Power_Opower_Opower(X3,X2,X1),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X2,
    inference(cnf_transformation,[],[f1993]) ).

fof(f1993,plain,
    ! [X0,X1,X2,X3] : hAPP(hAPP(c_Power_Opower_Opower(X3,X2,X1),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X2,
    inference(rectify,[],[f556]) ).

fof(f556,axiom,
    ! [X12,X58,X59,X4] : hAPP(hAPP(c_Power_Opower_Opower(X4,X59,X58),X12),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X59,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power_Opower_Opower__0) ).

fof(f8132,plain,
    spl38_422,
    inference(avatar_split_clause,[],[f4974,f8130]) ).

fof(f8130,plain,
    ( spl38_422
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_422])]) ).

fof(f4974,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X0) ),
    inference(cnf_transformation,[],[f3023]) ).

fof(f3023,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X0) ),
    inference(ennf_transformation,[],[f1956]) ).

fof(f1956,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X0)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0) ),
    inference(rectify,[],[f651]) ).

fof(f651,axiom,
    ! [X30,X37,X38] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X38,X37),X30)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X38,X30) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__lessD1) ).

fof(f8128,plain,
    ( ~ spl38_420
    | spl38_421
    | ~ spl38_3
    | ~ spl38_351 ),
    inference(avatar_split_clause,[],[f7793,f7647,f5906,f8126,f8122]) ).

fof(f7647,plain,
    ( spl38_351
  <=> ! [X0,X1] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X0),c_Groups_Ozero__class_Ozero(X1)))
        | ~ class_Rings_Ocomm__semiring__1(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_351])]) ).

fof(f7793,plain,
    ( ! [X0] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0),v_s____))
        | ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
    | ~ spl38_3
    | ~ spl38_351 ),
    inference(superposition,[],[f7648,f5908]) ).

fof(f7648,plain,
    ( ! [X0,X1] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X0),c_Groups_Ozero__class_Ozero(X1)))
        | ~ class_Rings_Ocomm__semiring__1(X1) )
    | ~ spl38_351 ),
    inference(avatar_component_clause,[],[f7647]) ).

fof(f8120,plain,
    spl38_419,
    inference(avatar_split_clause,[],[f4971,f8118]) ).

fof(f8118,plain,
    ( spl38_419
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_419])]) ).

fof(f4971,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X0) ),
    inference(cnf_transformation,[],[f3021]) ).

fof(f3021,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X0) ),
    inference(ennf_transformation,[],[f1954]) ).

fof(f1954,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X0)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0) ),
    inference(rectify,[],[f662]) ).

fof(f662,axiom,
    ! [X10,X30,X19] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X30),X10)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leD1) ).

fof(f8116,plain,
    spl38_418,
    inference(avatar_split_clause,[],[f4970,f8114]) ).

fof(f8114,plain,
    ( spl38_418
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_418])]) ).

fof(f4970,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X0) ),
    inference(cnf_transformation,[],[f3020]) ).

fof(f3020,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X0) ),
    inference(ennf_transformation,[],[f1953]) ).

fof(f1953,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X0)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
    inference(rectify,[],[f661]) ).

fof(f661,axiom,
    ! [X10,X30,X19] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X30),X10)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30,X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leD2) ).

fof(f8112,plain,
    spl38_417,
    inference(avatar_split_clause,[],[f4944,f8110]) ).

fof(f8110,plain,
    ( spl38_417
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0),X1)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_417])]) ).

fof(f4944,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0),X1)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
    inference(cnf_transformation,[],[f2986]) ).

fof(f2986,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0),X1)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
    inference(ennf_transformation,[],[f1933]) ).

fof(f1933,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0),X1) ),
    inference(rectify,[],[f963]) ).

fof(f963,axiom,
    ! [X10,X30,X37] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X37,X30)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X37,X10),X30) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__diff__less) ).

fof(f8108,plain,
    spl38_416,
    inference(avatar_split_clause,[],[f4941,f8106]) ).

fof(f8106,plain,
    ( spl38_416
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_416])]) ).

fof(f4941,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
    inference(cnf_transformation,[],[f2983]) ).

fof(f2983,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
    inference(ennf_transformation,[],[f1930]) ).

fof(f1930,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) ),
    inference(rectify,[],[f646]) ).

fof(f646,axiom,
    ! [X19,X37,X38] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X38,X37)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X38,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X37,X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__less__add1) ).

fof(f8104,plain,
    spl38_415,
    inference(avatar_split_clause,[],[f4940,f8102]) ).

fof(f8102,plain,
    ( spl38_415
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_415])]) ).

fof(f4940,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
    inference(cnf_transformation,[],[f2982]) ).

fof(f2982,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
    inference(ennf_transformation,[],[f1929]) ).

fof(f1929,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
    inference(rectify,[],[f667]) ).

fof(f667,axiom,
    ! [X28,X33,X13] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X13,X33)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X13,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X28,X33)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I2_J) ).

fof(f8100,plain,
    spl38_414,
    inference(avatar_split_clause,[],[f4917,f8098]) ).

fof(f8098,plain,
    ( spl38_414
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_414])]) ).

fof(f4917,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    inference(cnf_transformation,[],[f2957]) ).

fof(f2957,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    inference(ennf_transformation,[],[f1910]) ).

fof(f1910,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
    inference(rectify,[],[f665]) ).

fof(f665,axiom,
    ! [X28,X33,X13] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X13,X33)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X13,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X28,X33)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I4_J) ).

fof(f8096,plain,
    spl38_413,
    inference(avatar_split_clause,[],[f4916,f8094]) ).

fof(f8094,plain,
    ( spl38_413
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_413])]) ).

fof(f4916,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    inference(cnf_transformation,[],[f2956]) ).

fof(f2956,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    inference(ennf_transformation,[],[f1909]) ).

fof(f1909,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) ),
    inference(rectify,[],[f664]) ).

fof(f664,axiom,
    ! [X33,X28,X13] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X13,X28)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X13,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X28,X33)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I3_J) ).

fof(f8092,plain,
    spl38_412,
    inference(avatar_split_clause,[],[f4860,f8090]) ).

fof(f8090,plain,
    ( spl38_412
  <=> ! [X2,X0,X1] :
        ( c_Groups_Oplus__class_Oplus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X0,X1)
        | ~ class_Rings_Ocomm__semiring__1(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_412])]) ).

fof(f4860,plain,
    ! [X2,X0,X1] :
      ( c_Groups_Oplus__class_Oplus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X0,X1)
      | ~ class_Rings_Ocomm__semiring__1(X2) ),
    inference(cnf_transformation,[],[f2892]) ).

fof(f2892,plain,
    ! [X0,X1,X2] :
      ( c_Groups_Oplus__class_Oplus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X0,X1)
      | ~ class_Rings_Ocomm__semiring__1(X2) ),
    inference(ennf_transformation,[],[f1867]) ).

fof(f1867,plain,
    ! [X0,X1,X2] :
      ( class_Rings_Ocomm__semiring__1(X2)
     => c_Groups_Oplus__class_Oplus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X0,X1) ),
    inference(rectify,[],[f467]) ).

fof(f467,axiom,
    ! [X22,X18,X4] :
      ( class_Rings_Ocomm__semiring__1(X4)
     => c_Groups_Oplus__class_Oplus(X4,X18,X22) = c_Groups_Oplus__class_Oplus(X4,X22,X18) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).

fof(f8088,plain,
    spl38_411,
    inference(avatar_split_clause,[],[f4823,f8086]) ).

fof(f8086,plain,
    ( spl38_411
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,c_Polynomial_Omonom(X2,X1,X0)),X0)
        | ~ class_Groups_Ozero(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_411])]) ).

fof(f4823,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,c_Polynomial_Omonom(X2,X1,X0)),X0)
      | ~ class_Groups_Ozero(X2) ),
    inference(cnf_transformation,[],[f2858]) ).

fof(f2858,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,c_Polynomial_Omonom(X2,X1,X0)),X0)
      | ~ class_Groups_Ozero(X2) ),
    inference(ennf_transformation,[],[f1840]) ).

fof(f1840,plain,
    ! [X0,X1,X2] :
      ( class_Groups_Ozero(X2)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,c_Polynomial_Omonom(X2,X1,X0)),X0) ),
    inference(rectify,[],[f214]) ).

fof(f214,axiom,
    ! [X10,X18,X4] :
      ( class_Groups_Ozero(X4)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X4,c_Polynomial_Omonom(X4,X18,X10)),X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__monom__le) ).

fof(f8084,plain,
    spl38_410,
    inference(avatar_split_clause,[],[f4678,f8082]) ).

fof(f8082,plain,
    ( spl38_410
  <=> ! [X2,X0,X1] :
        ( c_Polynomial_Opos__poly(X2,c_Polynomial_OpCons(X2,X1,X0))
        | ~ c_Polynomial_Opos__poly(X2,X0)
        | ~ class_Rings_Olinordered__idom(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_410])]) ).

fof(f4678,plain,
    ! [X2,X0,X1] :
      ( c_Polynomial_Opos__poly(X2,c_Polynomial_OpCons(X2,X1,X0))
      | ~ c_Polynomial_Opos__poly(X2,X0)
      | ~ class_Rings_Olinordered__idom(X2) ),
    inference(cnf_transformation,[],[f3654]) ).

fof(f3654,plain,
    ! [X0,X1,X2] :
      ( ( ( c_Polynomial_Opos__poly(X2,c_Polynomial_OpCons(X2,X1,X0))
          | ( ( ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
              | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X0 )
            & ~ c_Polynomial_Opos__poly(X2,X0) ) )
        & ( ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
            & c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0 )
          | c_Polynomial_Opos__poly(X2,X0)
          | ~ c_Polynomial_Opos__poly(X2,c_Polynomial_OpCons(X2,X1,X0)) ) )
      | ~ class_Rings_Olinordered__idom(X2) ),
    inference(flattening,[],[f3653]) ).

fof(f3653,plain,
    ! [X0,X1,X2] :
      ( ( ( c_Polynomial_Opos__poly(X2,c_Polynomial_OpCons(X2,X1,X0))
          | ( ( ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
              | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X0 )
            & ~ c_Polynomial_Opos__poly(X2,X0) ) )
        & ( ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
            & c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0 )
          | c_Polynomial_Opos__poly(X2,X0)
          | ~ c_Polynomial_Opos__poly(X2,c_Polynomial_OpCons(X2,X1,X0)) ) )
      | ~ class_Rings_Olinordered__idom(X2) ),
    inference(nnf_transformation,[],[f2694]) ).

fof(f2694,plain,
    ! [X0,X1,X2] :
      ( ( c_Polynomial_Opos__poly(X2,c_Polynomial_OpCons(X2,X1,X0))
      <=> ( ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
            & c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0 )
          | c_Polynomial_Opos__poly(X2,X0) ) )
      | ~ class_Rings_Olinordered__idom(X2) ),
    inference(ennf_transformation,[],[f1733]) ).

fof(f1733,plain,
    ! [X0,X1,X2] :
      ( class_Rings_Olinordered__idom(X2)
     => ( c_Polynomial_Opos__poly(X2,c_Polynomial_OpCons(X2,X1,X0))
      <=> ( ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
            & c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0 )
          | c_Polynomial_Opos__poly(X2,X0) ) ) ),
    inference(rectify,[],[f703]) ).

fof(f703,axiom,
    ! [X7,X12,X4] :
      ( class_Rings_Olinordered__idom(X4)
     => ( c_Polynomial_Opos__poly(X4,c_Polynomial_OpCons(X4,X12,X7))
      <=> ( ( c_Orderings_Oord__class_Oless(X4,c_Groups_Ozero__class_Ozero(X4),X12)
            & c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X7 )
          | c_Polynomial_Opos__poly(X4,X7) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__poly__pCons) ).

fof(f8078,plain,
    spl38_409,
    inference(avatar_split_clause,[],[f4596,f8076]) ).

fof(f8076,plain,
    ( spl38_409
  <=> ! [X2,X0,X1] :
        ( c_Polynomial_Opoly__gcd(X2,X1,X0) = c_Polynomial_Opoly__gcd(X2,X0,X1)
        | ~ class_Fields_Ofield(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_409])]) ).

fof(f4596,plain,
    ! [X2,X0,X1] :
      ( c_Polynomial_Opoly__gcd(X2,X1,X0) = c_Polynomial_Opoly__gcd(X2,X0,X1)
      | ~ class_Fields_Ofield(X2) ),
    inference(cnf_transformation,[],[f2637]) ).

fof(f2637,plain,
    ! [X0,X1,X2] :
      ( c_Polynomial_Opoly__gcd(X2,X1,X0) = c_Polynomial_Opoly__gcd(X2,X0,X1)
      | ~ class_Fields_Ofield(X2) ),
    inference(ennf_transformation,[],[f1691]) ).

fof(f1691,plain,
    ! [X0,X1,X2] :
      ( class_Fields_Ofield(X2)
     => c_Polynomial_Opoly__gcd(X2,X1,X0) = c_Polynomial_Opoly__gcd(X2,X0,X1) ),
    inference(rectify,[],[f796]) ).

fof(f796,axiom,
    ! [X27,X18,X4] :
      ( class_Fields_Ofield(X4)
     => c_Polynomial_Opoly__gcd(X4,X18,X27) = c_Polynomial_Opoly__gcd(X4,X27,X18) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__gcd_Ocommute) ).

fof(f8074,plain,
    spl38_408,
    inference(avatar_split_clause,[],[f4507,f8072]) ).

fof(f8072,plain,
    ( spl38_408
  <=> ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
        | ~ sP1(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_408])]) ).

fof(f4507,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
      | ~ sP1(X0,X1) ),
    inference(cnf_transformation,[],[f3594]) ).

fof(f8070,plain,
    spl38_407,
    inference(avatar_split_clause,[],[f4499,f8068]) ).

fof(f8068,plain,
    ( spl38_407
  <=> ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
        | ~ sP0(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_407])]) ).

fof(f4499,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f3591]) ).

fof(f8066,plain,
    spl38_406,
    inference(avatar_split_clause,[],[f4488,f8064]) ).

fof(f8064,plain,
    ( spl38_406
  <=> ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_406])]) ).

fof(f4488,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) ),
    inference(cnf_transformation,[],[f3585]) ).

fof(f3585,plain,
    ! [X0,X1] :
      ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 )
      & ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
          & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) ) ),
    inference(flattening,[],[f3584]) ).

fof(f3584,plain,
    ! [X0,X1] :
      ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 )
      & ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
          & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) ) ),
    inference(nnf_transformation,[],[f1623]) ).

fof(f1623,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
    <=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
        & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 ) ),
    inference(rectify,[],[f638]) ).

fof(f638,axiom,
    ! [X11,X34] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X34,X11)
    <=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X11
        & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X34 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__is__0) ).

fof(f8062,plain,
    spl38_405,
    inference(avatar_split_clause,[],[f4487,f8060]) ).

fof(f8060,plain,
    ( spl38_405
  <=> ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_405])]) ).

fof(f4487,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) ),
    inference(cnf_transformation,[],[f3585]) ).

fof(f8058,plain,
    spl38_404,
    inference(avatar_split_clause,[],[f4483,f8056]) ).

fof(f8056,plain,
    ( spl38_404
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_404])]) ).

fof(f4483,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0) ),
    inference(cnf_transformation,[],[f3579]) ).

fof(f3579,plain,
    ! [X0,X1] :
      ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0) ) ),
    inference(nnf_transformation,[],[f1621]) ).

fof(f1621,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
    inference(rectify,[],[f952]) ).

fof(f952,axiom,
    ! [X11,X34] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X34,X11)
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__is__0__eq) ).

fof(f8054,plain,
    spl38_403,
    inference(avatar_split_clause,[],[f4453,f8052]) ).

fof(f8052,plain,
    ( spl38_403
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
        | X0 = X1
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_403])]) ).

fof(f4453,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
      | X0 = X1
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ),
    inference(cnf_transformation,[],[f3553]) ).

fof(f3553,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
        | X0 = X1
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) )
      & ( ( X0 != X1
          & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) )
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ) ),
    inference(flattening,[],[f3552]) ).

fof(f3552,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
        | X0 = X1
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) )
      & ( ( X0 != X1
          & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) )
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ) ),
    inference(nnf_transformation,[],[f1608]) ).

fof(f1608,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
    <=> ( X0 != X1
        & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ) ),
    inference(rectify,[],[f733]) ).

fof(f733,axiom,
    ! [X55,X8] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X8,X55)
    <=> ( X8 != X55
        & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X8,X55) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__le) ).

fof(f8050,plain,
    spl38_402,
    inference(avatar_split_clause,[],[f4355,f8048]) ).

fof(f8048,plain,
    ( spl38_402
  <=> ! [X0,X1] :
        ( X0 = X1
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_402])]) ).

fof(f4355,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
    inference(cnf_transformation,[],[f2518]) ).

fof(f2518,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
    inference(flattening,[],[f2517]) ).

fof(f2517,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
    inference(ennf_transformation,[],[f1536]) ).

fof(f1536,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
       => X0 = X1 ) ),
    inference(rectify,[],[f316]) ).

fof(f316,axiom,
    ! [X10,X19] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X10)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X10,X19)
       => X10 = X19 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__antisym) ).

fof(f8046,plain,
    spl38_401,
    inference(avatar_split_clause,[],[f4354,f8044]) ).

fof(f8044,plain,
    ( spl38_401
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
        | X0 = X1
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_401])]) ).

fof(f4354,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
      | X0 = X1
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
    inference(cnf_transformation,[],[f2516]) ).

fof(f2516,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
      | X0 = X1
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
    inference(flattening,[],[f2515]) ).

fof(f2515,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
      | X0 = X1
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
    inference(ennf_transformation,[],[f1535]) ).

fof(f1535,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
     => ( X0 != X1
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
    inference(rectify,[],[f362]) ).

fof(f362,axiom,
    ! [X10,X19] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X10)
     => ( X10 != X19
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X10) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__neq__implies__less) ).

fof(f8042,plain,
    spl38_400,
    inference(avatar_split_clause,[],[f4348,f8040]) ).

fof(f8040,plain,
    ( spl38_400
  <=> ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_400])]) ).

fof(f4348,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
    inference(cnf_transformation,[],[f2509]) ).

fof(f2509,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
    inference(ennf_transformation,[],[f1529]) ).

fof(f1529,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
     => c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0) ),
    inference(rectify,[],[f953]) ).

fof(f953,axiom,
    ! [X10,X19] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X10)
     => c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__is__0__eq_H) ).

fof(f8038,plain,
    spl38_399,
    inference(avatar_split_clause,[],[f4345,f8036]) ).

fof(f8036,plain,
    ( spl38_399
  <=> ! [X0,X1] :
        ( X0 = X1
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_399])]) ).

fof(f4345,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ),
    inference(cnf_transformation,[],[f2506]) ).

fof(f2506,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ),
    inference(flattening,[],[f2505]) ).

fof(f2505,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ),
    inference(ennf_transformation,[],[f1526]) ).

fof(f1526,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
       => X0 = X1 ) ),
    inference(rectify,[],[f736]) ).

fof(f736,axiom,
    ! [X74,X33] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X33,X74)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X74,X33)
       => X33 = X74 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__antisym) ).

fof(f8034,plain,
    spl38_398,
    inference(avatar_split_clause,[],[f4335,f8032]) ).

fof(f8032,plain,
    ( spl38_398
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_398])]) ).

fof(f4335,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
      | X0 = X1 ),
    inference(cnf_transformation,[],[f2495]) ).

fof(f2495,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
      | X0 = X1 ),
    inference(flattening,[],[f2494]) ).

fof(f2494,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
      | X0 = X1 ),
    inference(ennf_transformation,[],[f1518]) ).

fof(f1518,plain,
    ! [X0,X1] :
      ( X0 != X1
     => ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ) ),
    inference(rectify,[],[f313]) ).

fof(f313,axiom,
    ! [X28,X13] :
      ( X13 != X28
     => ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X13,X28)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X28,X13) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE__nat) ).

fof(f8030,plain,
    spl38_397,
    inference(avatar_split_clause,[],[f4319,f8028]) ).

fof(f8028,plain,
    ( spl38_397
  <=> ! [X0,X1] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X0) = X0
        | ~ class_Rings_Ocomm__semiring__1(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_397])]) ).

fof(f4319,plain,
    ! [X0,X1] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X0) = X0
      | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(cnf_transformation,[],[f2478]) ).

fof(f2478,plain,
    ! [X0,X1] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X0) = X0
      | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(ennf_transformation,[],[f1503]) ).

fof(f1503,plain,
    ! [X0,X1] :
      ( class_Rings_Ocomm__semiring__1(X1)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X0) = X0 ),
    inference(rectify,[],[f441]) ).

fof(f441,axiom,
    ! [X18,X4] :
      ( class_Rings_Ocomm__semiring__1(X4)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Groups_Oone__class_Oone(X4)),X18) = X18 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).

fof(f8026,plain,
    spl38_396,
    inference(avatar_split_clause,[],[f4318,f8024]) ).

fof(f8024,plain,
    ( spl38_396
  <=> ! [X0,X1] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Oone__class_Oone(X1)) = X0
        | ~ class_Rings_Ocomm__semiring__1(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_396])]) ).

fof(f4318,plain,
    ! [X0,X1] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Oone__class_Oone(X1)) = X0
      | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(cnf_transformation,[],[f2477]) ).

fof(f2477,plain,
    ! [X0,X1] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Oone__class_Oone(X1)) = X0
      | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(ennf_transformation,[],[f1502]) ).

fof(f1502,plain,
    ! [X0,X1] :
      ( class_Rings_Ocomm__semiring__1(X1)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Oone__class_Oone(X1)) = X0 ),
    inference(rectify,[],[f442]) ).

fof(f442,axiom,
    ! [X18,X4] :
      ( class_Rings_Ocomm__semiring__1(X4)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X18),c_Groups_Oone__class_Oone(X4)) = X18 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).

fof(f8022,plain,
    spl38_395,
    inference(avatar_split_clause,[],[f4317,f8020]) ).

fof(f8020,plain,
    ( spl38_395
  <=> ! [X0,X1] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0
        | ~ class_Rings_Ocomm__semiring__1(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_395])]) ).

fof(f4317,plain,
    ! [X0,X1] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0
      | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(cnf_transformation,[],[f2476]) ).

fof(f2476,plain,
    ! [X0,X1] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0
      | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(ennf_transformation,[],[f1501]) ).

fof(f1501,plain,
    ! [X0,X1] :
      ( class_Rings_Ocomm__semiring__1(X1)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0 ),
    inference(rectify,[],[f436]) ).

fof(f436,axiom,
    ! [X13,X4] :
      ( class_Rings_Ocomm__semiring__1(X4)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X4),X13),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X13 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).

fof(f8018,plain,
    spl38_394,
    inference(avatar_split_clause,[],[f4303,f8016]) ).

fof(f4303,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Osmult(X1,c_Groups_Ozero__class_Ozero(X1),X0)
      | ~ class_Rings_Ocomm__semiring__0(X1) ),
    inference(cnf_transformation,[],[f2462]) ).

fof(f2462,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Osmult(X1,c_Groups_Ozero__class_Ozero(X1),X0)
      | ~ class_Rings_Ocomm__semiring__0(X1) ),
    inference(ennf_transformation,[],[f1487]) ).

fof(f1487,plain,
    ! [X0,X1] :
      ( class_Rings_Ocomm__semiring__0(X1)
     => c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Osmult(X1,c_Groups_Ozero__class_Ozero(X1),X0) ),
    inference(rectify,[],[f13]) ).

fof(f13,axiom,
    ! [X14,X4] :
      ( class_Rings_Ocomm__semiring__0(X4)
     => c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = c_Polynomial_Osmult(X4,c_Groups_Ozero__class_Ozero(X4),X14) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__0__left) ).

fof(f8014,plain,
    spl38_393,
    inference(avatar_split_clause,[],[f4290,f8012]) ).

fof(f4290,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Omonom(X1,c_Groups_Ozero__class_Ozero(X1),X0)
      | ~ class_Groups_Ozero(X1) ),
    inference(cnf_transformation,[],[f2452]) ).

fof(f2452,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Omonom(X1,c_Groups_Ozero__class_Ozero(X1),X0)
      | ~ class_Groups_Ozero(X1) ),
    inference(ennf_transformation,[],[f1478]) ).

fof(f1478,plain,
    ! [X0,X1] :
      ( class_Groups_Ozero(X1)
     => c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Omonom(X1,c_Groups_Ozero__class_Ozero(X1),X0) ),
    inference(rectify,[],[f9]) ).

fof(f9,axiom,
    ! [X10,X4] :
      ( class_Groups_Ozero(X4)
     => c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = c_Polynomial_Omonom(X4,c_Groups_Ozero__class_Ozero(X4),X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_monom__eq__0) ).

fof(f8010,plain,
    spl38_392,
    inference(avatar_split_clause,[],[f4288,f8008]) ).

fof(f4288,plain,
    ! [X0,X1] :
      ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0) = X0
      | ~ class_Groups_Ocomm__monoid__add(X1) ),
    inference(cnf_transformation,[],[f2450]) ).

fof(f2450,plain,
    ! [X0,X1] :
      ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0) = X0
      | ~ class_Groups_Ocomm__monoid__add(X1) ),
    inference(ennf_transformation,[],[f1476]) ).

fof(f1476,plain,
    ! [X0,X1] :
      ( class_Groups_Ocomm__monoid__add(X1)
     => c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0) = X0 ),
    inference(rectify,[],[f500]) ).

fof(f500,axiom,
    ! [X21,X4] :
      ( class_Groups_Ocomm__monoid__add(X4)
     => c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X21) = X21 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__poly__code_I1_J) ).

fof(f8006,plain,
    spl38_391,
    inference(avatar_split_clause,[],[f4287,f8004]) ).

fof(f4287,plain,
    ! [X0,X1] :
      ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = X0
      | ~ class_Groups_Ocomm__monoid__add(X1) ),
    inference(cnf_transformation,[],[f2449]) ).

fof(f2449,plain,
    ! [X0,X1] :
      ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = X0
      | ~ class_Groups_Ocomm__monoid__add(X1) ),
    inference(ennf_transformation,[],[f1475]) ).

fof(f1475,plain,
    ! [X0,X1] :
      ( class_Groups_Ocomm__monoid__add(X1)
     => c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = X0 ),
    inference(rectify,[],[f499]) ).

fof(f499,axiom,
    ! [X14,X4] :
      ( class_Groups_Ocomm__monoid__add(X4)
     => c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),X14,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))) = X14 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__poly__code_I2_J) ).

fof(f8002,plain,
    spl38_390,
    inference(avatar_split_clause,[],[f4283,f8000]) ).

fof(f8000,plain,
    ( spl38_390
  <=> ! [X0,X1] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X0) = X0
        | ~ class_Groups_Omonoid__mult(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_390])]) ).

fof(f4283,plain,
    ! [X0,X1] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X0) = X0
      | ~ class_Groups_Omonoid__mult(X1) ),
    inference(cnf_transformation,[],[f2445]) ).

fof(f2445,plain,
    ! [X0,X1] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X0) = X0
      | ~ class_Groups_Omonoid__mult(X1) ),
    inference(ennf_transformation,[],[f1471]) ).

fof(f1471,plain,
    ! [X0,X1] :
      ( class_Groups_Omonoid__mult(X1)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X0) = X0 ),
    inference(rectify,[],[f147]) ).

fof(f147,axiom,
    ! [X18,X4] :
      ( class_Groups_Omonoid__mult(X4)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Groups_Oone__class_Oone(X4)),X18) = X18 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1__left) ).

fof(f7998,plain,
    ( spl38_389
    | ~ spl38_3
    | ~ spl38_122
    | ~ spl38_367 ),
    inference(avatar_split_clause,[],[f7932,f7711,f6501,f5906,f7995]) ).

fof(f7995,plain,
    ( spl38_389
  <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_s____) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_389])]) ).

fof(f7711,plain,
    ( spl38_367
  <=> ! [X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
        | ~ class_Groups_Ozero(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_367])]) ).

fof(f7932,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_s____)
    | ~ spl38_3
    | ~ spl38_122
    | ~ spl38_367 ),
    inference(forward_demodulation,[],[f7928,f5908]) ).

fof(f7928,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
    | ~ spl38_122
    | ~ spl38_367 ),
    inference(resolution,[],[f7712,f6503]) ).

fof(f7712,plain,
    ( ! [X1] :
        ( ~ class_Groups_Ozero(X1)
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) )
    | ~ spl38_367 ),
    inference(avatar_component_clause,[],[f7711]) ).

fof(f7993,plain,
    spl38_388,
    inference(avatar_split_clause,[],[f4282,f7991]) ).

fof(f7991,plain,
    ( spl38_388
  <=> ! [X0,X1] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Oone__class_Oone(X1)) = X0
        | ~ class_Groups_Omonoid__mult(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_388])]) ).

fof(f4282,plain,
    ! [X0,X1] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Oone__class_Oone(X1)) = X0
      | ~ class_Groups_Omonoid__mult(X1) ),
    inference(cnf_transformation,[],[f2444]) ).

fof(f2444,plain,
    ! [X0,X1] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Oone__class_Oone(X1)) = X0
      | ~ class_Groups_Omonoid__mult(X1) ),
    inference(ennf_transformation,[],[f1470]) ).

fof(f1470,plain,
    ! [X0,X1] :
      ( class_Groups_Omonoid__mult(X1)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Oone__class_Oone(X1)) = X0 ),
    inference(rectify,[],[f144]) ).

fof(f144,axiom,
    ! [X18,X4] :
      ( class_Groups_Omonoid__mult(X4)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X18),c_Groups_Oone__class_Oone(X4)) = X18 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1__right) ).

fof(f7989,plain,
    spl38_387,
    inference(avatar_split_clause,[],[f4281,f7987]) ).

fof(f7987,plain,
    ( spl38_387
  <=> ! [X0,X1] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0
        | ~ class_Groups_Omonoid__mult(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_387])]) ).

fof(f4281,plain,
    ! [X0,X1] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0
      | ~ class_Groups_Omonoid__mult(X1) ),
    inference(cnf_transformation,[],[f2443]) ).

fof(f2443,plain,
    ! [X0,X1] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0
      | ~ class_Groups_Omonoid__mult(X1) ),
    inference(ennf_transformation,[],[f1469]) ).

fof(f1469,plain,
    ! [X0,X1] :
      ( class_Groups_Omonoid__mult(X1)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0 ),
    inference(rectify,[],[f271]) ).

fof(f271,axiom,
    ! [X18,X4] :
      ( class_Groups_Omonoid__mult(X4)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X4),X18),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X18 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__one__right) ).

fof(f7985,plain,
    spl38_386,
    inference(avatar_split_clause,[],[f4277,f7983]) ).

fof(f7983,plain,
    ( spl38_386
  <=> ! [X0,X1] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X0) = X0
        | ~ class_Groups_Ocomm__monoid__mult(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_386])]) ).

fof(f4277,plain,
    ! [X0,X1] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X0) = X0
      | ~ class_Groups_Ocomm__monoid__mult(X1) ),
    inference(cnf_transformation,[],[f2439]) ).

fof(f2439,plain,
    ! [X0,X1] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X0) = X0
      | ~ class_Groups_Ocomm__monoid__mult(X1) ),
    inference(ennf_transformation,[],[f1465]) ).

fof(f1465,plain,
    ! [X0,X1] :
      ( class_Groups_Ocomm__monoid__mult(X1)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X0) = X0 ),
    inference(rectify,[],[f146]) ).

fof(f146,axiom,
    ! [X18,X4] :
      ( class_Groups_Ocomm__monoid__mult(X4)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Groups_Oone__class_Oone(X4)),X18) = X18 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1) ).

fof(f7981,plain,
    spl38_385,
    inference(avatar_split_clause,[],[f4276,f7979]) ).

fof(f7979,plain,
    ( spl38_385
  <=> ! [X0,X1] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Oone__class_Oone(X1)) = X0
        | ~ class_Groups_Ocomm__monoid__mult(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_385])]) ).

fof(f4276,plain,
    ! [X0,X1] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Oone__class_Oone(X1)) = X0
      | ~ class_Groups_Ocomm__monoid__mult(X1) ),
    inference(cnf_transformation,[],[f2438]) ).

fof(f2438,plain,
    ! [X0,X1] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Oone__class_Oone(X1)) = X0
      | ~ class_Groups_Ocomm__monoid__mult(X1) ),
    inference(ennf_transformation,[],[f1464]) ).

fof(f1464,plain,
    ! [X0,X1] :
      ( class_Groups_Ocomm__monoid__mult(X1)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Oone__class_Oone(X1)) = X0 ),
    inference(rectify,[],[f143]) ).

fof(f143,axiom,
    ! [X18,X4] :
      ( class_Groups_Ocomm__monoid__mult(X4)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X18),c_Groups_Oone__class_Oone(X4)) = X18 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ocomm__neutral) ).

fof(f7977,plain,
    spl38_384,
    inference(avatar_split_clause,[],[f4262,f7975]) ).

fof(f7975,plain,
    ( spl38_384
  <=> ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
        | ~ class_Groups_Ogroup__add(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_384])]) ).

fof(f4262,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
      | ~ class_Groups_Ogroup__add(X1) ),
    inference(cnf_transformation,[],[f2427]) ).

fof(f2427,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
      | ~ class_Groups_Ogroup__add(X1) ),
    inference(ennf_transformation,[],[f1453]) ).

fof(f1453,plain,
    ! [X0,X1] :
      ( class_Groups_Ogroup__add(X1)
     => c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0) ),
    inference(rectify,[],[f537]) ).

fof(f537,axiom,
    ! [X18,X4] :
      ( class_Groups_Ogroup__add(X4)
     => c_Groups_Ozero__class_Ozero(X4) = c_Groups_Oplus__class_Oplus(X4,c_Groups_Ouminus__class_Ouminus(X4,X18),X18) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__minus) ).

fof(f7973,plain,
    spl38_383,
    inference(avatar_split_clause,[],[f4261,f7971]) ).

fof(f7971,plain,
    ( spl38_383
  <=> ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0))
        | ~ class_Groups_Ogroup__add(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_383])]) ).

fof(f4261,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0))
      | ~ class_Groups_Ogroup__add(X1) ),
    inference(cnf_transformation,[],[f2426]) ).

fof(f2426,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0))
      | ~ class_Groups_Ogroup__add(X1) ),
    inference(ennf_transformation,[],[f1452]) ).

fof(f1452,plain,
    ! [X0,X1] :
      ( class_Groups_Ogroup__add(X1)
     => c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0)) ),
    inference(rectify,[],[f539]) ).

fof(f539,axiom,
    ! [X18,X4] :
      ( class_Groups_Ogroup__add(X4)
     => c_Groups_Ozero__class_Ozero(X4) = c_Groups_Oplus__class_Oplus(X4,X18,c_Groups_Ouminus__class_Ouminus(X4,X18)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__minus) ).

fof(f7969,plain,
    spl38_382,
    inference(avatar_split_clause,[],[f4256,f7967]) ).

fof(f7967,plain,
    ( spl38_382
  <=> ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
        | ~ class_Groups_Oab__group__add(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_382])]) ).

fof(f4256,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
      | ~ class_Groups_Oab__group__add(X1) ),
    inference(cnf_transformation,[],[f2421]) ).

fof(f2421,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
      | ~ class_Groups_Oab__group__add(X1) ),
    inference(ennf_transformation,[],[f1447]) ).

fof(f1447,plain,
    ! [X0,X1] :
      ( class_Groups_Oab__group__add(X1)
     => c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0) ),
    inference(rectify,[],[f536]) ).

fof(f536,axiom,
    ! [X18,X4] :
      ( class_Groups_Oab__group__add(X4)
     => c_Groups_Ozero__class_Ozero(X4) = c_Groups_Oplus__class_Oplus(X4,c_Groups_Ouminus__class_Ouminus(X4,X18),X18) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__left__minus) ).

fof(f7965,plain,
    spl38_381,
    inference(avatar_split_clause,[],[f4215,f7963]) ).

fof(f7963,plain,
    ( spl38_381
  <=> ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(X1) = X0
        | c_Groups_Ouminus__class_Ouminus(X1,X0) != X0
        | ~ class_Groups_Olinordered__ab__group__add(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_381])]) ).

fof(f4215,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X1) = X0
      | c_Groups_Ouminus__class_Ouminus(X1,X0) != X0
      | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(cnf_transformation,[],[f3498]) ).

fof(f3498,plain,
    ! [X0,X1] :
      ( ( ( c_Groups_Ouminus__class_Ouminus(X1,X0) = X0
          | c_Groups_Ozero__class_Ozero(X1) != X0 )
        & ( c_Groups_Ozero__class_Ozero(X1) = X0
          | c_Groups_Ouminus__class_Ouminus(X1,X0) != X0 ) )
      | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(nnf_transformation,[],[f2399]) ).

fof(f2399,plain,
    ! [X0,X1] :
      ( ( c_Groups_Ouminus__class_Ouminus(X1,X0) = X0
      <=> c_Groups_Ozero__class_Ozero(X1) = X0 )
      | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(ennf_transformation,[],[f1426]) ).

fof(f1426,plain,
    ! [X0,X1] :
      ( class_Groups_Olinordered__ab__group__add(X1)
     => ( c_Groups_Ouminus__class_Ouminus(X1,X0) = X0
      <=> c_Groups_Ozero__class_Ozero(X1) = X0 ) ),
    inference(rectify,[],[f187]) ).

fof(f187,axiom,
    ! [X12,X4] :
      ( class_Groups_Olinordered__ab__group__add(X4)
     => ( c_Groups_Ouminus__class_Ouminus(X4,X12) = X12
      <=> c_Groups_Ozero__class_Ozero(X4) = X12 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__equal__zero) ).

fof(f7961,plain,
    spl38_380,
    inference(avatar_split_clause,[],[f4188,f7959]) ).

fof(f7959,plain,
    ( spl38_380
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1)
        | X0 = X1
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_380])]) ).

fof(f4188,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1)
      | X0 = X1
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
    inference(cnf_transformation,[],[f1385]) ).

fof(f1385,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1)
      | X0 = X1
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
    inference(rectify,[],[f734]) ).

fof(f734,axiom,
    ! [X28,X13] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X28,X13)
      | X13 = X28
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,X13,X28) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__linear) ).

fof(f7957,plain,
    spl38_379,
    inference(avatar_split_clause,[],[f4109,f7955]) ).

fof(f7955,plain,
    ( spl38_379
  <=> ! [X0] :
        ( c_Power_Opower__class_Opower(X0) = c_Power_Opower_Opower(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Otimes__class_Otimes(X0))
        | ~ class_Power_Opower(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_379])]) ).

fof(f4109,plain,
    ! [X0] :
      ( c_Power_Opower__class_Opower(X0) = c_Power_Opower_Opower(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Otimes__class_Otimes(X0))
      | ~ class_Power_Opower(X0) ),
    inference(cnf_transformation,[],[f2336]) ).

fof(f2336,plain,
    ! [X0] :
      ( c_Power_Opower__class_Opower(X0) = c_Power_Opower_Opower(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Otimes__class_Otimes(X0))
      | ~ class_Power_Opower(X0) ),
    inference(ennf_transformation,[],[f1317]) ).

fof(f1317,plain,
    ! [X0] :
      ( class_Power_Opower(X0)
     => c_Power_Opower__class_Opower(X0) = c_Power_Opower_Opower(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Otimes__class_Otimes(X0)) ),
    inference(rectify,[],[f456]) ).

fof(f456,axiom,
    ! [X4] :
      ( class_Power_Opower(X4)
     => c_Power_Opower__class_Opower(X4) = c_Power_Opower_Opower(X4,c_Groups_Oone__class_Oone(X4),c_Groups_Otimes__class_Otimes(X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__power__power) ).

fof(f7952,plain,
    spl38_378,
    inference(avatar_split_clause,[],[f4050,f7950]) ).

fof(f7950,plain,
    ( spl38_378
  <=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_378])]) ).

fof(f4050,plain,
    ! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),X0),
    inference(cnf_transformation,[],[f1258]) ).

fof(f1258,plain,
    ! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),X0),
    inference(rectify,[],[f705]) ).

fof(f705,axiom,
    ! [X33] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X33),X33),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_odd__nonzero) ).

fof(f7927,plain,
    ( ~ spl38_376
    | spl38_377
    | spl38_340
    | ~ spl38_354 ),
    inference(avatar_split_clause,[],[f7799,f7659,f7591,f7924,f7920]) ).

fof(f7920,plain,
    ( spl38_376
  <=> class_Orderings_Olinorder(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_376])]) ).

fof(f7924,plain,
    ( spl38_377
  <=> c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(tc_Complex_Ocomplex),v_s____,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_377])]) ).

fof(f7591,plain,
    ( spl38_340
  <=> c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_340])]) ).

fof(f7659,plain,
    ( spl38_354
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
        | c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
        | ~ class_Orderings_Olinorder(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_354])]) ).

fof(f7799,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(tc_Complex_Ocomplex),v_s____,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
    | ~ class_Orderings_Olinorder(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | spl38_340
    | ~ spl38_354 ),
    inference(resolution,[],[f7660,f7593]) ).

fof(f7593,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____)
    | spl38_340 ),
    inference(avatar_component_clause,[],[f7591]) ).

fof(f7660,plain,
    ( ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
        | c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
        | ~ class_Orderings_Olinorder(X2) )
    | ~ spl38_354 ),
    inference(avatar_component_clause,[],[f7659]) ).

fof(f7758,plain,
    ( spl38_375
    | ~ spl38_3
    | ~ spl38_122
    | ~ spl38_343 ),
    inference(avatar_split_clause,[],[f7749,f7614,f6501,f5906,f7755]) ).

fof(f7755,plain,
    ( spl38_375
  <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_375])]) ).

fof(f7614,plain,
    ( spl38_343
  <=> ! [X0] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))
        | ~ class_Groups_Ozero(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_343])]) ).

fof(f7749,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)
    | ~ spl38_3
    | ~ spl38_122
    | ~ spl38_343 ),
    inference(forward_demodulation,[],[f7745,f5908]) ).

fof(f7745,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
    | ~ spl38_122
    | ~ spl38_343 ),
    inference(resolution,[],[f7615,f6503]) ).

fof(f7615,plain,
    ( ! [X0] :
        ( ~ class_Groups_Ozero(X0)
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) )
    | ~ spl38_343 ),
    inference(avatar_component_clause,[],[f7614]) ).

fof(f7742,plain,
    spl38_374,
    inference(avatar_split_clause,[],[f5846,f7740]) ).

fof(f7740,plain,
    ( spl38_374
  <=> ! [X1] : c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_374])]) ).

fof(f5846,plain,
    ! [X1] : c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(forward_demodulation,[],[f5845,f4029]) ).

fof(f5845,plain,
    ! [X1] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(forward_demodulation,[],[f5619,f4164]) ).

fof(f5619,plain,
    ! [X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(equality_resolution,[],[f5500]) ).

fof(f5500,plain,
    ! [X0,X1] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ),
    inference(definition_unfolding,[],[f4536,f4035]) ).

fof(f4536,plain,
    ! [X0,X1] :
      ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0)
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ),
    inference(cnf_transformation,[],[f3610]) ).

fof(f3610,plain,
    ! [X0,X1] :
      ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0)
        | ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1
          & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) )
      & ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
        | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0) ) ),
    inference(flattening,[],[f3609]) ).

fof(f3609,plain,
    ! [X0,X1] :
      ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0)
        | ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1
          & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) )
      & ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
        | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0) ) ),
    inference(nnf_transformation,[],[f1637]) ).

fof(f1637,plain,
    ! [X0,X1] :
      ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0)
    <=> ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) ),
    inference(rectify,[],[f283]) ).

fof(f283,axiom,
    ! [X34,X3] :
      ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X3),X34)
    <=> ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X3
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X34 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__power__eq__Suc__0__iff) ).

fof(f7738,plain,
    spl38_373,
    inference(avatar_split_clause,[],[f5842,f7736]) ).

fof(f7736,plain,
    ( spl38_373
  <=> ! [X0,X1] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
        | sP1(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_373])]) ).

fof(f5842,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
      | sP1(X0,X1) ),
    inference(forward_demodulation,[],[f5841,f4029]) ).

fof(f5841,plain,
    ! [X0,X1] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      | sP1(X0,X1) ),
    inference(forward_demodulation,[],[f5498,f4164]) ).

fof(f5498,plain,
    ! [X0,X1] :
      ( sP1(X0,X1)
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(definition_unfolding,[],[f4512,f4035]) ).

fof(f4512,plain,
    ! [X0,X1] :
      ( sP1(X0,X1)
      | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) ),
    inference(cnf_transformation,[],[f3595]) ).

fof(f3595,plain,
    ! [X0,X1] :
      ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
        | ~ sP1(X0,X1) )
      & ( sP1(X0,X1)
        | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) ) ),
    inference(nnf_transformation,[],[f3454]) ).

fof(f3454,plain,
    ! [X0,X1] :
      ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
    <=> sP1(X0,X1) ),
    inference(definition_folding,[],[f1628,f3453]) ).

fof(f1628,plain,
    ! [X0,X1] :
      ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
    <=> ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
          & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
        | ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
          & c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 ) ) ),
    inference(rectify,[],[f680]) ).

fof(f680,axiom,
    ! [X11,X34] :
      ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X34,X11)
    <=> ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X11
          & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X34 )
        | ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X11
          & c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X34 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__is__1) ).

fof(f7734,plain,
    spl38_372,
    inference(avatar_split_clause,[],[f5840,f7732]) ).

fof(f7732,plain,
    ( spl38_372
  <=> ! [X0,X1] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
        | ~ sP1(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_372])]) ).

fof(f5840,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
      | ~ sP1(X0,X1) ),
    inference(forward_demodulation,[],[f5839,f4029]) ).

fof(f5839,plain,
    ! [X0,X1] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      | ~ sP1(X0,X1) ),
    inference(forward_demodulation,[],[f5497,f4164]) ).

fof(f5497,plain,
    ! [X0,X1] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
      | ~ sP1(X0,X1) ),
    inference(definition_unfolding,[],[f4513,f4035]) ).

fof(f4513,plain,
    ! [X0,X1] :
      ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
      | ~ sP1(X0,X1) ),
    inference(cnf_transformation,[],[f3595]) ).

fof(f7730,plain,
    spl38_371,
    inference(avatar_split_clause,[],[f5826,f7728]) ).

fof(f7728,plain,
    ( spl38_371
  <=> ! [X0,X1] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
        | sP0(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_371])]) ).

fof(f5826,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
      | sP0(X0,X1) ),
    inference(forward_demodulation,[],[f5825,f4029]) ).

fof(f5825,plain,
    ! [X0,X1] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      | sP0(X0,X1) ),
    inference(forward_demodulation,[],[f5491,f4164]) ).

fof(f5491,plain,
    ! [X0,X1] :
      ( sP0(X0,X1)
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(definition_unfolding,[],[f4504,f4035]) ).

fof(f4504,plain,
    ! [X0,X1] :
      ( sP0(X0,X1)
      | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) ),
    inference(cnf_transformation,[],[f3592]) ).

fof(f3592,plain,
    ! [X0,X1] :
      ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
        | ~ sP0(X0,X1) )
      & ( sP0(X0,X1)
        | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) ) ),
    inference(nnf_transformation,[],[f3452]) ).

fof(f3452,plain,
    ! [X0,X1] :
      ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
    <=> sP0(X0,X1) ),
    inference(definition_folding,[],[f1627,f3451]) ).

fof(f1627,plain,
    ! [X0,X1] :
      ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
    <=> ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
          & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
        | ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
          & c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 ) ) ),
    inference(rectify,[],[f679]) ).

fof(f679,axiom,
    ! [X11,X34] :
      ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X34,X11)
    <=> ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X11
          & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X34 )
        | ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X11
          & c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X34 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__is__add) ).

fof(f7726,plain,
    spl38_370,
    inference(avatar_split_clause,[],[f5824,f7724]) ).

fof(f7724,plain,
    ( spl38_370
  <=> ! [X0,X1] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
        | ~ sP0(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_370])]) ).

fof(f5824,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
      | ~ sP0(X0,X1) ),
    inference(forward_demodulation,[],[f5823,f4029]) ).

fof(f5823,plain,
    ! [X0,X1] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      | ~ sP0(X0,X1) ),
    inference(forward_demodulation,[],[f5490,f4164]) ).

fof(f5490,plain,
    ! [X0,X1] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
      | ~ sP0(X0,X1) ),
    inference(definition_unfolding,[],[f4505,f4035]) ).

fof(f4505,plain,
    ! [X0,X1] :
      ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f3592]) ).

fof(f7722,plain,
    spl38_369,
    inference(avatar_split_clause,[],[f5768,f7720]) ).

fof(f7720,plain,
    ( spl38_369
  <=> ! [X0] : c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_369])]) ).

fof(f5768,plain,
    ! [X0] : c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0),
    inference(forward_demodulation,[],[f5767,f4029]) ).

fof(f5767,plain,
    ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X0),
    inference(forward_demodulation,[],[f5411,f5407]) ).

fof(f5411,plain,
    ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X0),
    inference(definition_unfolding,[],[f4051,f4035,f4035]) ).

fof(f4051,plain,
    ! [X0] : c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X0),
    inference(cnf_transformation,[],[f1259]) ).

fof(f1259,plain,
    ! [X0] : c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X0),
    inference(rectify,[],[f284]) ).

fof(f284,axiom,
    ! [X10] : c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X10),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc__0) ).

fof(f7718,plain,
    ( ~ spl38_368
    | ~ spl38_257
    | ~ spl38_272 ),
    inference(avatar_split_clause,[],[f7174,f7148,f7088,f7715]) ).

fof(f7715,plain,
    ( spl38_368
  <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_368])]) ).

fof(f7088,plain,
    ( spl38_257
  <=> ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_257])]) ).

fof(f7148,plain,
    ( spl38_272
  <=> ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_272])]) ).

fof(f7174,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ spl38_257
    | ~ spl38_272 ),
    inference(superposition,[],[f7149,f7089]) ).

fof(f7089,plain,
    ( ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) = X0
    | ~ spl38_257 ),
    inference(avatar_component_clause,[],[f7088]) ).

fof(f7149,plain,
    ( ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X0
    | ~ spl38_272 ),
    inference(avatar_component_clause,[],[f7148]) ).

fof(f7713,plain,
    spl38_367,
    inference(avatar_split_clause,[],[f5559,f7711]) ).

fof(f5559,plain,
    ! [X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
      | ~ class_Groups_Ozero(X1) ),
    inference(equality_resolution,[],[f4294]) ).

fof(f4294,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X0)
      | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) != X0
      | ~ class_Groups_Ozero(X1) ),
    inference(cnf_transformation,[],[f2456]) ).

fof(f2456,plain,
    ! [X0,X1] :
      ( ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X0) = c_Nat_OSuc(c_Polynomial_Odegree(X1,X0))
          | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X0 )
        & ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X0)
          | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) != X0 ) )
      | ~ class_Groups_Ozero(X1) ),
    inference(ennf_transformation,[],[f1482]) ).

fof(f1482,plain,
    ! [X0,X1] :
      ( class_Groups_Ozero(X1)
     => ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) != X0
         => c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X0) = c_Nat_OSuc(c_Polynomial_Odegree(X1,X0)) )
        & ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X0
         => c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X0) ) ) ),
    inference(rectify,[],[f61]) ).

fof(f61,axiom,
    ! [X14,X4] :
      ( class_Groups_Ozero(X4)
     => ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) != X14
         => c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X4,X14) = c_Nat_OSuc(c_Polynomial_Odegree(X4,X14)) )
        & ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X14
         => c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X4,X14) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psize__def) ).

fof(f7709,plain,
    spl38_366,
    inference(avatar_split_clause,[],[f5315,f7707]) ).

fof(f7707,plain,
    ( spl38_366
  <=> ! [X4,X0,X3,X2,X1] :
        ( sP15(X2,X1,X0)
        | ~ sP16(X0,X1,X2,X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_366])]) ).

fof(f5315,plain,
    ! [X2,X3,X0,X1,X4] :
      ( sP15(X2,X1,X0)
      | ~ sP16(X0,X1,X2,X3,X4) ),
    inference(cnf_transformation,[],[f3819]) ).

fof(f7705,plain,
    spl38_365,
    inference(avatar_split_clause,[],[f5069,f7703]) ).

fof(f7703,plain,
    ( spl38_365
  <=> ! [X2,X0,X1,X3] :
        ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X2
        | ~ sP8(X0,X1,X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_365])]) ).

fof(f5069,plain,
    ! [X2,X3,X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X2
      | ~ sP8(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f3764]) ).

fof(f3764,plain,
    ! [X0,X1,X2,X3] :
      ( ( c_Groups_Ozero__class_Ozero(X1) != hAPP(c_Polynomial_Ocoeff(X1,X0),c_Polynomial_Odegree(X1,X0))
        & c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X2
        & c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X3 )
      | ~ sP8(X0,X1,X2,X3) ),
    inference(rectify,[],[f3763]) ).

fof(f3763,plain,
    ! [X2,X3,X0,X1] :
      ( ( c_Groups_Ozero__class_Ozero(X3) != hAPP(c_Polynomial_Ocoeff(X3,X2),c_Polynomial_Odegree(X3,X2))
        & c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X0
        & c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X1 )
      | ~ sP8(X2,X3,X0,X1) ),
    inference(nnf_transformation,[],[f3464]) ).

fof(f3464,plain,
    ! [X2,X3,X0,X1] :
      ( ( c_Groups_Ozero__class_Ozero(X3) != hAPP(c_Polynomial_Ocoeff(X3,X2),c_Polynomial_Odegree(X3,X2))
        & c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X0
        & c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X1 )
      | ~ sP8(X2,X3,X0,X1) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).

fof(f7701,plain,
    spl38_364,
    inference(avatar_split_clause,[],[f5068,f7699]) ).

fof(f7699,plain,
    ( spl38_364
  <=> ! [X2,X0,X1,X3] :
        ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X3
        | ~ sP8(X0,X1,X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_364])]) ).

fof(f5068,plain,
    ! [X2,X3,X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X3
      | ~ sP8(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f3764]) ).

fof(f7697,plain,
    spl38_363,
    inference(avatar_split_clause,[],[f5000,f7695]) ).

fof(f5000,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP(hAPP(X2,X1),X0))
      | ~ sP6(X0,X1,X2) ),
    inference(cnf_transformation,[],[f3735]) ).

fof(f3735,plain,
    ! [X0,X1,X2] :
      ( ( ~ hBOOL(hAPP(hAPP(X2,X1),X0))
        & c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) )
      | ~ sP6(X0,X1,X2) ),
    inference(rectify,[],[f3734]) ).

fof(f3734,plain,
    ! [X2,X1,X0] :
      ( ( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
        & c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) )
      | ~ sP6(X2,X1,X0) ),
    inference(nnf_transformation,[],[f3461]) ).

fof(f3461,plain,
    ! [X2,X1,X0] :
      ( ( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
        & c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) )
      | ~ sP6(X2,X1,X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).

fof(f7693,plain,
    spl38_362,
    inference(avatar_split_clause,[],[f4900,f7691]) ).

fof(f7691,plain,
    ( spl38_362
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
        | ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
        | ~ class_Orderings_Oorder(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_362])]) ).

fof(f4900,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
      | ~ class_Orderings_Oorder(X2) ),
    inference(cnf_transformation,[],[f3709]) ).

fof(f3709,plain,
    ! [X0,X1,X2] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
          | ( X0 != X1
            & ~ c_Orderings_Oord__class_Oless(X2,X1,X0) ) )
        & ( X0 = X1
          | c_Orderings_Oord__class_Oless(X2,X1,X0)
          | ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ) )
      | ~ class_Orderings_Oorder(X2) ),
    inference(flattening,[],[f3708]) ).

fof(f3708,plain,
    ! [X0,X1,X2] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
          | ( X0 != X1
            & ~ c_Orderings_Oord__class_Oless(X2,X1,X0) ) )
        & ( X0 = X1
          | c_Orderings_Oord__class_Oless(X2,X1,X0)
          | ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ) )
      | ~ class_Orderings_Oorder(X2) ),
    inference(nnf_transformation,[],[f2944]) ).

fof(f2944,plain,
    ! [X0,X1,X2] :
      ( ( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
      <=> ( X0 = X1
          | c_Orderings_Oord__class_Oless(X2,X1,X0) ) )
      | ~ class_Orderings_Oorder(X2) ),
    inference(ennf_transformation,[],[f1900]) ).

fof(f1900,plain,
    ! [X0,X1,X2] :
      ( class_Orderings_Oorder(X2)
     => ( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
      <=> ( X0 = X1
          | c_Orderings_Oord__class_Oless(X2,X1,X0) ) ) ),
    inference(rectify,[],[f620]) ).

fof(f620,axiom,
    ! [X17,X3,X4] :
      ( class_Orderings_Oorder(X4)
     => ( c_Orderings_Oord__class_Oless__eq(X4,X3,X17)
      <=> ( X3 = X17
          | c_Orderings_Oord__class_Oless(X4,X3,X17) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__less) ).

fof(f7689,plain,
    spl38_361,
    inference(avatar_split_clause,[],[f4895,f7687]) ).

fof(f7687,plain,
    ( spl38_361
  <=> ! [X2,X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
        | ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
        | ~ class_Orderings_Oorder(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_361])]) ).

fof(f4895,plain,
    ! [X2,X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
      | ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
      | ~ class_Orderings_Oorder(X2) ),
    inference(cnf_transformation,[],[f2942]) ).

fof(f2942,plain,
    ! [X0,X1,X2] :
      ( ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
      | ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
      | ~ class_Orderings_Oorder(X2) ),
    inference(flattening,[],[f2941]) ).

fof(f2941,plain,
    ! [X0,X1,X2] :
      ( ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
      | ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
      | ~ class_Orderings_Oorder(X2) ),
    inference(ennf_transformation,[],[f1898]) ).

fof(f1898,plain,
    ! [X0,X1,X2] :
      ( class_Orderings_Oorder(X2)
     => ( c_Orderings_Oord__class_Oless(X2,X1,X0)
       => ~ c_Orderings_Oord__class_Oless(X2,X0,X1) ) ),
    inference(rectify,[],[f582]) ).

fof(f582,axiom,
    ! [X18,X27,X4] :
      ( class_Orderings_Oorder(X4)
     => ( c_Orderings_Oord__class_Oless(X4,X27,X18)
       => ~ c_Orderings_Oord__class_Oless(X4,X18,X27) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I9_J) ).

fof(f7685,plain,
    spl38_360,
    inference(avatar_split_clause,[],[f4881,f7683]) ).

fof(f7683,plain,
    ( spl38_360
  <=> ! [X2,X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
        | ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
        | ~ class_Orderings_Opreorder(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_360])]) ).

fof(f4881,plain,
    ! [X2,X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
      | ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
      | ~ class_Orderings_Opreorder(X2) ),
    inference(cnf_transformation,[],[f3704]) ).

fof(f7681,plain,
    spl38_359,
    inference(avatar_split_clause,[],[f4879,f7679]) ).

fof(f7679,plain,
    ( spl38_359
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
        | ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
        | ~ class_Orderings_Opreorder(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_359])]) ).

fof(f4879,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
      | ~ class_Orderings_Opreorder(X2) ),
    inference(cnf_transformation,[],[f2917]) ).

fof(f2917,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
      | ~ class_Orderings_Opreorder(X2) ),
    inference(flattening,[],[f2916]) ).

fof(f2916,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
      | ~ class_Orderings_Opreorder(X2) ),
    inference(ennf_transformation,[],[f1885]) ).

fof(f1885,plain,
    ! [X0,X1,X2] :
      ( class_Orderings_Opreorder(X2)
     => ( c_Orderings_Oord__class_Oless(X2,X1,X0)
       => c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ) ),
    inference(rectify,[],[f613]) ).

fof(f613,axiom,
    ! [X28,X13,X4] :
      ( class_Orderings_Opreorder(X4)
     => ( c_Orderings_Oord__class_Oless(X4,X13,X28)
       => c_Orderings_Oord__class_Oless__eq(X4,X13,X28) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__le) ).

fof(f7677,plain,
    spl38_358,
    inference(avatar_split_clause,[],[f4875,f7675]) ).

fof(f7675,plain,
    ( spl38_358
  <=> ! [X2,X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
        | ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
        | ~ class_Orderings_Opreorder(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_358])]) ).

fof(f4875,plain,
    ! [X2,X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
      | ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
      | ~ class_Orderings_Opreorder(X2) ),
    inference(cnf_transformation,[],[f2909]) ).

fof(f2909,plain,
    ! [X0,X1,X2] :
      ( ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
      | ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
      | ~ class_Orderings_Opreorder(X2) ),
    inference(flattening,[],[f2908]) ).

fof(f2908,plain,
    ! [X0,X1,X2] :
      ( ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
      | ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
      | ~ class_Orderings_Opreorder(X2) ),
    inference(ennf_transformation,[],[f1881]) ).

fof(f1881,plain,
    ! [X0,X1,X2] :
      ( class_Orderings_Opreorder(X2)
     => ( c_Orderings_Oord__class_Oless(X2,X1,X0)
       => ~ c_Orderings_Oord__class_Oless(X2,X0,X1) ) ),
    inference(rectify,[],[f587]) ).

fof(f587,axiom,
    ! [X28,X13,X4] :
      ( class_Orderings_Opreorder(X4)
     => ( c_Orderings_Oord__class_Oless(X4,X13,X28)
       => ~ c_Orderings_Oord__class_Oless(X4,X28,X13) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__not__sym) ).

fof(f7673,plain,
    spl38_357,
    inference(avatar_split_clause,[],[f4743,f7671]) ).

fof(f7671,plain,
    ( spl38_357
  <=> ! [X2,X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
        | ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
        | ~ class_Orderings_Olinorder(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_357])]) ).

fof(f4743,plain,
    ! [X2,X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
      | ~ class_Orderings_Olinorder(X2) ),
    inference(cnf_transformation,[],[f3669]) ).

fof(f3669,plain,
    ! [X0,X1,X2] :
      ( ( ( ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
          | ( X0 != X1
            & ~ c_Orderings_Oord__class_Oless(X2,X0,X1) ) )
        & ( X0 = X1
          | c_Orderings_Oord__class_Oless(X2,X0,X1)
          | c_Orderings_Oord__class_Oless(X2,X1,X0) ) )
      | ~ class_Orderings_Olinorder(X2) ),
    inference(flattening,[],[f3668]) ).

fof(f3668,plain,
    ! [X0,X1,X2] :
      ( ( ( ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
          | ( X0 != X1
            & ~ c_Orderings_Oord__class_Oless(X2,X0,X1) ) )
        & ( X0 = X1
          | c_Orderings_Oord__class_Oless(X2,X0,X1)
          | c_Orderings_Oord__class_Oless(X2,X1,X0) ) )
      | ~ class_Orderings_Olinorder(X2) ),
    inference(nnf_transformation,[],[f2776]) ).

fof(f2776,plain,
    ! [X0,X1,X2] :
      ( ( ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
      <=> ( X0 = X1
          | c_Orderings_Oord__class_Oless(X2,X0,X1) ) )
      | ~ class_Orderings_Olinorder(X2) ),
    inference(ennf_transformation,[],[f1782]) ).

fof(f1782,plain,
    ! [X0,X1,X2] :
      ( class_Orderings_Olinorder(X2)
     => ( ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
      <=> ( X0 = X1
          | c_Orderings_Oord__class_Oless(X2,X0,X1) ) ) ),
    inference(rectify,[],[f592]) ).

fof(f592,axiom,
    ! [X17,X3,X4] :
      ( class_Orderings_Olinorder(X4)
     => ( ~ c_Orderings_Oord__class_Oless(X4,X3,X17)
      <=> ( X3 = X17
          | c_Orderings_Oord__class_Oless(X4,X17,X3) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__iff__gr__or__eq) ).

fof(f7669,plain,
    spl38_356,
    inference(avatar_split_clause,[],[f4726,f7667]) ).

fof(f7667,plain,
    ( spl38_356
  <=> ! [X2,X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
        | ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
        | ~ class_Orderings_Olinorder(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_356])]) ).

fof(f4726,plain,
    ! [X2,X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
      | ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
      | ~ class_Orderings_Olinorder(X2) ),
    inference(cnf_transformation,[],[f2758]) ).

fof(f2758,plain,
    ! [X0,X1,X2] :
      ( ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
      | ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
      | ~ class_Orderings_Olinorder(X2) ),
    inference(flattening,[],[f2757]) ).

fof(f2757,plain,
    ! [X0,X1,X2] :
      ( ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
      | ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
      | ~ class_Orderings_Olinorder(X2) ),
    inference(ennf_transformation,[],[f1771]) ).

fof(f1771,plain,
    ! [X0,X1,X2] :
      ( class_Orderings_Olinorder(X2)
     => ( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
       => ~ c_Orderings_Oord__class_Oless(X2,X0,X1) ) ),
    inference(rectify,[],[f614]) ).

fof(f614,axiom,
    ! [X13,X28,X4] :
      ( class_Orderings_Olinorder(X4)
     => ( c_Orderings_Oord__class_Oless__eq(X4,X28,X13)
       => ~ c_Orderings_Oord__class_Oless(X4,X13,X28) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_leD) ).

fof(f7665,plain,
    spl38_355,
    inference(avatar_split_clause,[],[f4715,f7663]) ).

fof(f7663,plain,
    ( spl38_355
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless(X2,X0,X1)
        | c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
        | ~ class_Orderings_Olinorder(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_355])]) ).

fof(f4715,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless(X2,X0,X1)
      | c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
      | ~ class_Orderings_Olinorder(X2) ),
    inference(cnf_transformation,[],[f2740]) ).

fof(f2740,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(X2,X0,X1)
      | c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
      | ~ class_Orderings_Olinorder(X2) ),
    inference(flattening,[],[f2739]) ).

fof(f2739,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(X2,X0,X1)
      | c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
      | ~ class_Orderings_Olinorder(X2) ),
    inference(ennf_transformation,[],[f1762]) ).

fof(f1762,plain,
    ! [X0,X1,X2] :
      ( class_Orderings_Olinorder(X2)
     => ( c_Orderings_Oord__class_Oless(X2,X0,X1)
        | c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ) ),
    inference(rectify,[],[f623]) ).

fof(f623,axiom,
    ! [X28,X13,X4] :
      ( class_Orderings_Olinorder(X4)
     => ( c_Orderings_Oord__class_Oless(X4,X28,X13)
        | c_Orderings_Oord__class_Oless__eq(X4,X13,X28) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__le__less__linear) ).

fof(f7661,plain,
    spl38_354,
    inference(avatar_split_clause,[],[f4714,f7659]) ).

fof(f4714,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
      | c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
      | ~ class_Orderings_Olinorder(X2) ),
    inference(cnf_transformation,[],[f2738]) ).

fof(f2738,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
      | c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
      | ~ class_Orderings_Olinorder(X2) ),
    inference(flattening,[],[f2737]) ).

fof(f2737,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
      | c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
      | ~ class_Orderings_Olinorder(X2) ),
    inference(ennf_transformation,[],[f1761]) ).

fof(f1761,plain,
    ! [X0,X1,X2] :
      ( class_Orderings_Olinorder(X2)
     => ( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
        | c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ) ),
    inference(rectify,[],[f572]) ).

fof(f572,axiom,
    ! [X28,X13,X4] :
      ( class_Orderings_Olinorder(X4)
     => ( c_Orderings_Oord__class_Oless__eq(X4,X28,X13)
        | c_Orderings_Oord__class_Oless__eq(X4,X13,X28) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__linear) ).

fof(f7657,plain,
    spl38_353,
    inference(avatar_split_clause,[],[f4398,f7655]) ).

fof(f7655,plain,
    ( spl38_353
  <=> ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) != X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_353])]) ).

fof(f4398,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) != X1 ),
    inference(cnf_transformation,[],[f2566]) ).

fof(f2566,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) != X1 ),
    inference(ennf_transformation,[],[f1572]) ).

fof(f1572,plain,
    ! [X0,X1] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = X1
     => c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
    inference(rectify,[],[f639]) ).

fof(f639,axiom,
    ! [X10,X19] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X10) = X19
     => c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X10 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__eq__self__zero) ).

fof(f7653,plain,
    spl38_352,
    inference(avatar_split_clause,[],[f4316,f7651]) ).

fof(f7651,plain,
    ( spl38_352
  <=> ! [X0,X1] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),c_Groups_Oone__class_Oone(X1)),X0))
        | ~ class_Rings_Ocomm__semiring__1(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_352])]) ).

fof(f4316,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),c_Groups_Oone__class_Oone(X1)),X0))
      | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(cnf_transformation,[],[f2475]) ).

fof(f2475,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),c_Groups_Oone__class_Oone(X1)),X0))
      | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(ennf_transformation,[],[f1500]) ).

fof(f1500,plain,
    ! [X0,X1] :
      ( class_Rings_Ocomm__semiring__1(X1)
     => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),c_Groups_Oone__class_Oone(X1)),X0)) ),
    inference(rectify,[],[f183]) ).

fof(f183,axiom,
    ! [X18,X4] :
      ( class_Rings_Ocomm__semiring__1(X4)
     => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),c_Groups_Oone__class_Oone(X4)),X18)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__dvd) ).

fof(f7649,plain,
    spl38_351,
    inference(avatar_split_clause,[],[f4315,f7647]) ).

fof(f4315,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X0),c_Groups_Ozero__class_Ozero(X1)))
      | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(cnf_transformation,[],[f2474]) ).

fof(f2474,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X0),c_Groups_Ozero__class_Ozero(X1)))
      | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(ennf_transformation,[],[f1499]) ).

fof(f1499,plain,
    ! [X0,X1] :
      ( class_Rings_Ocomm__semiring__1(X1)
     => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X0),c_Groups_Ozero__class_Ozero(X1))) ),
    inference(rectify,[],[f57]) ).

fof(f57,axiom,
    ! [X18,X4] :
      ( class_Rings_Ocomm__semiring__1(X4)
     => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),X18),c_Groups_Ozero__class_Ozero(X4))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__0__right) ).

fof(f7645,plain,
    spl38_350,
    inference(avatar_split_clause,[],[f4271,f7643]) ).

fof(f7643,plain,
    ( spl38_350
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Oone__class_Oone(X1)))
        | ~ class_Rings_Olinordered__semidom(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_350])]) ).

fof(f4271,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Oone__class_Oone(X1)))
      | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(cnf_transformation,[],[f2434]) ).

fof(f2434,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Oone__class_Oone(X1)))
      | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(ennf_transformation,[],[f1460]) ).

fof(f1460,plain,
    ! [X0,X1] :
      ( class_Rings_Olinordered__semidom(X1)
     => c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Oone__class_Oone(X1))) ),
    inference(rectify,[],[f534]) ).

fof(f534,axiom,
    ! [X18,X4] :
      ( class_Rings_Olinordered__semidom(X4)
     => c_Orderings_Oord__class_Oless(X4,X18,c_Groups_Oplus__class_Oplus(X4,X18,c_Groups_Oone__class_Oone(X4))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__one) ).

fof(f7641,plain,
    spl38_349,
    inference(avatar_split_clause,[],[f4270,f7639]) ).

fof(f7639,plain,
    ( spl38_349
  <=> ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Omod(X1,c_Groups_Ozero__class_Ozero(X1),X0)
        | ~ class_Divides_Osemiring__div(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_349])]) ).

fof(f4270,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Omod(X1,c_Groups_Ozero__class_Ozero(X1),X0)
      | ~ class_Divides_Osemiring__div(X1) ),
    inference(cnf_transformation,[],[f2433]) ).

fof(f2433,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Omod(X1,c_Groups_Ozero__class_Ozero(X1),X0)
      | ~ class_Divides_Osemiring__div(X1) ),
    inference(ennf_transformation,[],[f1459]) ).

fof(f1459,plain,
    ! [X0,X1] :
      ( class_Divides_Osemiring__div(X1)
     => c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Omod(X1,c_Groups_Ozero__class_Ozero(X1),X0) ),
    inference(rectify,[],[f870]) ).

fof(f870,axiom,
    ! [X18,X4] :
      ( class_Divides_Osemiring__div(X4)
     => c_Groups_Ozero__class_Ozero(X4) = c_Divides_Odiv__class_Omod(X4,c_Groups_Ozero__class_Ozero(X4),X18) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__0) ).

fof(f7637,plain,
    spl38_348,
    inference(avatar_split_clause,[],[f4269,f7635]) ).

fof(f7635,plain,
    ( spl38_348
  <=> ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Omod(X1,X0,c_Groups_Oone__class_Oone(X1))
        | ~ class_Divides_Osemiring__div(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_348])]) ).

fof(f4269,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Omod(X1,X0,c_Groups_Oone__class_Oone(X1))
      | ~ class_Divides_Osemiring__div(X1) ),
    inference(cnf_transformation,[],[f2432]) ).

fof(f2432,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Omod(X1,X0,c_Groups_Oone__class_Oone(X1))
      | ~ class_Divides_Osemiring__div(X1) ),
    inference(ennf_transformation,[],[f1458]) ).

fof(f1458,plain,
    ! [X0,X1] :
      ( class_Divides_Osemiring__div(X1)
     => c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Omod(X1,X0,c_Groups_Oone__class_Oone(X1)) ),
    inference(rectify,[],[f873]) ).

fof(f873,axiom,
    ! [X18,X4] :
      ( class_Divides_Osemiring__div(X4)
     => c_Groups_Ozero__class_Ozero(X4) = c_Divides_Odiv__class_Omod(X4,X18,c_Groups_Oone__class_Oone(X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__by__1) ).

fof(f7632,plain,
    spl38_347,
    inference(avatar_split_clause,[],[f4180,f7630]) ).

fof(f7630,plain,
    ( spl38_347
  <=> ! [X0,X1] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0) = X1
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_347])]) ).

fof(f4180,plain,
    ! [X0,X1] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0) = X1
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
    inference(cnf_transformation,[],[f2366]) ).

fof(f2366,plain,
    ! [X0,X1] :
      ( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0),X0)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) )
      & ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0) = X1
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
    inference(ennf_transformation,[],[f1379]) ).

fof(f1379,plain,
    ! [X0,X1] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0),X0) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0) = X1 ) ),
    inference(rectify,[],[f916]) ).

fof(f916,axiom,
    ! [X10,X19] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X10)
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X10) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X10),X10) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X10)
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X10) = X19 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__if) ).

fof(f7628,plain,
    spl38_346,
    inference(avatar_split_clause,[],[f4141,f7626]) ).

fof(f7626,plain,
    ( spl38_346
  <=> ! [X0] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_346])]) ).

fof(f4141,plain,
    ! [X0] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
    inference(cnf_transformation,[],[f3486]) ).

fof(f3486,plain,
    ! [X0] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0) ) ),
    inference(nnf_transformation,[],[f1346]) ).

fof(f1346,plain,
    ! [X0] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
    inference(rectify,[],[f744]) ).

fof(f744,axiom,
    ! [X8] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X8)
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X8) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__one__le__iff__zero__less) ).

fof(f7624,plain,
    spl38_345,
    inference(avatar_split_clause,[],[f4140,f7622]) ).

fof(f7622,plain,
    ( spl38_345
  <=> ! [X0] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_345])]) ).

fof(f4140,plain,
    ! [X0] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0) ),
    inference(cnf_transformation,[],[f3486]) ).

fof(f7620,plain,
    spl38_344,
    inference(avatar_split_clause,[],[f4129,f7618]) ).

fof(f7618,plain,
    ( spl38_344
  <=> ! [X0] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X0,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X0)))
        | ~ class_Rings_Ocomm__semiring__1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_344])]) ).

fof(f4129,plain,
    ! [X0] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X0,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X0)))
      | ~ class_Rings_Ocomm__semiring__1(X0) ),
    inference(cnf_transformation,[],[f2356]) ).

fof(f2356,plain,
    ! [X0] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X0,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X0)))
      | ~ class_Rings_Ocomm__semiring__1(X0) ),
    inference(ennf_transformation,[],[f1337]) ).

fof(f1337,plain,
    ! [X0] :
      ( class_Rings_Ocomm__semiring__1(X0)
     => c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X0,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X0))) ),
    inference(rectify,[],[f304]) ).

fof(f304,axiom,
    ! [X4] :
      ( class_Rings_Ocomm__semiring__1(X4)
     => c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X4,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X4))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__1) ).

fof(f7616,plain,
    spl38_343,
    inference(avatar_split_clause,[],[f4114,f7614]) ).

fof(f4114,plain,
    ! [X0] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))
      | ~ class_Groups_Ozero(X0) ),
    inference(cnf_transformation,[],[f2341]) ).

fof(f2341,plain,
    ! [X0] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))
      | ~ class_Groups_Ozero(X0) ),
    inference(ennf_transformation,[],[f1322]) ).

fof(f1322,plain,
    ! [X0] :
      ( class_Groups_Ozero(X0)
     => c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) ),
    inference(rectify,[],[f46]) ).

fof(f46,axiom,
    ! [X4] :
      ( class_Groups_Ozero(X4)
     => c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X4,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__0) ).

fof(f7612,plain,
    spl38_342,
    inference(avatar_split_clause,[],[f4049,f7610]) ).

fof(f7610,plain,
    ( spl38_342
  <=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_342])]) ).

fof(f4049,plain,
    ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0),
    inference(cnf_transformation,[],[f1257]) ).

fof(f1257,plain,
    ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0),
    inference(rectify,[],[f268]) ).

fof(f268,axiom,
    ! [X10] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__0) ).

fof(f7608,plain,
    spl38_341,
    inference(avatar_split_clause,[],[f4048,f7606]) ).

fof(f7606,plain,
    ( spl38_341
  <=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_341])]) ).

fof(f4048,plain,
    ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(cnf_transformation,[],[f1256]) ).

fof(f1256,plain,
    ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(rectify,[],[f267]) ).

fof(f267,axiom,
    ! [X19] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__0__right) ).

fof(f7594,plain,
    ( ~ spl38_339
    | ~ spl38_340
    | ~ spl38_3
    | ~ spl38_282 ),
    inference(avatar_split_clause,[],[f7281,f7208,f5906,f7591,f7587]) ).

fof(f7587,plain,
    ( spl38_339
  <=> class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_339])]) ).

fof(f7208,plain,
    ( spl38_282
  <=> ! [X0] :
        ( ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Ozero__class_Ozero(X0))
        | ~ class_Rings_Olinordered__semidom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_282])]) ).

fof(f7281,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____)
    | ~ class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl38_3
    | ~ spl38_282 ),
    inference(superposition,[],[f7209,f5908]) ).

fof(f7209,plain,
    ( ! [X0] :
        ( ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Ozero__class_Ozero(X0))
        | ~ class_Rings_Olinordered__semidom(X0) )
    | ~ spl38_282 ),
    inference(avatar_component_clause,[],[f7208]) ).

fof(f7528,plain,
    ( spl38_338
    | ~ spl38_3
    | ~ spl38_296 ),
    inference(avatar_split_clause,[],[f7305,f7264,f5906,f7526]) ).

fof(f7526,plain,
    ( spl38_338
  <=> ! [X0] : sP9(c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex),v_s____) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_338])]) ).

fof(f7264,plain,
    ( spl38_296
  <=> ! [X2,X1] : sP9(c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X1,X2,c_Groups_Ozero__class_Ozero(X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_296])]) ).

fof(f7305,plain,
    ( ! [X0] : sP9(c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex),v_s____)
    | ~ spl38_3
    | ~ spl38_296 ),
    inference(superposition,[],[f7265,f5908]) ).

fof(f7265,plain,
    ( ! [X2,X1] : sP9(c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X1,X2,c_Groups_Ozero__class_Ozero(X2))
    | ~ spl38_296 ),
    inference(avatar_component_clause,[],[f7264]) ).

fof(f7459,plain,
    spl38_337,
    inference(avatar_split_clause,[],[f5775,f7457]) ).

fof(f7457,plain,
    ( spl38_337
  <=> ! [X0] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_337])]) ).

fof(f5775,plain,
    ! [X0] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
    inference(forward_demodulation,[],[f5774,f4029]) ).

fof(f5774,plain,
    ! [X0] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
    inference(forward_demodulation,[],[f5416,f5407]) ).

fof(f5416,plain,
    ! [X0] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(definition_unfolding,[],[f4146,f4035]) ).

fof(f4146,plain,
    ! [X0] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(cnf_transformation,[],[f3492]) ).

fof(f3492,plain,
    ! [X0] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 )
      & ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
    inference(nnf_transformation,[],[f1349]) ).

fof(f1349,plain,
    ! [X0] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
    inference(rectify,[],[f379]) ).

fof(f379,axiom,
    ! [X11] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X11,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X11 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc0) ).

fof(f7455,plain,
    spl38_336,
    inference(avatar_split_clause,[],[f5666,f7453]) ).

fof(f7453,plain,
    ( spl38_336
  <=> ! [X2,X1] :
        ( c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Ozero__class_Ozero(X2)) = X1
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_336])]) ).

fof(f5666,plain,
    ! [X2,X1] :
      ( c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Ozero__class_Ozero(X2)) = X1
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ),
    inference(equality_resolution,[],[f4816]) ).

fof(f4816,plain,
    ! [X2,X0,X1] :
      ( c_Groups_Oplus__class_Oplus(X2,X1,X0) = X1
      | c_Groups_Ozero__class_Ozero(X2) != X0
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ),
    inference(cnf_transformation,[],[f3688]) ).

fof(f7451,plain,
    spl38_335,
    inference(avatar_split_clause,[],[f5649,f7449]) ).

fof(f7449,plain,
    ( spl38_335
  <=> ! [X2,X1] :
        ( c_Groups_Ozero__class_Ozero(X2) = c_Groups_Ominus__class_Ominus(X2,X1,X1)
        | ~ class_Groups_Oab__group__add(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_335])]) ).

fof(f5649,plain,
    ! [X2,X1] :
      ( c_Groups_Ozero__class_Ozero(X2) = c_Groups_Ominus__class_Ominus(X2,X1,X1)
      | ~ class_Groups_Oab__group__add(X2) ),
    inference(equality_resolution,[],[f4750]) ).

fof(f4750,plain,
    ! [X2,X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X2) = c_Groups_Ominus__class_Ominus(X2,X1,X0)
      | X0 != X1
      | ~ class_Groups_Oab__group__add(X2) ),
    inference(cnf_transformation,[],[f3670]) ).

fof(f7447,plain,
    spl38_334,
    inference(avatar_split_clause,[],[f5549,f7445]) ).

fof(f7445,plain,
    ( spl38_334
  <=> ! [X1] :
        ( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ozero__class_Ozero(X1))
        | ~ class_Groups_Olinordered__ab__group__add(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_334])]) ).

fof(f5549,plain,
    ! [X1] :
      ( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ozero__class_Ozero(X1))
      | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(equality_resolution,[],[f4216]) ).

fof(f4216,plain,
    ! [X0,X1] :
      ( c_Groups_Ouminus__class_Ouminus(X1,X0) = X0
      | c_Groups_Ozero__class_Ozero(X1) != X0
      | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(cnf_transformation,[],[f3498]) ).

fof(f7443,plain,
    spl38_333,
    inference(avatar_split_clause,[],[f5547,f7441]) ).

fof(f7441,plain,
    ( spl38_333
  <=> ! [X1] :
        ( c_Groups_Oone__class_Oone(X1) = c_Rings_Oinverse__class_Oinverse(X1,c_Groups_Oone__class_Oone(X1))
        | ~ class_Fields_Ofield__inverse__zero(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_333])]) ).

fof(f5547,plain,
    ! [X1] :
      ( c_Groups_Oone__class_Oone(X1) = c_Rings_Oinverse__class_Oinverse(X1,c_Groups_Oone__class_Oone(X1))
      | ~ class_Fields_Ofield__inverse__zero(X1) ),
    inference(equality_resolution,[],[f4190]) ).

fof(f4190,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(X1) = c_Rings_Oinverse__class_Oinverse(X1,X0)
      | c_Groups_Oone__class_Oone(X1) != X0
      | ~ class_Fields_Ofield__inverse__zero(X1) ),
    inference(cnf_transformation,[],[f3496]) ).

fof(f7439,plain,
    spl38_332,
    inference(avatar_split_clause,[],[f5406,f7437]) ).

fof(f7437,plain,
    ( spl38_332
  <=> ! [X0] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_332])]) ).

fof(f5406,plain,
    ! [X0] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
    inference(definition_unfolding,[],[f4022,f4035]) ).

fof(f4022,plain,
    ! [X0] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(X0)),
    inference(cnf_transformation,[],[f1230]) ).

fof(f1230,plain,
    ! [X0] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(X0)),
    inference(rectify,[],[f227]) ).

fof(f227,axiom,
    ! [X10] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(X10)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__Suc) ).

fof(f7435,plain,
    ( spl38_331
    | ~ spl38_3
    | ~ spl38_296 ),
    inference(avatar_split_clause,[],[f7304,f7264,f5906,f7433]) ).

fof(f7433,plain,
    ( spl38_331
  <=> ! [X0] : sP9(v_s____,X0,tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_331])]) ).

fof(f7304,plain,
    ( ! [X0] : sP9(v_s____,X0,tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))
    | ~ spl38_3
    | ~ spl38_296 ),
    inference(superposition,[],[f7265,f5908]) ).

fof(f7431,plain,
    spl38_330,
    inference(avatar_split_clause,[],[f4559,f7429]) ).

fof(f7429,plain,
    ( spl38_330
  <=> ! [X2,X0,X1] : hAPP(c_Nat_Onat_Onat__case(X2,X1,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_330])]) ).

fof(f4559,plain,
    ! [X2,X0,X1] : hAPP(c_Nat_Onat_Onat__case(X2,X1,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
    inference(cnf_transformation,[],[f1645]) ).

fof(f1645,plain,
    ! [X0,X1,X2] : hAPP(c_Nat_Onat_Onat__case(X2,X1,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
    inference(rectify,[],[f366]) ).

fof(f366,axiom,
    ! [X46,X47,X4] : hAPP(c_Nat_Onat_Onat__case(X4,X47,X46),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X47,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__case__0) ).

fof(f7427,plain,
    spl38_329,
    inference(avatar_split_clause,[],[f4314,f7425]) ).

fof(f7425,plain,
    ( spl38_329
  <=> ! [X0,X1] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X0),X0))
        | ~ class_Rings_Ocomm__semiring__1(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_329])]) ).

fof(f4314,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X0),X0))
      | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(cnf_transformation,[],[f2473]) ).

fof(f2473,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X0),X0))
      | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(ennf_transformation,[],[f1498]) ).

fof(f1498,plain,
    ! [X0,X1] :
      ( class_Rings_Ocomm__semiring__1(X1)
     => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X0),X0)) ),
    inference(rectify,[],[f221]) ).

fof(f221,axiom,
    ! [X18,X4] :
      ( class_Rings_Ocomm__semiring__1(X4)
     => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),X18),X18)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__refl) ).

fof(f7423,plain,
    spl38_328,
    inference(avatar_split_clause,[],[f4313,f7421]) ).

fof(f7421,plain,
    ( spl38_328
  <=> ! [X0,X1] :
        ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X0) = X0
        | ~ class_Rings_Ocomm__semiring__1(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_328])]) ).

fof(f4313,plain,
    ! [X0,X1] :
      ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X0) = X0
      | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(cnf_transformation,[],[f2472]) ).

fof(f2472,plain,
    ! [X0,X1] :
      ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X0) = X0
      | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(ennf_transformation,[],[f1497]) ).

fof(f1497,plain,
    ! [X0,X1] :
      ( class_Rings_Ocomm__semiring__1(X1)
     => c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X0) = X0 ),
    inference(rectify,[],[f459]) ).

fof(f459,axiom,
    ! [X18,X4] :
      ( class_Rings_Ocomm__semiring__1(X4)
     => c_Groups_Oplus__class_Oplus(X4,c_Groups_Ozero__class_Ozero(X4),X18) = X18 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).

fof(f7419,plain,
    spl38_327,
    inference(avatar_split_clause,[],[f4312,f7417]) ).

fof(f7417,plain,
    ( spl38_327
  <=> ! [X0,X1] :
        ( c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0
        | ~ class_Rings_Ocomm__semiring__1(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_327])]) ).

fof(f4312,plain,
    ! [X0,X1] :
      ( c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0
      | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(cnf_transformation,[],[f2471]) ).

fof(f2471,plain,
    ! [X0,X1] :
      ( c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0
      | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(ennf_transformation,[],[f1496]) ).

fof(f1496,plain,
    ! [X0,X1] :
      ( class_Rings_Ocomm__semiring__1(X1)
     => c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0 ),
    inference(rectify,[],[f460]) ).

fof(f460,axiom,
    ! [X18,X4] :
      ( class_Rings_Ocomm__semiring__1(X4)
     => c_Groups_Oplus__class_Oplus(X4,X18,c_Groups_Ozero__class_Ozero(X4)) = X18 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).

fof(f7415,plain,
    spl38_326,
    inference(avatar_split_clause,[],[f4311,f7413]) ).

fof(f7413,plain,
    ( spl38_326
  <=> ! [X0,X1] :
        ( c_Polynomial_Osmult(X1,c_Groups_Oone__class_Oone(X1),X0) = X0
        | ~ class_Rings_Ocomm__semiring__1(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_326])]) ).

fof(f4311,plain,
    ! [X0,X1] :
      ( c_Polynomial_Osmult(X1,c_Groups_Oone__class_Oone(X1),X0) = X0
      | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(cnf_transformation,[],[f2470]) ).

fof(f2470,plain,
    ! [X0,X1] :
      ( c_Polynomial_Osmult(X1,c_Groups_Oone__class_Oone(X1),X0) = X0
      | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(ennf_transformation,[],[f1495]) ).

fof(f1495,plain,
    ! [X0,X1] :
      ( class_Rings_Ocomm__semiring__1(X1)
     => c_Polynomial_Osmult(X1,c_Groups_Oone__class_Oone(X1),X0) = X0 ),
    inference(rectify,[],[f199]) ).

fof(f199,axiom,
    ! [X14,X4] :
      ( class_Rings_Ocomm__semiring__1(X4)
     => c_Polynomial_Osmult(X4,c_Groups_Oone__class_Oone(X4),X14) = X14 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__1__left) ).

fof(f7411,plain,
    spl38_325,
    inference(avatar_split_clause,[],[f4289,f7409]) ).

fof(f7409,plain,
    ( spl38_325
  <=> ! [X0,X1] :
        ( c_Polynomial_OAbs__poly(X1,c_Polynomial_Ocoeff(X1,X0)) = X0
        | ~ class_Groups_Ozero(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_325])]) ).

fof(f4289,plain,
    ! [X0,X1] :
      ( c_Polynomial_OAbs__poly(X1,c_Polynomial_Ocoeff(X1,X0)) = X0
      | ~ class_Groups_Ozero(X1) ),
    inference(cnf_transformation,[],[f2451]) ).

fof(f2451,plain,
    ! [X0,X1] :
      ( c_Polynomial_OAbs__poly(X1,c_Polynomial_Ocoeff(X1,X0)) = X0
      | ~ class_Groups_Ozero(X1) ),
    inference(ennf_transformation,[],[f1477]) ).

fof(f1477,plain,
    ! [X0,X1] :
      ( class_Groups_Ozero(X1)
     => c_Polynomial_OAbs__poly(X1,c_Polynomial_Ocoeff(X1,X0)) = X0 ),
    inference(rectify,[],[f803]) ).

fof(f803,axiom,
    ! [X3,X4] :
      ( class_Groups_Ozero(X4)
     => c_Polynomial_OAbs__poly(X4,c_Polynomial_Ocoeff(X4,X3)) = X3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__inverse) ).

fof(f7407,plain,
    spl38_324,
    inference(avatar_split_clause,[],[f4286,f7405]) ).

fof(f7405,plain,
    ( spl38_324
  <=> ! [X0,X1] :
        ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X0) = X0
        | ~ class_Groups_Ocomm__monoid__add(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_324])]) ).

fof(f4286,plain,
    ! [X0,X1] :
      ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X0) = X0
      | ~ class_Groups_Ocomm__monoid__add(X1) ),
    inference(cnf_transformation,[],[f2448]) ).

fof(f2448,plain,
    ! [X0,X1] :
      ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X0) = X0
      | ~ class_Groups_Ocomm__monoid__add(X1) ),
    inference(ennf_transformation,[],[f1474]) ).

fof(f1474,plain,
    ! [X0,X1] :
      ( class_Groups_Ocomm__monoid__add(X1)
     => c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X0) = X0 ),
    inference(rectify,[],[f476]) ).

fof(f476,axiom,
    ! [X18,X4] :
      ( class_Groups_Ocomm__monoid__add(X4)
     => c_Groups_Oplus__class_Oplus(X4,c_Groups_Ozero__class_Ozero(X4),X18) = X18 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0) ).

fof(f7403,plain,
    spl38_323,
    inference(avatar_split_clause,[],[f4285,f7401]) ).

fof(f7401,plain,
    ( spl38_323
  <=> ! [X0,X1] :
        ( c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0
        | ~ class_Groups_Ocomm__monoid__add(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_323])]) ).

fof(f4285,plain,
    ! [X0,X1] :
      ( c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0
      | ~ class_Groups_Ocomm__monoid__add(X1) ),
    inference(cnf_transformation,[],[f2447]) ).

fof(f2447,plain,
    ! [X0,X1] :
      ( c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0
      | ~ class_Groups_Ocomm__monoid__add(X1) ),
    inference(ennf_transformation,[],[f1473]) ).

fof(f1473,plain,
    ! [X0,X1] :
      ( class_Groups_Ocomm__monoid__add(X1)
     => c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0 ),
    inference(rectify,[],[f473]) ).

fof(f473,axiom,
    ! [X18,X4] :
      ( class_Groups_Ocomm__monoid__add(X4)
     => c_Groups_Oplus__class_Oplus(X4,X18,c_Groups_Ozero__class_Ozero(X4)) = X18 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add_Ocomm__neutral) ).

fof(f7399,plain,
    spl38_322,
    inference(avatar_split_clause,[],[f4275,f7397]) ).

fof(f7397,plain,
    ( spl38_322
  <=> ! [X0,X1] :
        ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X0) = X0
        | ~ class_Groups_Omonoid__add(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_322])]) ).

fof(f4275,plain,
    ! [X0,X1] :
      ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X0) = X0
      | ~ class_Groups_Omonoid__add(X1) ),
    inference(cnf_transformation,[],[f2437]) ).

fof(f2437,plain,
    ! [X0,X1] :
      ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X0) = X0
      | ~ class_Groups_Omonoid__add(X1) ),
    inference(ennf_transformation,[],[f1463]) ).

fof(f1463,plain,
    ! [X0,X1] :
      ( class_Groups_Omonoid__add(X1)
     => c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X0) = X0 ),
    inference(rectify,[],[f477]) ).

fof(f477,axiom,
    ! [X18,X4] :
      ( class_Groups_Omonoid__add(X4)
     => c_Groups_Oplus__class_Oplus(X4,c_Groups_Ozero__class_Ozero(X4),X18) = X18 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__left) ).

fof(f7395,plain,
    spl38_321,
    inference(avatar_split_clause,[],[f4274,f7393]) ).

fof(f7393,plain,
    ( spl38_321
  <=> ! [X0,X1] :
        ( c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0
        | ~ class_Groups_Omonoid__add(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_321])]) ).

fof(f4274,plain,
    ! [X0,X1] :
      ( c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0
      | ~ class_Groups_Omonoid__add(X1) ),
    inference(cnf_transformation,[],[f2436]) ).

fof(f2436,plain,
    ! [X0,X1] :
      ( c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0
      | ~ class_Groups_Omonoid__add(X1) ),
    inference(ennf_transformation,[],[f1462]) ).

fof(f1462,plain,
    ! [X0,X1] :
      ( class_Groups_Omonoid__add(X1)
     => c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0 ),
    inference(rectify,[],[f474]) ).

fof(f474,axiom,
    ! [X18,X4] :
      ( class_Groups_Omonoid__add(X4)
     => c_Groups_Oplus__class_Oplus(X4,X18,c_Groups_Ozero__class_Ozero(X4)) = X18 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__right) ).

fof(f7391,plain,
    spl38_320,
    inference(avatar_split_clause,[],[f4268,f7389]) ).

fof(f7389,plain,
    ( spl38_320
  <=> ! [X0,X1] :
        ( c_Divides_Odiv__class_Omod(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0
        | ~ class_Divides_Osemiring__div(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_320])]) ).

fof(f4268,plain,
    ! [X0,X1] :
      ( c_Divides_Odiv__class_Omod(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0
      | ~ class_Divides_Osemiring__div(X1) ),
    inference(cnf_transformation,[],[f2431]) ).

fof(f2431,plain,
    ! [X0,X1] :
      ( c_Divides_Odiv__class_Omod(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0
      | ~ class_Divides_Osemiring__div(X1) ),
    inference(ennf_transformation,[],[f1457]) ).

fof(f1457,plain,
    ! [X0,X1] :
      ( class_Divides_Osemiring__div(X1)
     => c_Divides_Odiv__class_Omod(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0 ),
    inference(rectify,[],[f871]) ).

fof(f871,axiom,
    ! [X18,X4] :
      ( class_Divides_Osemiring__div(X4)
     => c_Divides_Odiv__class_Omod(X4,X18,c_Groups_Ozero__class_Ozero(X4)) = X18 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__by__0) ).

fof(f7387,plain,
    spl38_319,
    inference(avatar_split_clause,[],[f4267,f7385]) ).

fof(f7385,plain,
    ( spl38_319
  <=> ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Omod(X1,X0,X0)
        | ~ class_Divides_Osemiring__div(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_319])]) ).

fof(f4267,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Omod(X1,X0,X0)
      | ~ class_Divides_Osemiring__div(X1) ),
    inference(cnf_transformation,[],[f2430]) ).

fof(f2430,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Omod(X1,X0,X0)
      | ~ class_Divides_Osemiring__div(X1) ),
    inference(ennf_transformation,[],[f1456]) ).

fof(f1456,plain,
    ! [X0,X1] :
      ( class_Divides_Osemiring__div(X1)
     => c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Omod(X1,X0,X0) ),
    inference(rectify,[],[f872]) ).

fof(f872,axiom,
    ! [X18,X4] :
      ( class_Divides_Osemiring__div(X4)
     => c_Groups_Ozero__class_Ozero(X4) = c_Divides_Odiv__class_Omod(X4,X18,X18) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__self) ).

fof(f7383,plain,
    spl38_318,
    inference(avatar_split_clause,[],[f4260,f7381]) ).

fof(f7381,plain,
    ( spl38_318
  <=> ! [X0,X1] :
        ( c_Groups_Ominus__class_Ominus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0
        | ~ class_Groups_Ogroup__add(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_318])]) ).

fof(f4260,plain,
    ! [X0,X1] :
      ( c_Groups_Ominus__class_Ominus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0
      | ~ class_Groups_Ogroup__add(X1) ),
    inference(cnf_transformation,[],[f2425]) ).

fof(f2425,plain,
    ! [X0,X1] :
      ( c_Groups_Ominus__class_Ominus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0
      | ~ class_Groups_Ogroup__add(X1) ),
    inference(ennf_transformation,[],[f1451]) ).

fof(f1451,plain,
    ! [X0,X1] :
      ( class_Groups_Ogroup__add(X1)
     => c_Groups_Ominus__class_Ominus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0 ),
    inference(rectify,[],[f969]) ).

fof(f969,axiom,
    ! [X18,X4] :
      ( class_Groups_Ogroup__add(X4)
     => c_Groups_Ominus__class_Ominus(X4,X18,c_Groups_Ozero__class_Ozero(X4)) = X18 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__0__right) ).

fof(f7379,plain,
    spl38_317,
    inference(avatar_split_clause,[],[f4259,f7377]) ).

fof(f7377,plain,
    ( spl38_317
  <=> ! [X0,X1] :
        ( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0)) = X0
        | ~ class_Groups_Ogroup__add(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_317])]) ).

fof(f4259,plain,
    ! [X0,X1] :
      ( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0)) = X0
      | ~ class_Groups_Ogroup__add(X1) ),
    inference(cnf_transformation,[],[f2424]) ).

fof(f2424,plain,
    ! [X0,X1] :
      ( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0)) = X0
      | ~ class_Groups_Ogroup__add(X1) ),
    inference(ennf_transformation,[],[f1450]) ).

fof(f1450,plain,
    ! [X0,X1] :
      ( class_Groups_Ogroup__add(X1)
     => c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0)) = X0 ),
    inference(rectify,[],[f148]) ).

fof(f148,axiom,
    ! [X18,X4] :
      ( class_Groups_Ogroup__add(X4)
     => c_Groups_Ouminus__class_Ouminus(X4,c_Groups_Ouminus__class_Ouminus(X4,X18)) = X18 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__minus) ).

fof(f7375,plain,
    spl38_316,
    inference(avatar_split_clause,[],[f4258,f7373]) ).

fof(f7373,plain,
    ( spl38_316
  <=> ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ominus__class_Ominus(X1,X0,X0)
        | ~ class_Groups_Ogroup__add(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_316])]) ).

fof(f4258,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ominus__class_Ominus(X1,X0,X0)
      | ~ class_Groups_Ogroup__add(X1) ),
    inference(cnf_transformation,[],[f2423]) ).

fof(f2423,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ominus__class_Ominus(X1,X0,X0)
      | ~ class_Groups_Ogroup__add(X1) ),
    inference(ennf_transformation,[],[f1449]) ).

fof(f1449,plain,
    ! [X0,X1] :
      ( class_Groups_Ogroup__add(X1)
     => c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ominus__class_Ominus(X1,X0,X0) ),
    inference(rectify,[],[f970]) ).

fof(f970,axiom,
    ! [X18,X4] :
      ( class_Groups_Ogroup__add(X4)
     => c_Groups_Ozero__class_Ozero(X4) = c_Groups_Ominus__class_Ominus(X4,X18,X18) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__self) ).

fof(f7371,plain,
    spl38_315,
    inference(avatar_split_clause,[],[f4214,f7369]) ).

fof(f7369,plain,
    ( spl38_315
  <=> ! [X0,X1] :
        ( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0)) = X0
        | ~ class_Lattices_Oboolean__algebra(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_315])]) ).

fof(f4214,plain,
    ! [X0,X1] :
      ( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0)) = X0
      | ~ class_Lattices_Oboolean__algebra(X1) ),
    inference(cnf_transformation,[],[f2398]) ).

fof(f2398,plain,
    ! [X0,X1] :
      ( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0)) = X0
      | ~ class_Lattices_Oboolean__algebra(X1) ),
    inference(ennf_transformation,[],[f1425]) ).

fof(f1425,plain,
    ! [X0,X1] :
      ( class_Lattices_Oboolean__algebra(X1)
     => c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0)) = X0 ),
    inference(rectify,[],[f780]) ).

fof(f780,axiom,
    ! [X13,X4] :
      ( class_Lattices_Oboolean__algebra(X4)
     => c_Groups_Ouminus__class_Ouminus(X4,c_Groups_Ouminus__class_Ouminus(X4,X13)) = X13 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__compl) ).

fof(f7367,plain,
    spl38_314,
    inference(avatar_split_clause,[],[f4191,f7365]) ).

fof(f7365,plain,
    ( spl38_314
  <=> ! [X0,X1] :
        ( c_Rings_Oinverse__class_Oinverse(X1,c_Rings_Oinverse__class_Oinverse(X1,X0)) = X0
        | ~ class_Rings_Odivision__ring__inverse__zero(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_314])]) ).

fof(f4191,plain,
    ! [X0,X1] :
      ( c_Rings_Oinverse__class_Oinverse(X1,c_Rings_Oinverse__class_Oinverse(X1,X0)) = X0
      | ~ class_Rings_Odivision__ring__inverse__zero(X1) ),
    inference(cnf_transformation,[],[f2369]) ).

fof(f2369,plain,
    ! [X0,X1] :
      ( c_Rings_Oinverse__class_Oinverse(X1,c_Rings_Oinverse__class_Oinverse(X1,X0)) = X0
      | ~ class_Rings_Odivision__ring__inverse__zero(X1) ),
    inference(ennf_transformation,[],[f1403]) ).

fof(f1403,plain,
    ! [X0,X1] :
      ( class_Rings_Odivision__ring__inverse__zero(X1)
     => c_Rings_Oinverse__class_Oinverse(X1,c_Rings_Oinverse__class_Oinverse(X1,X0)) = X0 ),
    inference(rectify,[],[f819]) ).

fof(f819,axiom,
    ! [X18,X4] :
      ( class_Rings_Odivision__ring__inverse__zero(X4)
     => c_Rings_Oinverse__class_Oinverse(X4,c_Rings_Oinverse__class_Oinverse(X4,X18)) = X18 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__inverse__eq) ).

fof(f7363,plain,
    spl38_313,
    inference(avatar_split_clause,[],[f4164,f7361]) ).

fof(f7361,plain,
    ( spl38_313
  <=> ! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_313])]) ).

fof(f7359,plain,
    spl38_312,
    inference(avatar_split_clause,[],[f4163,f7357]) ).

fof(f7357,plain,
    ( spl38_312
  <=> ! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_312])]) ).

fof(f4163,plain,
    ! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1),
    inference(cnf_transformation,[],[f1362]) ).

fof(f1362,plain,
    ! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1),
    inference(rectify,[],[f716]) ).

fof(f716,axiom,
    ! [X74,X33] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X33,X74) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X74,X33),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__commute) ).

fof(f7355,plain,
    spl38_311,
    inference(avatar_split_clause,[],[f4142,f7353]) ).

fof(f7353,plain,
    ( spl38_311
  <=> ! [X0] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_311])]) ).

fof(f4142,plain,
    ! [X0] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(cnf_transformation,[],[f3487]) ).

fof(f3487,plain,
    ! [X0] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 )
      & ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(nnf_transformation,[],[f1347]) ).

fof(f1347,plain,
    ! [X0] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
    inference(rectify,[],[f352]) ).

fof(f352,axiom,
    ! [X11] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X11,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X11 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__0__eq) ).

fof(f7351,plain,
    spl38_310,
    inference(avatar_split_clause,[],[f4131,f7349]) ).

fof(f7349,plain,
    ( spl38_310
  <=> ! [X0] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_310])]) ).

fof(f4131,plain,
    ! [X0] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
    inference(cnf_transformation,[],[f2358]) ).

fof(f2358,plain,
    ! [X0] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
    inference(ennf_transformation,[],[f1339]) ).

fof(f1339,plain,
    ! [X0] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
    inference(rectify,[],[f334]) ).

fof(f334,axiom,
    ! [X10] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X10
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr0I) ).

fof(f7347,plain,
    spl38_309,
    inference(avatar_split_clause,[],[f4093,f7345]) ).

fof(f7345,plain,
    ( spl38_309
  <=> ! [X0] :
        ( c_Groups_Ozero__class_Ozero(X0) = c_Groups_Ouminus__class_Ouminus(X0,c_Groups_Ozero__class_Ozero(X0))
        | ~ class_Groups_Ogroup__add(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_309])]) ).

fof(f4093,plain,
    ! [X0] :
      ( c_Groups_Ozero__class_Ozero(X0) = c_Groups_Ouminus__class_Ouminus(X0,c_Groups_Ozero__class_Ozero(X0))
      | ~ class_Groups_Ogroup__add(X0) ),
    inference(cnf_transformation,[],[f2320]) ).

fof(f2320,plain,
    ! [X0] :
      ( c_Groups_Ozero__class_Ozero(X0) = c_Groups_Ouminus__class_Ouminus(X0,c_Groups_Ozero__class_Ozero(X0))
      | ~ class_Groups_Ogroup__add(X0) ),
    inference(ennf_transformation,[],[f1301]) ).

fof(f1301,plain,
    ! [X0] :
      ( class_Groups_Ogroup__add(X0)
     => c_Groups_Ozero__class_Ozero(X0) = c_Groups_Ouminus__class_Ouminus(X0,c_Groups_Ozero__class_Ozero(X0)) ),
    inference(rectify,[],[f191]) ).

fof(f191,axiom,
    ! [X4] :
      ( class_Groups_Ogroup__add(X4)
     => c_Groups_Ozero__class_Ozero(X4) = c_Groups_Ouminus__class_Ouminus(X4,c_Groups_Ozero__class_Ozero(X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__zero) ).

fof(f7343,plain,
    spl38_308,
    inference(avatar_split_clause,[],[f4055,f7341]) ).

fof(f7341,plain,
    ( spl38_308
  <=> ! [X0] :
        ( c_Groups_Oone__class_Oone(X0) = c_Rings_Oinverse__class_Oinverse(X0,c_Groups_Oone__class_Oone(X0))
        | ~ class_Rings_Odivision__ring(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_308])]) ).

fof(f4055,plain,
    ! [X0] :
      ( c_Groups_Oone__class_Oone(X0) = c_Rings_Oinverse__class_Oinverse(X0,c_Groups_Oone__class_Oone(X0))
      | ~ class_Rings_Odivision__ring(X0) ),
    inference(cnf_transformation,[],[f2282]) ).

fof(f2282,plain,
    ! [X0] :
      ( c_Groups_Oone__class_Oone(X0) = c_Rings_Oinverse__class_Oinverse(X0,c_Groups_Oone__class_Oone(X0))
      | ~ class_Rings_Odivision__ring(X0) ),
    inference(ennf_transformation,[],[f1263]) ).

fof(f1263,plain,
    ! [X0] :
      ( class_Rings_Odivision__ring(X0)
     => c_Groups_Oone__class_Oone(X0) = c_Rings_Oinverse__class_Oinverse(X0,c_Groups_Oone__class_Oone(X0)) ),
    inference(rectify,[],[f820]) ).

fof(f820,axiom,
    ! [X4] :
      ( class_Rings_Odivision__ring(X4)
     => c_Groups_Oone__class_Oone(X4) = c_Rings_Oinverse__class_Oinverse(X4,c_Groups_Oone__class_Oone(X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__1) ).

fof(f7339,plain,
    spl38_307,
    inference(avatar_split_clause,[],[f4054,f7337]) ).

fof(f7337,plain,
    ( spl38_307
  <=> ! [X0] :
        ( c_Groups_Ozero__class_Ozero(X0) = c_Rings_Oinverse__class_Oinverse(X0,c_Groups_Ozero__class_Ozero(X0))
        | ~ class_Rings_Odivision__ring__inverse__zero(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_307])]) ).

fof(f4054,plain,
    ! [X0] :
      ( c_Groups_Ozero__class_Ozero(X0) = c_Rings_Oinverse__class_Oinverse(X0,c_Groups_Ozero__class_Ozero(X0))
      | ~ class_Rings_Odivision__ring__inverse__zero(X0) ),
    inference(cnf_transformation,[],[f2281]) ).

fof(f2281,plain,
    ! [X0] :
      ( c_Groups_Ozero__class_Ozero(X0) = c_Rings_Oinverse__class_Oinverse(X0,c_Groups_Ozero__class_Ozero(X0))
      | ~ class_Rings_Odivision__ring__inverse__zero(X0) ),
    inference(ennf_transformation,[],[f1262]) ).

fof(f1262,plain,
    ! [X0] :
      ( class_Rings_Odivision__ring__inverse__zero(X0)
     => c_Groups_Ozero__class_Ozero(X0) = c_Rings_Oinverse__class_Oinverse(X0,c_Groups_Ozero__class_Ozero(X0)) ),
    inference(rectify,[],[f815]) ).

fof(f815,axiom,
    ! [X4] :
      ( class_Rings_Odivision__ring__inverse__zero(X4)
     => c_Groups_Ozero__class_Ozero(X4) = c_Rings_Oinverse__class_Oinverse(X4,c_Groups_Ozero__class_Ozero(X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__zero) ).

fof(f7335,plain,
    spl38_306,
    inference(avatar_split_clause,[],[f4053,f7333]) ).

fof(f7333,plain,
    ( spl38_306
  <=> ! [X0] :
        ( c_Groups_Ozero__class_Ozero(X0) = c_Rings_Oinverse__class_Oinverse(X0,c_Groups_Ozero__class_Ozero(X0))
        | ~ class_Fields_Ofield__inverse__zero(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_306])]) ).

fof(f4053,plain,
    ! [X0] :
      ( c_Groups_Ozero__class_Ozero(X0) = c_Rings_Oinverse__class_Oinverse(X0,c_Groups_Ozero__class_Ozero(X0))
      | ~ class_Fields_Ofield__inverse__zero(X0) ),
    inference(cnf_transformation,[],[f2280]) ).

fof(f2280,plain,
    ! [X0] :
      ( c_Groups_Ozero__class_Ozero(X0) = c_Rings_Oinverse__class_Oinverse(X0,c_Groups_Ozero__class_Ozero(X0))
      | ~ class_Fields_Ofield__inverse__zero(X0) ),
    inference(ennf_transformation,[],[f1261]) ).

fof(f1261,plain,
    ! [X0] :
      ( class_Fields_Ofield__inverse__zero(X0)
     => c_Groups_Ozero__class_Ozero(X0) = c_Rings_Oinverse__class_Oinverse(X0,c_Groups_Ozero__class_Ozero(X0)) ),
    inference(rectify,[],[f828]) ).

fof(f828,axiom,
    ! [X4] :
      ( class_Fields_Ofield__inverse__zero(X4)
     => c_Groups_Ozero__class_Ozero(X4) = c_Rings_Oinverse__class_Oinverse(X4,c_Groups_Ozero__class_Ozero(X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_field__inverse__zero) ).

fof(f7331,plain,
    spl38_305,
    inference(avatar_split_clause,[],[f4047,f7329]) ).

fof(f7329,plain,
    ( spl38_305
  <=> ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_305])]) ).

fof(f4047,plain,
    ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X0)),
    inference(cnf_transformation,[],[f1255]) ).

fof(f1255,plain,
    ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X0)),
    inference(rectify,[],[f276]) ).

fof(f276,axiom,
    ! [X19] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__square) ).

fof(f7327,plain,
    spl38_304,
    inference(avatar_split_clause,[],[f4045,f7325]) ).

fof(f7325,plain,
    ( spl38_304
  <=> ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_304])]) ).

fof(f4045,plain,
    ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) = X0,
    inference(cnf_transformation,[],[f1253]) ).

fof(f1253,plain,
    ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) = X0,
    inference(rectify,[],[f419]) ).

fof(f419,axiom,
    ! [X10] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X10) = X10,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__1) ).

fof(f7323,plain,
    spl38_303,
    inference(avatar_split_clause,[],[f4044,f7321]) ).

fof(f7321,plain,
    ( spl38_303
  <=> ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_303])]) ).

fof(f4044,plain,
    ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X0) = X0,
    inference(cnf_transformation,[],[f1252]) ).

fof(f1252,plain,
    ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X0) = X0,
    inference(rectify,[],[f741]) ).

fof(f741,axiom,
    ! [X33] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X33) = X33,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__1) ).

fof(f7319,plain,
    spl38_302,
    inference(avatar_split_clause,[],[f4043,f7317]) ).

fof(f7317,plain,
    ( spl38_302
  <=> ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_302])]) ).

fof(f4043,plain,
    ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0,
    inference(cnf_transformation,[],[f1251]) ).

fof(f1251,plain,
    ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0,
    inference(rectify,[],[f421]) ).

fof(f421,axiom,
    ! [X10] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X10),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X10,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__1__right) ).

fof(f7315,plain,
    spl38_301,
    inference(avatar_split_clause,[],[f4042,f7313]) ).

fof(f7313,plain,
    ( spl38_301
  <=> ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_301])]) ).

fof(f4042,plain,
    ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X0,
    inference(cnf_transformation,[],[f1250]) ).

fof(f1250,plain,
    ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X0,
    inference(rectify,[],[f740]) ).

fof(f740,axiom,
    ! [X33] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X33),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X33,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__1__right) ).

fof(f7311,plain,
    ( ~ spl38_128
    | ~ spl38_216
    | spl38_298 ),
    inference(avatar_split_clause,[],[f7293,f7272,f6910,f6531]) ).

fof(f6910,plain,
    ( spl38_216
  <=> ! [X0] :
        ( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Ocomm__semiring__1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_216])]) ).

fof(f7272,plain,
    ( spl38_298
  <=> class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_298])]) ).

fof(f7293,plain,
    ( ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)
    | ~ spl38_216
    | spl38_298 ),
    inference(resolution,[],[f7274,f6911]) ).

fof(f6911,plain,
    ( ! [X0] :
        ( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Ocomm__semiring__1(X0) )
    | ~ spl38_216 ),
    inference(avatar_component_clause,[],[f6910]) ).

fof(f7274,plain,
    ( ~ class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | spl38_298 ),
    inference(avatar_component_clause,[],[f7272]) ).

fof(f7310,plain,
    spl38_300,
    inference(avatar_split_clause,[],[f4040,f7308]) ).

fof(f7308,plain,
    ( spl38_300
  <=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_300])]) ).

fof(f4040,plain,
    ! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X0),
    inference(cnf_transformation,[],[f1248]) ).

fof(f1248,plain,
    ! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X0),
    inference(rectify,[],[f728]) ).

fof(f728,axiom,
    ! [X33] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X33),X33),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zminus__inverse2) ).

fof(f7279,plain,
    ( ~ spl38_298
    | ~ spl38_299
    | ~ spl38_3
    | ~ spl38_261 ),
    inference(avatar_split_clause,[],[f7153,f7104,f5906,f7276,f7272]) ).

fof(f7276,plain,
    ( spl38_299
  <=> v_s____ = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_299])]) ).

fof(f7104,plain,
    ( spl38_261
  <=> ! [X0] :
        ( c_Groups_Ozero__class_Ozero(X0) != c_Groups_Oone__class_Oone(X0)
        | ~ class_Rings_Ozero__neq__one(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_261])]) ).

fof(f7153,plain,
    ( v_s____ != c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl38_3
    | ~ spl38_261 ),
    inference(superposition,[],[f7105,f5908]) ).

fof(f7105,plain,
    ( ! [X0] :
        ( c_Groups_Ozero__class_Ozero(X0) != c_Groups_Oone__class_Oone(X0)
        | ~ class_Rings_Ozero__neq__one(X0) )
    | ~ spl38_261 ),
    inference(avatar_component_clause,[],[f7104]) ).

fof(f7270,plain,
    spl38_297,
    inference(avatar_split_clause,[],[f5764,f7268]) ).

fof(f7268,plain,
    ( spl38_297
  <=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_297])]) ).

fof(f5764,plain,
    ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(forward_demodulation,[],[f5763,f4029]) ).

fof(f5763,plain,
    ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(forward_demodulation,[],[f5409,f5407]) ).

fof(f5409,plain,
    ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
    inference(definition_unfolding,[],[f4041,f4035]) ).

fof(f4041,plain,
    ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(cnf_transformation,[],[f1249]) ).

fof(f1249,plain,
    ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(rectify,[],[f911]) ).

fof(f911,axiom,
    ! [X19] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__1) ).

fof(f7266,plain,
    spl38_296,
    inference(avatar_split_clause,[],[f5713,f7264]) ).

fof(f5713,plain,
    ! [X2,X1] : sP9(c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X1,X2,c_Groups_Ozero__class_Ozero(X2)),
    inference(equality_resolution,[],[f5712]) ).

fof(f5712,plain,
    ! [X2,X0,X1] :
      ( sP9(X0,X1,X2,c_Groups_Ozero__class_Ozero(X2))
      | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X0 ),
    inference(equality_resolution,[],[f5091]) ).

fof(f5091,plain,
    ! [X2,X3,X0,X1] :
      ( sP9(X0,X1,X2,X3)
      | c_Groups_Ozero__class_Ozero(X2) != X3
      | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X0 ),
    inference(cnf_transformation,[],[f3779]) ).

fof(f7262,plain,
    spl38_295,
    inference(avatar_split_clause,[],[f5611,f7260]) ).

fof(f7260,plain,
    ( spl38_295
  <=> ! [X1] : c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_295])]) ).

fof(f5611,plain,
    ! [X1] : c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(equality_resolution,[],[f4520]) ).

fof(f4520,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
      | X0 != X1 ),
    inference(cnf_transformation,[],[f3599]) ).

fof(f7258,plain,
    spl38_294,
    inference(avatar_split_clause,[],[f5405,f7256]) ).

fof(f7256,plain,
    ( spl38_294
  <=> ! [X0] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_294])]) ).

fof(f5405,plain,
    ! [X0] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
    inference(definition_unfolding,[],[f4021,f4035]) ).

fof(f4021,plain,
    ! [X0] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X0)),
    inference(cnf_transformation,[],[f1229]) ).

fof(f1229,plain,
    ! [X0] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X0)),
    inference(rectify,[],[f230]) ).

fof(f230,axiom,
    ! [X10] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,c_Nat_OSuc(X10)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lessI) ).

fof(f7254,plain,
    spl38_293,
    inference(avatar_split_clause,[],[f5404,f7252]) ).

fof(f7252,plain,
    ( spl38_293
  <=> ! [X0] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_293])]) ).

fof(f5404,plain,
    ! [X0] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0),
    inference(definition_unfolding,[],[f4018,f4035]) ).

fof(f4018,plain,
    ! [X0] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X0),X0),
    inference(cnf_transformation,[],[f1226]) ).

fof(f1226,plain,
    ! [X0] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X0),X0),
    inference(rectify,[],[f360]) ).

fof(f360,axiom,
    ! [X10] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X10),X10),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__le__n) ).

fof(f7250,plain,
    spl38_292,
    inference(avatar_split_clause,[],[f5398,f7248]) ).

fof(f7248,plain,
    ( spl38_292
  <=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_292])]) ).

fof(f5398,plain,
    ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(definition_unfolding,[],[f4009,f4035]) ).

fof(f4009,plain,
    ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X0),
    inference(cnf_transformation,[],[f1217]) ).

fof(f1217,plain,
    ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X0),
    inference(rectify,[],[f329]) ).

fof(f329,axiom,
    ! [X44] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X44),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osimps_I3_J) ).

fof(f7246,plain,
    spl38_291,
    inference(avatar_split_clause,[],[f5322,f7244]) ).

fof(f7244,plain,
    ( spl38_291
  <=> ! [X4,X0,X3,X2,X1] :
        ( sP17(X3,X1,X2,X4,X0)
        | ~ class_Fields_Ofield(X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_291])]) ).

fof(f5322,plain,
    ! [X2,X3,X0,X1,X4] :
      ( sP17(X3,X1,X2,X4,X0)
      | ~ class_Fields_Ofield(X4) ),
    inference(cnf_transformation,[],[f3478]) ).

fof(f3478,plain,
    ! [X0,X1,X2,X3,X4] :
      ( sP17(X3,X1,X2,X4,X0)
      | ~ class_Fields_Ofield(X4) ),
    inference(definition_folding,[],[f3359,f3477,f3476,f3475]) ).

fof(f3477,plain,
    ! [X3,X1,X2,X4,X0] :
      ( ( c_Polynomial_Opdivmod__rel(X4,X3,X2,X1,X0)
      <=> sP16(X0,X4,X2,X1,X3) )
      | ~ sP17(X3,X1,X2,X4,X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP17])]) ).

fof(f3359,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ( c_Polynomial_Opdivmod__rel(X4,X3,X2,X1,X0)
      <=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X4,X0),c_Polynomial_Odegree(X4,X2))
            | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X0
            | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X2 )
          & ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X1
            | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) != X2 )
          & c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4)),X1),X2),X0) = X3 ) )
      | ~ class_Fields_Ofield(X4) ),
    inference(flattening,[],[f3358]) ).

fof(f3358,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ( c_Polynomial_Opdivmod__rel(X4,X3,X2,X1,X0)
      <=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X4,X0),c_Polynomial_Odegree(X4,X2))
            | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X0
            | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X2 )
          & ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X1
            | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) != X2 )
          & c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4)),X1),X2),X0) = X3 ) )
      | ~ class_Fields_Ofield(X4) ),
    inference(ennf_transformation,[],[f2194]) ).

fof(f2194,plain,
    ! [X0,X1,X2,X3,X4] :
      ( class_Fields_Ofield(X4)
     => ( c_Polynomial_Opdivmod__rel(X4,X3,X2,X1,X0)
      <=> ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) != X2
           => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X4,X0),c_Polynomial_Odegree(X4,X2))
              | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X0 ) )
          & ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X2
           => c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X1 )
          & c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4)),X1),X2),X0) = X3 ) ) ),
    inference(rectify,[],[f629]) ).

fof(f629,axiom,
    ! [X63,X15,X17,X3,X4] :
      ( class_Fields_Ofield(X4)
     => ( c_Polynomial_Opdivmod__rel(X4,X3,X17,X15,X63)
      <=> ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) != X17
           => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X4,X63),c_Polynomial_Odegree(X4,X17))
              | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X63 ) )
          & ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X17
           => c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X15 )
          & c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4)),X15),X17),X63) = X3 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__rel__def) ).

fof(f7242,plain,
    spl38_290,
    inference(avatar_split_clause,[],[f4999,f7240]) ).

fof(f7240,plain,
    ( spl38_290
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
        | ~ sP6(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_290])]) ).

fof(f4999,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
      | ~ sP6(X0,X1,X2) ),
    inference(cnf_transformation,[],[f3735]) ).

fof(f7238,plain,
    spl38_289,
    inference(avatar_split_clause,[],[f4451,f7236]) ).

fof(f7236,plain,
    ( spl38_289
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_289])]) ).

fof(f4451,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
    inference(cnf_transformation,[],[f3553]) ).

fof(f7234,plain,
    spl38_288,
    inference(avatar_split_clause,[],[f4362,f7232]) ).

fof(f7232,plain,
    ( spl38_288
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_288])]) ).

fof(f4362,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
    inference(cnf_transformation,[],[f2524]) ).

fof(f2524,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
    inference(ennf_transformation,[],[f1542]) ).

fof(f1542,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
    inference(rectify,[],[f363]) ).

fof(f363,axiom,
    ! [X10,X19] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X10)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__le__nat) ).

fof(f7230,plain,
    spl38_287,
    inference(avatar_split_clause,[],[f4187,f7228]) ).

fof(f7228,plain,
    ( spl38_287
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_287])]) ).

fof(f4187,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
    inference(cnf_transformation,[],[f1384]) ).

fof(f1384,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
    inference(rectify,[],[f319]) ).

fof(f319,axiom,
    ! [X10,X19] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X10,X19)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__linear) ).

fof(f7226,plain,
    spl38_286,
    inference(avatar_split_clause,[],[f4186,f7224]) ).

fof(f7224,plain,
    ( spl38_286
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_286])]) ).

fof(f4186,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ),
    inference(cnf_transformation,[],[f1383]) ).

fof(f1383,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ),
    inference(rectify,[],[f732]) ).

fof(f732,axiom,
    ! [X74,X33] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X74,X33)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X33,X74) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__linear) ).

fof(f7222,plain,
    spl38_285,
    inference(avatar_split_clause,[],[f4102,f7220]) ).

fof(f7220,plain,
    ( spl38_285
  <=> ! [X0] :
        ( c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oone__class_Oone(X0))
        | ~ class_Rings_Olinordered__semidom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_285])]) ).

fof(f4102,plain,
    ! [X0] :
      ( c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oone__class_Oone(X0))
      | ~ class_Rings_Olinordered__semidom(X0) ),
    inference(cnf_transformation,[],[f2329]) ).

fof(f2329,plain,
    ! [X0] :
      ( c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oone__class_Oone(X0))
      | ~ class_Rings_Olinordered__semidom(X0) ),
    inference(ennf_transformation,[],[f1310]) ).

fof(f1310,plain,
    ! [X0] :
      ( class_Rings_Olinordered__semidom(X0)
     => c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oone__class_Oone(X0)) ),
    inference(rectify,[],[f74]) ).

fof(f74,axiom,
    ! [X4] :
      ( class_Rings_Olinordered__semidom(X4)
     => c_Orderings_Oord__class_Oless(X4,c_Groups_Ozero__class_Ozero(X4),c_Groups_Oone__class_Oone(X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__one) ).

fof(f7218,plain,
    spl38_284,
    inference(avatar_split_clause,[],[f4101,f7216]) ).

fof(f7216,plain,
    ( spl38_284
  <=> ! [X0] :
        ( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oone__class_Oone(X0))
        | ~ class_Rings_Olinordered__semidom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_284])]) ).

fof(f4101,plain,
    ! [X0] :
      ( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oone__class_Oone(X0))
      | ~ class_Rings_Olinordered__semidom(X0) ),
    inference(cnf_transformation,[],[f2328]) ).

fof(f2328,plain,
    ! [X0] :
      ( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oone__class_Oone(X0))
      | ~ class_Rings_Olinordered__semidom(X0) ),
    inference(ennf_transformation,[],[f1309]) ).

fof(f1309,plain,
    ! [X0] :
      ( class_Rings_Olinordered__semidom(X0)
     => c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oone__class_Oone(X0)) ),
    inference(rectify,[],[f75]) ).

fof(f75,axiom,
    ! [X4] :
      ( class_Rings_Olinordered__semidom(X4)
     => c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),c_Groups_Oone__class_Oone(X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__one) ).

fof(f7214,plain,
    spl38_283,
    inference(avatar_split_clause,[],[f4100,f7212]) ).

fof(f7212,plain,
    ( spl38_283
  <=> ! [X0] :
        ( ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Ozero__class_Ozero(X0))
        | ~ class_Rings_Olinordered__semidom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_283])]) ).

fof(f4100,plain,
    ! [X0] :
      ( ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Ozero__class_Ozero(X0))
      | ~ class_Rings_Olinordered__semidom(X0) ),
    inference(cnf_transformation,[],[f2327]) ).

fof(f2327,plain,
    ! [X0] :
      ( ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Ozero__class_Ozero(X0))
      | ~ class_Rings_Olinordered__semidom(X0) ),
    inference(ennf_transformation,[],[f1308]) ).

fof(f1308,plain,
    ! [X0] :
      ( class_Rings_Olinordered__semidom(X0)
     => ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Ozero__class_Ozero(X0)) ),
    inference(rectify,[],[f71]) ).

fof(f71,axiom,
    ! [X4] :
      ( class_Rings_Olinordered__semidom(X4)
     => ~ c_Orderings_Oord__class_Oless(X4,c_Groups_Oone__class_Oone(X4),c_Groups_Ozero__class_Ozero(X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__one__less__zero) ).

fof(f7210,plain,
    spl38_282,
    inference(avatar_split_clause,[],[f4099,f7208]) ).

fof(f4099,plain,
    ! [X0] :
      ( ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Ozero__class_Ozero(X0))
      | ~ class_Rings_Olinordered__semidom(X0) ),
    inference(cnf_transformation,[],[f2326]) ).

fof(f2326,plain,
    ! [X0] :
      ( ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Ozero__class_Ozero(X0))
      | ~ class_Rings_Olinordered__semidom(X0) ),
    inference(ennf_transformation,[],[f1307]) ).

fof(f1307,plain,
    ! [X0] :
      ( class_Rings_Olinordered__semidom(X0)
     => ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Ozero__class_Ozero(X0)) ),
    inference(rectify,[],[f72]) ).

fof(f72,axiom,
    ! [X4] :
      ( class_Rings_Olinordered__semidom(X4)
     => ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Oone__class_Oone(X4),c_Groups_Ozero__class_Ozero(X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__one__le__zero) ).

fof(f7206,plain,
    spl38_281,
    inference(avatar_split_clause,[],[f4039,f7204]) ).

fof(f7204,plain,
    ( spl38_281
  <=> ! [X0] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_281])]) ).

fof(f4039,plain,
    ! [X0] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)),
    inference(cnf_transformation,[],[f1247]) ).

fof(f1247,plain,
    ! [X0] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)),
    inference(rectify,[],[f438]) ).

fof(f438,axiom,
    ! [X13] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X13)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gcd__lcm__complete__lattice__nat_Obot__least) ).

fof(f7202,plain,
    spl38_280,
    inference(avatar_split_clause,[],[f4038,f7200]) ).

fof(f7200,plain,
    ( spl38_280
  <=> ! [X0] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_280])]) ).

fof(f4038,plain,
    ! [X0] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(cnf_transformation,[],[f1246]) ).

fof(f1246,plain,
    ! [X0] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(rectify,[],[f447]) ).

fof(f447,axiom,
    ! [X13] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X13),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gcd__lcm__complete__lattice__nat_Otop__greatest) ).

fof(f7198,plain,
    spl38_279,
    inference(avatar_split_clause,[],[f4034,f7196]) ).

fof(f7196,plain,
    ( spl38_279
  <=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_279])]) ).

fof(f4034,plain,
    ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0),
    inference(cnf_transformation,[],[f1242]) ).

fof(f1242,plain,
    ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0),
    inference(rectify,[],[f967]) ).

fof(f967,axiom,
    ! [X10] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X10),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__0__eq__0) ).

fof(f7194,plain,
    spl38_278,
    inference(avatar_split_clause,[],[f4033,f7192]) ).

fof(f7192,plain,
    ( spl38_278
  <=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_278])]) ).

fof(f4033,plain,
    ! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0),
    inference(cnf_transformation,[],[f1241]) ).

fof(f1241,plain,
    ! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0),
    inference(rectify,[],[f919]) ).

fof(f919,axiom,
    ! [X27] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X27),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zero) ).

fof(f7190,plain,
    spl38_277,
    inference(avatar_split_clause,[],[f3994,f7187]) ).

fof(f7187,plain,
    ( spl38_277
  <=> c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_a____) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_277])]) ).

fof(f3994,plain,
    c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_a____),
    inference(cnf_transformation,[],[f18]) ).

fof(f18,axiom,
    c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_a____),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_a) ).

fof(f7185,plain,
    ( ~ spl38_276
    | spl38_275 ),
    inference(avatar_split_clause,[],[f7180,f7176,f7182]) ).

fof(f7182,plain,
    ( spl38_276
  <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),v_s____))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))),v_pa____)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_276])]) ).

fof(f7176,plain,
    ( spl38_275
  <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),v_s____))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_pa____)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_275])]) ).

fof(f7180,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),v_s____))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))),v_pa____))
    | spl38_275 ),
    inference(forward_demodulation,[],[f7178,f4164]) ).

fof(f7178,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),v_s____))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_pa____))
    | spl38_275 ),
    inference(avatar_component_clause,[],[f7176]) ).

fof(f7179,plain,
    ~ spl38_275,
    inference(avatar_split_clause,[],[f5758,f7176]) ).

fof(f5758,plain,
    ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),v_s____))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_pa____)),
    inference(forward_demodulation,[],[f5395,f3837]) ).

fof(f3837,plain,
    c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_s____,
    inference(cnf_transformation,[],[f1208]) ).

fof(f1208,plain,
    c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_s____,
    inference(flattening,[],[f1207]) ).

fof(f1207,negated_conjecture,
    ~ ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_s____ ),
    inference(negated_conjecture,[],[f1206]) ).

fof(f1206,conjecture,
    c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_s____,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

fof(f5395,plain,
    ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_pa____)),
    inference(definition_unfolding,[],[f3998,f4035]) ).

fof(f3998,plain,
    ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Nat_OSuc(c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))),v_pa____)),
    inference(cnf_transformation,[],[f70]) ).

fof(f70,axiom,
    ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Nat_OSuc(c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))),v_pa____)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ap_I2_J) ).

fof(f7173,plain,
    ( ~ spl38_273
    | ~ spl38_274
    | ~ spl38_3
    | ~ spl38_260 ),
    inference(avatar_split_clause,[],[f7152,f7100,f5906,f7170,f7166]) ).

fof(f7166,plain,
    ( spl38_273
  <=> class_Rings_Olinordered__idom(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_273])]) ).

fof(f7170,plain,
    ( spl38_274
  <=> c_Polynomial_Opos__poly(tc_Complex_Ocomplex,v_s____) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_274])]) ).

fof(f7100,plain,
    ( spl38_260
  <=> ! [X0] :
        ( ~ c_Polynomial_Opos__poly(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))
        | ~ class_Rings_Olinordered__idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_260])]) ).

fof(f7152,plain,
    ( ~ c_Polynomial_Opos__poly(tc_Complex_Ocomplex,v_s____)
    | ~ class_Rings_Olinordered__idom(tc_Complex_Ocomplex)
    | ~ spl38_3
    | ~ spl38_260 ),
    inference(superposition,[],[f7101,f5908]) ).

fof(f7101,plain,
    ( ! [X0] :
        ( ~ c_Polynomial_Opos__poly(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))
        | ~ class_Rings_Olinordered__idom(X0) )
    | ~ spl38_260 ),
    inference(avatar_component_clause,[],[f7100]) ).

fof(f7150,plain,
    spl38_272,
    inference(avatar_split_clause,[],[f5396,f7148]) ).

fof(f5396,plain,
    ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X0,
    inference(definition_unfolding,[],[f4003,f4035]) ).

fof(f4003,plain,
    ! [X0] : c_Nat_OSuc(X0) != X0,
    inference(cnf_transformation,[],[f1211]) ).

fof(f1211,plain,
    ! [X0] : c_Nat_OSuc(X0) != X0,
    inference(rectify,[],[f307]) ).

fof(f307,axiom,
    ! [X10] : c_Nat_OSuc(X10) != X10,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).

fof(f7146,plain,
    spl38_271,
    inference(avatar_split_clause,[],[f5128,f7144]) ).

fof(f7144,plain,
    ( spl38_271
  <=> ! [X0,X3,X2,X1] :
        ( sP14(X1,X3,X0,X2)
        | ~ class_Rings_Olinordered__ring__strict(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_271])]) ).

fof(f5128,plain,
    ! [X2,X3,X0,X1] :
      ( sP14(X1,X3,X0,X2)
      | ~ class_Rings_Olinordered__ring__strict(X3) ),
    inference(cnf_transformation,[],[f3474]) ).

fof(f3474,plain,
    ! [X0,X1,X2,X3] :
      ( sP14(X1,X3,X0,X2)
      | ~ class_Rings_Olinordered__ring__strict(X3) ),
    inference(definition_folding,[],[f3109,f3473,f3472]) ).

fof(f3473,plain,
    ! [X1,X3,X0,X2] :
      ( ( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
      <=> sP13(X2,X0,X3,X1) )
      | ~ sP14(X1,X3,X0,X2) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP14])]) ).

fof(f3109,plain,
    ! [X0,X1,X2,X3] :
      ( ( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
      <=> ( ( c_Orderings_Oord__class_Oless(X3,X0,X2)
            & c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Ozero__class_Ozero(X3)) )
          | ( c_Orderings_Oord__class_Oless(X3,X2,X0)
            & c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1) ) ) )
      | ~ class_Rings_Olinordered__ring__strict(X3) ),
    inference(ennf_transformation,[],[f2029]) ).

fof(f2029,plain,
    ! [X0,X1,X2,X3] :
      ( class_Rings_Olinordered__ring__strict(X3)
     => ( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
      <=> ( ( c_Orderings_Oord__class_Oless(X3,X0,X2)
            & c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Ozero__class_Ozero(X3)) )
          | ( c_Orderings_Oord__class_Oless(X3,X2,X0)
            & c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1) ) ) ) ),
    inference(rectify,[],[f80]) ).

fof(f80,axiom,
    ! [X20,X23,X12,X4] :
      ( class_Rings_Olinordered__ring__strict(X4)
     => ( c_Orderings_Oord__class_Oless(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X23),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X20),X23))
      <=> ( ( c_Orderings_Oord__class_Oless(X4,X20,X12)
            & c_Orderings_Oord__class_Oless(X4,X23,c_Groups_Ozero__class_Ozero(X4)) )
          | ( c_Orderings_Oord__class_Oless(X4,X12,X20)
            & c_Orderings_Oord__class_Oless(X4,c_Groups_Ozero__class_Ozero(X4),X23) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__right__disj) ).

fof(f7142,plain,
    spl38_270,
    inference(avatar_split_clause,[],[f5119,f7140]) ).

fof(f7140,plain,
    ( spl38_270
  <=> ! [X0,X3,X2,X1] :
        ( sP12(X2,X3,X0,X1)
        | ~ class_Rings_Olinordered__ring__strict(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_270])]) ).

fof(f5119,plain,
    ! [X2,X3,X0,X1] :
      ( sP12(X2,X3,X0,X1)
      | ~ class_Rings_Olinordered__ring__strict(X3) ),
    inference(cnf_transformation,[],[f3471]) ).

fof(f3471,plain,
    ! [X0,X1,X2,X3] :
      ( sP12(X2,X3,X0,X1)
      | ~ class_Rings_Olinordered__ring__strict(X3) ),
    inference(definition_folding,[],[f3108,f3470,f3469]) ).

fof(f3470,plain,
    ! [X2,X3,X0,X1] :
      ( ( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
      <=> sP11(X1,X0,X3,X2) )
      | ~ sP12(X2,X3,X0,X1) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP12])]) ).

fof(f3108,plain,
    ! [X0,X1,X2,X3] :
      ( ( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
      <=> ( ( c_Orderings_Oord__class_Oless(X3,X0,X1)
            & c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3)) )
          | ( c_Orderings_Oord__class_Oless(X3,X1,X0)
            & c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2) ) ) )
      | ~ class_Rings_Olinordered__ring__strict(X3) ),
    inference(ennf_transformation,[],[f2028]) ).

fof(f2028,plain,
    ! [X0,X1,X2,X3] :
      ( class_Rings_Olinordered__ring__strict(X3)
     => ( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
      <=> ( ( c_Orderings_Oord__class_Oless(X3,X0,X1)
            & c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3)) )
          | ( c_Orderings_Oord__class_Oless(X3,X1,X0)
            & c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2) ) ) ) ),
    inference(rectify,[],[f81]) ).

fof(f81,axiom,
    ! [X20,X12,X23,X4] :
      ( class_Rings_Olinordered__ring__strict(X4)
     => ( c_Orderings_Oord__class_Oless(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X23),X12),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X23),X20))
      <=> ( ( c_Orderings_Oord__class_Oless(X4,X20,X12)
            & c_Orderings_Oord__class_Oless(X4,X23,c_Groups_Ozero__class_Ozero(X4)) )
          | ( c_Orderings_Oord__class_Oless(X4,X12,X20)
            & c_Orderings_Oord__class_Oless(X4,c_Groups_Ozero__class_Ozero(X4),X23) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__disj) ).

fof(f7138,plain,
    spl38_269,
    inference(avatar_split_clause,[],[f5094,f7136]) ).

fof(f7136,plain,
    ( spl38_269
  <=> ! [X0,X3,X2,X1] :
        ( sP10(X2,X3,X1,X0)
        | ~ class_Fields_Ofield(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_269])]) ).

fof(f5094,plain,
    ! [X2,X3,X0,X1] :
      ( sP10(X2,X3,X1,X0)
      | ~ class_Fields_Ofield(X3) ),
    inference(cnf_transformation,[],[f3468]) ).

fof(f3468,plain,
    ! [X0,X1,X2,X3] :
      ( sP10(X2,X3,X1,X0)
      | ~ class_Fields_Ofield(X3) ),
    inference(definition_folding,[],[f3086,f3467,f3466]) ).

fof(f3467,plain,
    ! [X2,X3,X1,X0] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),c_Polynomial_Osmult(X3,X2,X1)),X0))
      <=> sP9(X0,X1,X3,X2) )
      | ~ sP10(X2,X3,X1,X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP10])]) ).

fof(f3086,plain,
    ! [X0,X1,X2,X3] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),c_Polynomial_Osmult(X3,X2,X1)),X0))
      <=> ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X1),X0))
            | c_Groups_Ozero__class_Ozero(X3) = X2 )
          & ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X0
            | c_Groups_Ozero__class_Ozero(X3) != X2 ) ) )
      | ~ class_Fields_Ofield(X3) ),
    inference(ennf_transformation,[],[f2015]) ).

fof(f2015,plain,
    ! [X0,X1,X2,X3] :
      ( class_Fields_Ofield(X3)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),c_Polynomial_Osmult(X3,X2,X1)),X0))
      <=> ( ( c_Groups_Ozero__class_Ozero(X3) != X2
           => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X1),X0)) )
          & ( c_Groups_Ozero__class_Ozero(X3) = X2
           => c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X0 ) ) ) ),
    inference(rectify,[],[f33]) ).

fof(f33,axiom,
    ! [X15,X7,X12,X4] :
      ( class_Fields_Ofield(X4)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4)),c_Polynomial_Osmult(X4,X12,X7)),X15))
      <=> ( ( c_Groups_Ozero__class_Ozero(X4) != X12
           => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4)),X7),X15)) )
          & ( c_Groups_Ozero__class_Ozero(X4) = X12
           => c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X15 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__dvd__iff) ).

fof(f7134,plain,
    spl38_268,
    inference(avatar_split_clause,[],[f4185,f7132]) ).

fof(f7132,plain,
    ( spl38_268
  <=> ! [X0,X1] :
        ( X0 = X1
        | ~ hBOOL(c_fequal(X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_268])]) ).

fof(f4185,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ hBOOL(c_fequal(X1,X0)) ),
    inference(cnf_transformation,[],[f1382]) ).

fof(f1382,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ hBOOL(c_fequal(X1,X0)) ),
    inference(rectify,[],[f1204]) ).

fof(f1204,axiom,
    ! [X17,X3] :
      ( X3 = X17
      | ~ hBOOL(c_fequal(X3,X17)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__1) ).

fof(f7130,plain,
    spl38_267,
    inference(avatar_split_clause,[],[f4159,f7128]) ).

fof(f7128,plain,
    ( spl38_267
  <=> ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_267])]) ).

fof(f4159,plain,
    ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0),X1),
    inference(cnf_transformation,[],[f1358]) ).

fof(f1358,plain,
    ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0),X1),
    inference(rectify,[],[f926]) ).

fof(f926,axiom,
    ! [X10,X19] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X10),X19),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__less__eq__dividend) ).

fof(f7126,plain,
    spl38_266,
    inference(avatar_split_clause,[],[f4158,f7124]) ).

fof(f7124,plain,
    ( spl38_266
  <=> ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_266])]) ).

fof(f4158,plain,
    ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0),X1),
    inference(cnf_transformation,[],[f1357]) ).

fof(f1357,plain,
    ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0),X1),
    inference(rectify,[],[f980]) ).

fof(f980,axiom,
    ! [X10,X19] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X10),X19),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__le__self) ).

fof(f7122,plain,
    spl38_265,
    inference(avatar_split_clause,[],[f4157,f7120]) ).

fof(f7120,plain,
    ( spl38_265
  <=> ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_265])]) ).

fof(f4157,plain,
    ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)),
    inference(cnf_transformation,[],[f1356]) ).

fof(f1356,plain,
    ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)),
    inference(rectify,[],[f654]) ).

fof(f654,axiom,
    ! [X19,X10] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X10,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add1) ).

fof(f7118,plain,
    spl38_264,
    inference(avatar_split_clause,[],[f4156,f7116]) ).

fof(f7116,plain,
    ( spl38_264
  <=> ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_264])]) ).

fof(f4156,plain,
    ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)),
    inference(cnf_transformation,[],[f1355]) ).

fof(f1355,plain,
    ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)),
    inference(rectify,[],[f653]) ).

fof(f653,axiom,
    ! [X19,X10] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X10,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X10)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add2) ).

fof(f7114,plain,
    spl38_263,
    inference(avatar_split_clause,[],[f4155,f7112]) ).

fof(f7112,plain,
    ( spl38_263
  <=> ! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_263])]) ).

fof(f4155,plain,
    ! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X0),
    inference(cnf_transformation,[],[f1354]) ).

fof(f1354,plain,
    ! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X0),
    inference(rectify,[],[f644]) ).

fof(f644,axiom,
    ! [X38,X37] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X37,X38),X38),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__add__less2) ).

fof(f7110,plain,
    spl38_262,
    inference(avatar_split_clause,[],[f4154,f7108]) ).

fof(f7108,plain,
    ( spl38_262
  <=> ! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_262])]) ).

fof(f4154,plain,
    ! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X1),
    inference(cnf_transformation,[],[f1353]) ).

fof(f1353,plain,
    ! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X1),
    inference(rectify,[],[f643]) ).

fof(f643,axiom,
    ! [X37,X38] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X38,X37),X38),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__add__less1) ).

fof(f7106,plain,
    spl38_261,
    inference(avatar_split_clause,[],[f4107,f7104]) ).

fof(f4107,plain,
    ! [X0] :
      ( c_Groups_Ozero__class_Ozero(X0) != c_Groups_Oone__class_Oone(X0)
      | ~ class_Rings_Ozero__neq__one(X0) ),
    inference(cnf_transformation,[],[f2334]) ).

fof(f2334,plain,
    ! [X0] :
      ( c_Groups_Ozero__class_Ozero(X0) != c_Groups_Oone__class_Oone(X0)
      | ~ class_Rings_Ozero__neq__one(X0) ),
    inference(ennf_transformation,[],[f1315]) ).

fof(f1315,plain,
    ! [X0] :
      ( class_Rings_Ozero__neq__one(X0)
     => c_Groups_Ozero__class_Ozero(X0) != c_Groups_Oone__class_Oone(X0) ),
    inference(rectify,[],[f169]) ).

fof(f169,axiom,
    ! [X4] :
      ( class_Rings_Ozero__neq__one(X4)
     => c_Groups_Ozero__class_Ozero(X4) != c_Groups_Oone__class_Oone(X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__neq__zero) ).

fof(f7102,plain,
    spl38_260,
    inference(avatar_split_clause,[],[f4083,f7100]) ).

fof(f4083,plain,
    ! [X0] :
      ( ~ c_Polynomial_Opos__poly(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(cnf_transformation,[],[f2310]) ).

fof(f2310,plain,
    ! [X0] :
      ( ~ c_Polynomial_Opos__poly(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(ennf_transformation,[],[f1291]) ).

fof(f1291,plain,
    ! [X0] :
      ( class_Rings_Olinordered__idom(X0)
     => ~ c_Polynomial_Opos__poly(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) ),
    inference(rectify,[],[f747]) ).

fof(f747,axiom,
    ! [X4] :
      ( class_Rings_Olinordered__idom(X4)
     => ~ c_Polynomial_Opos__poly(X4,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__pos__poly__0) ).

fof(f7098,plain,
    spl38_259,
    inference(avatar_split_clause,[],[f4032,f7096]) ).

fof(f7096,plain,
    ( spl38_259
  <=> ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,X0,v_pa____),v_na____) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_259])]) ).

fof(f4032,plain,
    ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,X0,v_pa____),v_na____),
    inference(cnf_transformation,[],[f1240]) ).

fof(f1240,plain,
    ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,X0,v_pa____),v_na____),
    inference(rectify,[],[f58]) ).

fof(f58,axiom,
    ! [X18] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,X18,v_pa____),v_na____),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_oop) ).

fof(f7094,plain,
    spl38_258,
    inference(avatar_split_clause,[],[f4031,f7092]) ).

fof(f7092,plain,
    ( spl38_258
  <=> ! [X0] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_258])]) ).

fof(f4031,plain,
    ! [X0] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X0)),
    inference(cnf_transformation,[],[f1239]) ).

fof(f1239,plain,
    ! [X0] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X0)),
    inference(rectify,[],[f235]) ).

fof(f235,axiom,
    ! [X13] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X13),X13)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oorder__refl) ).

fof(f7090,plain,
    spl38_257,
    inference(avatar_split_clause,[],[f4030,f7088]) ).

fof(f4030,plain,
    ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) = X0,
    inference(cnf_transformation,[],[f1238]) ).

fof(f1238,plain,
    ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) = X0,
    inference(rectify,[],[f636]) ).

fof(f636,axiom,
    ! [X10] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X10) = X10,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).

fof(f7086,plain,
    spl38_256,
    inference(avatar_split_clause,[],[f4029,f7084]) ).

fof(f7084,plain,
    ( spl38_256
  <=> ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_256])]) ).

fof(f7082,plain,
    spl38_255,
    inference(avatar_split_clause,[],[f4028,f7080]) ).

fof(f7080,plain,
    ( spl38_255
  <=> ! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_255])]) ).

fof(f4028,plain,
    ! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) = X0,
    inference(cnf_transformation,[],[f1236]) ).

fof(f1236,plain,
    ! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) = X0,
    inference(rectify,[],[f718]) ).

fof(f718,axiom,
    ! [X33] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X33) = X33,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__0) ).

fof(f7078,plain,
    spl38_254,
    inference(avatar_split_clause,[],[f4027,f7076]) ).

fof(f7076,plain,
    ( spl38_254
  <=> ! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_254])]) ).

fof(f4027,plain,
    ! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X0,
    inference(cnf_transformation,[],[f1235]) ).

fof(f1235,plain,
    ! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X0,
    inference(rectify,[],[f717]) ).

fof(f717,axiom,
    ! [X33] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X33,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X33,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__0__right) ).

fof(f7074,plain,
    spl38_253,
    inference(avatar_split_clause,[],[f4026,f7072]) ).

fof(f7072,plain,
    ( spl38_253
  <=> ! [X0] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_253])]) ).

fof(f4026,plain,
    ! [X0] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
    inference(cnf_transformation,[],[f1234]) ).

fof(f1234,plain,
    ! [X0] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
    inference(rectify,[],[f966]) ).

fof(f966,axiom,
    ! [X19] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X19,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__nat_Odiff__0) ).

fof(f7070,plain,
    ( spl38_252
    | ~ spl38_3
    | ~ spl38_241 ),
    inference(avatar_split_clause,[],[f7025,f7016,f5906,f7068]) ).

fof(f7068,plain,
    ( spl38_252
  <=> ! [X0] : sP15(v_s____,tc_Complex_Ocomplex,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_252])]) ).

fof(f7016,plain,
    ( spl38_241
  <=> ! [X2,X1] : sP15(c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_241])]) ).

fof(f7025,plain,
    ( ! [X0] : sP15(v_s____,tc_Complex_Ocomplex,X0)
    | ~ spl38_3
    | ~ spl38_241 ),
    inference(superposition,[],[f7017,f5908]) ).

fof(f7017,plain,
    ( ! [X2,X1] : sP15(c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1,X2)
    | ~ spl38_241 ),
    inference(avatar_component_clause,[],[f7016]) ).

fof(f7066,plain,
    spl38_251,
    inference(avatar_split_clause,[],[f4025,f7064]) ).

fof(f7064,plain,
    ( spl38_251
  <=> ! [X0] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_251])]) ).

fof(f4025,plain,
    ! [X0] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) = X0,
    inference(cnf_transformation,[],[f1233]) ).

fof(f1233,plain,
    ! [X0] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) = X0,
    inference(rectify,[],[f731]) ).

fof(f731,axiom,
    ! [X33] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X33)) = X33,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__zminus) ).

fof(f7062,plain,
    spl38_250,
    inference(avatar_split_clause,[],[f4024,f7060]) ).

fof(f7060,plain,
    ( spl38_250
  <=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_250])]) ).

fof(f4024,plain,
    ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X0),
    inference(cnf_transformation,[],[f1232]) ).

fof(f1232,plain,
    ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X0),
    inference(rectify,[],[f965]) ).

fof(f965,axiom,
    ! [X19] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X19),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__self__eq__0) ).

fof(f7058,plain,
    spl38_249,
    inference(avatar_split_clause,[],[f4023,f7056]) ).

fof(f7056,plain,
    ( spl38_249
  <=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_249])]) ).

fof(f4023,plain,
    ! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X0),
    inference(cnf_transformation,[],[f1231]) ).

fof(f1231,plain,
    ! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X0),
    inference(rectify,[],[f920]) ).

fof(f920,axiom,
    ! [X18] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X18,X18),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__self) ).

fof(f7054,plain,
    spl38_248,
    inference(avatar_split_clause,[],[f3993,f7051]) ).

fof(f7051,plain,
    ( spl38_248
  <=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_248])]) ).

fof(f3993,plain,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(cnf_transformation,[],[f729]) ).

fof(f729,axiom,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__0) ).

fof(f7049,plain,
    ~ spl38_247,
    inference(avatar_split_clause,[],[f3992,f7046]) ).

fof(f7046,plain,
    ( spl38_247
  <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_247])]) ).

fof(f3992,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____),
    inference(cnf_transformation,[],[f28]) ).

fof(f28,axiom,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_oa) ).

fof(f7044,plain,
    spl38_246,
    inference(avatar_split_clause,[],[f5762,f7041]) ).

fof(f7041,plain,
    ( spl38_246
  <=> v_pa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),v_s____))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),sK19) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_246])]) ).

fof(f5762,plain,
    v_pa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),v_s____))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),sK19),
    inference(forward_demodulation,[],[f4002,f3837]) ).

fof(f4002,plain,
    v_pa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),sK19),
    inference(cnf_transformation,[],[f3482]) ).

fof(f3482,plain,
    v_pa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),sK19),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f2279,f3481]) ).

fof(f3481,plain,
    ( ? [X0] : v_pa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),X0)
   => v_pa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),sK19) ),
    introduced(choice_axiom,[]) ).

fof(f2279,plain,
    ? [X0] : v_pa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),X0),
    inference(ennf_transformation,[],[f1210]) ).

fof(f1210,plain,
    ~ ! [X0] : v_pa____ != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),X0),
    inference(rectify,[],[f225]) ).

fof(f225,axiom,
    ~ ! [X31] : v_pa____ != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),X31),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_Bs_O_Ap_A_061_A_091_058_N_Aa_M_A1_058_093_A_094_Aorder_Aa_Ap_A_K_As_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).

fof(f7039,plain,
    spl38_245,
    inference(avatar_split_clause,[],[f5759,f7036]) ).

fof(f5759,plain,
    v_pa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),v_s____))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),v_s____),
    inference(forward_demodulation,[],[f3999,f3837]) ).

fof(f3999,plain,
    v_pa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),v_s____),
    inference(cnf_transformation,[],[f62]) ).

fof(f62,axiom,
    v_pa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),v_s____),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_s) ).

fof(f7034,plain,
    ( spl38_244
    | ~ spl38_3
    | ~ spl38_240 ),
    inference(avatar_split_clause,[],[f7024,f7012,f5906,f7032]) ).

fof(f7032,plain,
    ( spl38_244
  <=> ! [X0] : sP15(X0,tc_Complex_Ocomplex,v_s____) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_244])]) ).

fof(f7012,plain,
    ( spl38_240
  <=> ! [X0,X1] : sP15(X0,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_240])]) ).

fof(f7024,plain,
    ( ! [X0] : sP15(X0,tc_Complex_Ocomplex,v_s____)
    | ~ spl38_3
    | ~ spl38_240 ),
    inference(superposition,[],[f7013,f5908]) ).

fof(f7013,plain,
    ( ! [X0,X1] : sP15(X0,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
    | ~ spl38_240 ),
    inference(avatar_component_clause,[],[f7012]) ).

fof(f7030,plain,
    spl38_243,
    inference(avatar_split_clause,[],[f5757,f7027]) ).

fof(f7027,plain,
    ( spl38_243
  <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),v_s____))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),v_pa____)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_243])]) ).

fof(f5757,plain,
    hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),v_s____))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),v_pa____)),
    inference(forward_demodulation,[],[f3997,f3837]) ).

fof(f3997,plain,
    hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),v_pa____)),
    inference(cnf_transformation,[],[f69]) ).

fof(f69,axiom,
    hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),v_pa____)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ap_I1_J) ).

fof(f7023,plain,
    spl38_242,
    inference(avatar_split_clause,[],[f5861,f7020]) ).

fof(f7020,plain,
    ( spl38_242
  <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_242])]) ).

fof(f5861,plain,
    c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(forward_demodulation,[],[f5622,f5846]) ).

fof(f5622,plain,
    ! [X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(equality_resolution,[],[f4544]) ).

fof(f4544,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0))
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ),
    inference(cnf_transformation,[],[f3615]) ).

fof(f3615,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0))
        | ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
          & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0)) ) ),
    inference(flattening,[],[f3614]) ).

fof(f3614,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0))
        | ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
          & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0)) ) ),
    inference(nnf_transformation,[],[f1640]) ).

fof(f1640,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0))
    <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) ),
    inference(rectify,[],[f446]) ).

fof(f446,axiom,
    ! [X11,X3] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X3),X11))
    <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X11 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__power__nat__eq) ).

fof(f7018,plain,
    spl38_241,
    inference(avatar_split_clause,[],[f5737,f7016]) ).

fof(f5737,plain,
    ! [X2,X1] : sP15(c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1,X2),
    inference(equality_resolution,[],[f5319]) ).

fof(f5319,plain,
    ! [X2,X0,X1] :
      ( sP15(X0,X1,X2)
      | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) != X0 ),
    inference(cnf_transformation,[],[f3822]) ).

fof(f7014,plain,
    spl38_240,
    inference(avatar_split_clause,[],[f5736,f7012]) ).

fof(f5736,plain,
    ! [X0,X1] : sP15(X0,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),
    inference(equality_resolution,[],[f5320]) ).

fof(f5320,plain,
    ! [X2,X0,X1] :
      ( sP15(X0,X1,X2)
      | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) != X2 ),
    inference(cnf_transformation,[],[f3822]) ).

fof(f7010,plain,
    spl38_239,
    inference(avatar_split_clause,[],[f5680,f7008]) ).

fof(f7008,plain,
    ( spl38_239
  <=> ! [X2,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X2,X1,X1)
        | ~ class_Orderings_Oorder(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_239])]) ).

fof(f5680,plain,
    ! [X2,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X2,X1,X1)
      | ~ class_Orderings_Oorder(X2) ),
    inference(equality_resolution,[],[f4897]) ).

fof(f4897,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
      | X0 != X1
      | ~ class_Orderings_Oorder(X2) ),
    inference(cnf_transformation,[],[f3707]) ).

fof(f3707,plain,
    ! [X0,X1,X2] :
      ( ( ( X0 = X1
          | ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
          | ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0) )
        & ( ( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
            & c_Orderings_Oord__class_Oless__eq(X2,X1,X0) )
          | X0 != X1 ) )
      | ~ class_Orderings_Oorder(X2) ),
    inference(flattening,[],[f3706]) ).

fof(f3706,plain,
    ! [X0,X1,X2] :
      ( ( ( X0 = X1
          | ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
          | ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0) )
        & ( ( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
            & c_Orderings_Oord__class_Oless__eq(X2,X1,X0) )
          | X0 != X1 ) )
      | ~ class_Orderings_Oorder(X2) ),
    inference(nnf_transformation,[],[f2943]) ).

fof(f2943,plain,
    ! [X0,X1,X2] :
      ( ( X0 = X1
      <=> ( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
          & c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ) )
      | ~ class_Orderings_Oorder(X2) ),
    inference(ennf_transformation,[],[f1899]) ).

fof(f1899,plain,
    ! [X0,X1,X2] :
      ( class_Orderings_Oorder(X2)
     => ( X0 = X1
      <=> ( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
          & c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ) ) ),
    inference(rectify,[],[f571]) ).

fof(f571,axiom,
    ! [X17,X3,X4] :
      ( class_Orderings_Oorder(X4)
     => ( X3 = X17
      <=> ( c_Orderings_Oord__class_Oless__eq(X4,X17,X3)
          & c_Orderings_Oord__class_Oless__eq(X4,X3,X17) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__eq__iff) ).

fof(f7006,plain,
    spl38_238,
    inference(avatar_split_clause,[],[f5677,f7004]) ).

fof(f7004,plain,
    ( spl38_238
  <=> ! [X2,X1] :
        ( ~ c_Orderings_Oord__class_Oless(X2,X1,X1)
        | ~ class_Orderings_Oorder(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_238])]) ).

fof(f5677,plain,
    ! [X2,X1] :
      ( ~ c_Orderings_Oord__class_Oless(X2,X1,X1)
      | ~ class_Orderings_Oorder(X2) ),
    inference(equality_resolution,[],[f4892]) ).

fof(f4892,plain,
    ! [X2,X0,X1] :
      ( X0 != X1
      | ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
      | ~ class_Orderings_Oorder(X2) ),
    inference(cnf_transformation,[],[f2936]) ).

fof(f2936,plain,
    ! [X0,X1,X2] :
      ( X0 != X1
      | ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
      | ~ class_Orderings_Oorder(X2) ),
    inference(flattening,[],[f2935]) ).

fof(f2935,plain,
    ! [X0,X1,X2] :
      ( X0 != X1
      | ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
      | ~ class_Orderings_Oorder(X2) ),
    inference(ennf_transformation,[],[f1895]) ).

fof(f1895,plain,
    ! [X0,X1,X2] :
      ( class_Orderings_Oorder(X2)
     => ( c_Orderings_Oord__class_Oless(X2,X1,X0)
       => X0 != X1 ) ),
    inference(rectify,[],[f584]) ).

fof(f584,axiom,
    ! [X28,X13,X4] :
      ( class_Orderings_Oorder(X4)
     => ( c_Orderings_Oord__class_Oless(X4,X13,X28)
       => X13 != X28 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__eq2) ).

fof(f7002,plain,
    spl38_237,
    inference(avatar_split_clause,[],[f5646,f7000]) ).

fof(f7000,plain,
    ( spl38_237
  <=> ! [X2,X1] :
        ( ~ c_Orderings_Oord__class_Oless(X2,X1,X1)
        | ~ class_Orderings_Olinorder(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_237])]) ).

fof(f5646,plain,
    ! [X2,X1] :
      ( ~ c_Orderings_Oord__class_Oless(X2,X1,X1)
      | ~ class_Orderings_Olinorder(X2) ),
    inference(equality_resolution,[],[f4737]) ).

fof(f4737,plain,
    ! [X2,X0,X1] :
      ( X0 != X1
      | ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
      | ~ class_Orderings_Olinorder(X2) ),
    inference(cnf_transformation,[],[f3665]) ).

fof(f3665,plain,
    ! [X0,X1,X2] :
      ( ( ( X0 != X1
          | ( ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
            & ~ c_Orderings_Oord__class_Oless(X2,X1,X0) ) )
        & ( c_Orderings_Oord__class_Oless(X2,X0,X1)
          | c_Orderings_Oord__class_Oless(X2,X1,X0)
          | X0 = X1 ) )
      | ~ class_Orderings_Olinorder(X2) ),
    inference(flattening,[],[f3664]) ).

fof(f3664,plain,
    ! [X0,X1,X2] :
      ( ( ( X0 != X1
          | ( ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
            & ~ c_Orderings_Oord__class_Oless(X2,X1,X0) ) )
        & ( c_Orderings_Oord__class_Oless(X2,X0,X1)
          | c_Orderings_Oord__class_Oless(X2,X1,X0)
          | X0 = X1 ) )
      | ~ class_Orderings_Olinorder(X2) ),
    inference(nnf_transformation,[],[f2773]) ).

fof(f2773,plain,
    ! [X0,X1,X2] :
      ( ( X0 != X1
      <=> ( c_Orderings_Oord__class_Oless(X2,X0,X1)
          | c_Orderings_Oord__class_Oless(X2,X1,X0) ) )
      | ~ class_Orderings_Olinorder(X2) ),
    inference(ennf_transformation,[],[f1779]) ).

fof(f1779,plain,
    ! [X0,X1,X2] :
      ( class_Orderings_Olinorder(X2)
     => ( X0 != X1
      <=> ( c_Orderings_Oord__class_Oless(X2,X0,X1)
          | c_Orderings_Oord__class_Oless(X2,X1,X0) ) ) ),
    inference(rectify,[],[f593]) ).

fof(f593,axiom,
    ! [X17,X3,X4] :
      ( class_Orderings_Olinorder(X4)
     => ( X3 != X17
      <=> ( c_Orderings_Oord__class_Oless(X4,X17,X3)
          | c_Orderings_Oord__class_Oless(X4,X3,X17) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neq__iff) ).

fof(f6998,plain,
    spl38_236,
    inference(avatar_split_clause,[],[f4644,f6996]) ).

fof(f6996,plain,
    ( spl38_236
  <=> ! [X2,X0,X1] :
        ( sP5(X1,X2,X0)
        | ~ class_Rings_Olinordered__ring__strict(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_236])]) ).

fof(f4644,plain,
    ! [X2,X0,X1] :
      ( sP5(X1,X2,X0)
      | ~ class_Rings_Olinordered__ring__strict(X2) ),
    inference(cnf_transformation,[],[f3460]) ).

fof(f3460,plain,
    ! [X0,X1,X2] :
      ( sP5(X1,X2,X0)
      | ~ class_Rings_Olinordered__ring__strict(X2) ),
    inference(definition_folding,[],[f2670,f3459,f3458]) ).

fof(f3459,plain,
    ! [X1,X2,X0] :
      ( ( c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),c_Groups_Ozero__class_Ozero(X2))
      <=> sP4(X0,X2,X1) )
      | ~ sP5(X1,X2,X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).

fof(f2670,plain,
    ! [X0,X1,X2] :
      ( ( c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),c_Groups_Ozero__class_Ozero(X2))
      <=> ( ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
            & c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2)) )
          | ( c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
            & c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1) ) ) )
      | ~ class_Rings_Olinordered__ring__strict(X2) ),
    inference(ennf_transformation,[],[f1715]) ).

fof(f1715,plain,
    ! [X0,X1,X2] :
      ( class_Rings_Olinordered__ring__strict(X2)
     => ( c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),c_Groups_Ozero__class_Ozero(X2))
      <=> ( ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
            & c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2)) )
          | ( c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
            & c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1) ) ) ) ),
    inference(rectify,[],[f79]) ).

fof(f79,axiom,
    ! [X20,X12,X4] :
      ( class_Rings_Olinordered__ring__strict(X4)
     => ( c_Orderings_Oord__class_Oless__eq(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X20),c_Groups_Ozero__class_Ozero(X4))
      <=> ( ( c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X20)
            & c_Orderings_Oord__class_Oless__eq(X4,X12,c_Groups_Ozero__class_Ozero(X4)) )
          | ( c_Orderings_Oord__class_Oless__eq(X4,X20,c_Groups_Ozero__class_Ozero(X4))
            & c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X12) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__0__iff) ).

fof(f6994,plain,
    spl38_235,
    inference(avatar_split_clause,[],[f4635,f6992]) ).

fof(f6992,plain,
    ( spl38_235
  <=> ! [X2,X0,X1] :
        ( sP3(X1,X0,X2)
        | ~ class_Rings_Olinordered__ring__strict(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_235])]) ).

fof(f4635,plain,
    ! [X2,X0,X1] :
      ( sP3(X1,X0,X2)
      | ~ class_Rings_Olinordered__ring__strict(X2) ),
    inference(cnf_transformation,[],[f3457]) ).

fof(f3457,plain,
    ! [X0,X1,X2] :
      ( sP3(X1,X0,X2)
      | ~ class_Rings_Olinordered__ring__strict(X2) ),
    inference(definition_folding,[],[f2669,f3456,f3455]) ).

fof(f3456,plain,
    ! [X1,X0,X2] :
      ( ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))
      <=> sP2(X2,X0,X1) )
      | ~ sP3(X1,X0,X2) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).

fof(f2669,plain,
    ! [X0,X1,X2] :
      ( ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))
      <=> ( ( c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
            & c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2)) )
          | ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
            & c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1) ) ) )
      | ~ class_Rings_Olinordered__ring__strict(X2) ),
    inference(ennf_transformation,[],[f1714]) ).

fof(f1714,plain,
    ! [X0,X1,X2] :
      ( class_Rings_Olinordered__ring__strict(X2)
     => ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))
      <=> ( ( c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
            & c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2)) )
          | ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
            & c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1) ) ) ) ),
    inference(rectify,[],[f77]) ).

fof(f77,axiom,
    ! [X20,X12,X4] :
      ( class_Rings_Olinordered__ring__strict(X4)
     => ( c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X20))
      <=> ( ( c_Orderings_Oord__class_Oless__eq(X4,X20,c_Groups_Ozero__class_Ozero(X4))
            & c_Orderings_Oord__class_Oless__eq(X4,X12,c_Groups_Ozero__class_Ozero(X4)) )
          | ( c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X20)
            & c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X12) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__mult__iff) ).

fof(f6990,plain,
    spl38_234,
    inference(avatar_split_clause,[],[f4334,f6988]) ).

fof(f6988,plain,
    ( spl38_234
  <=> ! [X0,X1] :
        ( class_Groups_Ominus(tc_fun(X0,X1))
        | ~ class_Groups_Ominus(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_234])]) ).

fof(f4334,plain,
    ! [X0,X1] :
      ( class_Groups_Ominus(tc_fun(X0,X1))
      | ~ class_Groups_Ominus(X1) ),
    inference(cnf_transformation,[],[f2493]) ).

fof(f2493,plain,
    ! [X0,X1] :
      ( class_Groups_Ominus(tc_fun(X0,X1))
      | ~ class_Groups_Ominus(X1) ),
    inference(ennf_transformation,[],[f1517]) ).

fof(f1517,plain,
    ! [X0,X1] :
      ( class_Groups_Ominus(X1)
     => class_Groups_Ominus(tc_fun(X0,X1)) ),
    inference(rectify,[],[f1005]) ).

fof(f1005,axiom,
    ! [X91,X90] :
      ( class_Groups_Ominus(X90)
     => class_Groups_Ominus(tc_fun(X91,X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Groups_Ominus) ).

fof(f6986,plain,
    spl38_233,
    inference(avatar_split_clause,[],[f4333,f6984]) ).

fof(f6984,plain,
    ( spl38_233
  <=> ! [X0,X1] :
        ( class_Orderings_Oorder(tc_fun(X0,X1))
        | ~ class_Orderings_Oorder(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_233])]) ).

fof(f4333,plain,
    ! [X0,X1] :
      ( class_Orderings_Oorder(tc_fun(X0,X1))
      | ~ class_Orderings_Oorder(X1) ),
    inference(cnf_transformation,[],[f2492]) ).

fof(f2492,plain,
    ! [X0,X1] :
      ( class_Orderings_Oorder(tc_fun(X0,X1))
      | ~ class_Orderings_Oorder(X1) ),
    inference(ennf_transformation,[],[f1516]) ).

fof(f1516,plain,
    ! [X0,X1] :
      ( class_Orderings_Oorder(X1)
     => class_Orderings_Oorder(tc_fun(X0,X1)) ),
    inference(rectify,[],[f1002]) ).

fof(f1002,axiom,
    ! [X91,X90] :
      ( class_Orderings_Oorder(X90)
     => class_Orderings_Oorder(tc_fun(X91,X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oorder) ).

fof(f6982,plain,
    spl38_232,
    inference(avatar_split_clause,[],[f4332,f6980]) ).

fof(f6980,plain,
    ( spl38_232
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X1,X0,X0)
        | ~ class_Orderings_Opreorder(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_232])]) ).

fof(f4332,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X1,X0,X0)
      | ~ class_Orderings_Opreorder(X1) ),
    inference(cnf_transformation,[],[f2491]) ).

fof(f2491,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X1,X0,X0)
      | ~ class_Orderings_Opreorder(X1) ),
    inference(ennf_transformation,[],[f1515]) ).

fof(f1515,plain,
    ! [X0,X1] :
      ( class_Orderings_Opreorder(X1)
     => c_Orderings_Oord__class_Oless__eq(X1,X0,X0) ),
    inference(rectify,[],[f455]) ).

fof(f455,axiom,
    ! [X13,X4] :
      ( class_Orderings_Opreorder(X4)
     => c_Orderings_Oord__class_Oless__eq(X4,X13,X13) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__refl) ).

fof(f6978,plain,
    spl38_231,
    inference(avatar_split_clause,[],[f4331,f6976]) ).

fof(f6976,plain,
    ( spl38_231
  <=> ! [X0,X1] :
        ( class_Orderings_Opreorder(tc_fun(X0,X1))
        | ~ class_Orderings_Opreorder(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_231])]) ).

fof(f4331,plain,
    ! [X0,X1] :
      ( class_Orderings_Opreorder(tc_fun(X0,X1))
      | ~ class_Orderings_Opreorder(X1) ),
    inference(cnf_transformation,[],[f2490]) ).

fof(f2490,plain,
    ! [X0,X1] :
      ( class_Orderings_Opreorder(tc_fun(X0,X1))
      | ~ class_Orderings_Opreorder(X1) ),
    inference(ennf_transformation,[],[f1514]) ).

fof(f1514,plain,
    ! [X0,X1] :
      ( class_Orderings_Opreorder(X1)
     => class_Orderings_Opreorder(tc_fun(X0,X1)) ),
    inference(rectify,[],[f1001]) ).

fof(f1001,axiom,
    ! [X91,X90] :
      ( class_Orderings_Opreorder(X90)
     => class_Orderings_Opreorder(tc_fun(X91,X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Opreorder) ).

fof(f6974,plain,
    spl38_230,
    inference(avatar_split_clause,[],[f4330,f6972]) ).

fof(f6972,plain,
    ( spl38_230
  <=> ! [X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless(X1,X0,X0)
        | ~ class_Orderings_Opreorder(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_230])]) ).

fof(f4330,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(X1,X0,X0)
      | ~ class_Orderings_Opreorder(X1) ),
    inference(cnf_transformation,[],[f2489]) ).

fof(f2489,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(X1,X0,X0)
      | ~ class_Orderings_Opreorder(X1) ),
    inference(ennf_transformation,[],[f1513]) ).

fof(f1513,plain,
    ! [X0,X1] :
      ( class_Orderings_Opreorder(X1)
     => ~ c_Orderings_Oord__class_Oless(X1,X0,X0) ),
    inference(rectify,[],[f594]) ).

fof(f594,axiom,
    ! [X13,X4] :
      ( class_Orderings_Opreorder(X4)
     => ~ c_Orderings_Oord__class_Oless(X4,X13,X13) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__irrefl) ).

fof(f6970,plain,
    spl38_229,
    inference(avatar_split_clause,[],[f4329,f6968]) ).

fof(f6968,plain,
    ( spl38_229
  <=> ! [X0,X1] :
        ( class_Orderings_Oord(tc_fun(X0,X1))
        | ~ class_Orderings_Oord(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_229])]) ).

fof(f4329,plain,
    ! [X0,X1] :
      ( class_Orderings_Oord(tc_fun(X0,X1))
      | ~ class_Orderings_Oord(X1) ),
    inference(cnf_transformation,[],[f2488]) ).

fof(f2488,plain,
    ! [X0,X1] :
      ( class_Orderings_Oord(tc_fun(X0,X1))
      | ~ class_Orderings_Oord(X1) ),
    inference(ennf_transformation,[],[f1512]) ).

fof(f1512,plain,
    ! [X0,X1] :
      ( class_Orderings_Oord(X1)
     => class_Orderings_Oord(tc_fun(X0,X1)) ),
    inference(rectify,[],[f1003]) ).

fof(f1003,axiom,
    ! [X91,X90] :
      ( class_Orderings_Oord(X90)
     => class_Orderings_Oord(tc_fun(X91,X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).

fof(f6966,plain,
    spl38_228,
    inference(avatar_split_clause,[],[f4328,f6964]) ).

fof(f6964,plain,
    ( spl38_228
  <=> ! [X0,X1] :
        ( class_Groups_Ouminus(tc_fun(X0,X1))
        | ~ class_Groups_Ouminus(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_228])]) ).

fof(f4328,plain,
    ! [X0,X1] :
      ( class_Groups_Ouminus(tc_fun(X0,X1))
      | ~ class_Groups_Ouminus(X1) ),
    inference(cnf_transformation,[],[f2487]) ).

fof(f2487,plain,
    ! [X0,X1] :
      ( class_Groups_Ouminus(tc_fun(X0,X1))
      | ~ class_Groups_Ouminus(X1) ),
    inference(ennf_transformation,[],[f1511]) ).

fof(f1511,plain,
    ! [X0,X1] :
      ( class_Groups_Ouminus(X1)
     => class_Groups_Ouminus(tc_fun(X0,X1)) ),
    inference(rectify,[],[f1004]) ).

fof(f1004,axiom,
    ! [X91,X90] :
      ( class_Groups_Ouminus(X90)
     => class_Groups_Ouminus(tc_fun(X91,X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Groups_Ouminus) ).

fof(f6962,plain,
    spl38_227,
    inference(avatar_split_clause,[],[f4213,f6960]) ).

fof(f6960,plain,
    ( spl38_227
  <=> ! [X0,X1] :
        ( class_Lattices_Oboolean__algebra(tc_fun(X0,X1))
        | ~ class_Lattices_Oboolean__algebra(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_227])]) ).

fof(f4213,plain,
    ! [X0,X1] :
      ( class_Lattices_Oboolean__algebra(tc_fun(X0,X1))
      | ~ class_Lattices_Oboolean__algebra(X1) ),
    inference(cnf_transformation,[],[f2397]) ).

fof(f2397,plain,
    ! [X0,X1] :
      ( class_Lattices_Oboolean__algebra(tc_fun(X0,X1))
      | ~ class_Lattices_Oboolean__algebra(X1) ),
    inference(ennf_transformation,[],[f1424]) ).

fof(f1424,plain,
    ! [X0,X1] :
      ( class_Lattices_Oboolean__algebra(X1)
     => class_Lattices_Oboolean__algebra(tc_fun(X0,X1)) ),
    inference(rectify,[],[f1000]) ).

fof(f1000,axiom,
    ! [X91,X90] :
      ( class_Lattices_Oboolean__algebra(X90)
     => class_Lattices_Oboolean__algebra(tc_fun(X91,X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Oboolean__algebra) ).

fof(f6958,plain,
    spl38_226,
    inference(avatar_split_clause,[],[f3991,f6955]) ).

fof(f6955,plain,
    ( spl38_226
  <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_226])]) ).

fof(f3991,plain,
    c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(cnf_transformation,[],[f745]) ).

fof(f745,axiom,
    c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__0__less__1) ).

fof(f6953,plain,
    spl38_225,
    inference(avatar_split_clause,[],[f3989,f6950]) ).

fof(f6950,plain,
    ( spl38_225
  <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_225])]) ).

fof(f3989,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(cnf_transformation,[],[f773]) ).

fof(f773,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).

fof(f6948,plain,
    spl38_224,
    inference(avatar_split_clause,[],[f5830,f6945]) ).

fof(f6945,plain,
    ( spl38_224
  <=> sP1(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_224])]) ).

fof(f5830,plain,
    sP1(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(forward_demodulation,[],[f5829,f4029]) ).

fof(f5829,plain,
    sP1(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(forward_demodulation,[],[f5610,f4164]) ).

fof(f5610,plain,
    sP1(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
    inference(equality_resolution,[],[f5609]) ).

fof(f5609,plain,
    ! [X1] :
      ( sP1(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X1 ),
    inference(equality_resolution,[],[f5493]) ).

fof(f5493,plain,
    ! [X0,X1] :
      ( sP1(X0,X1)
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X1 ),
    inference(definition_unfolding,[],[f4510,f4035]) ).

fof(f4510,plain,
    ! [X0,X1] :
      ( sP1(X0,X1)
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
      | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ),
    inference(cnf_transformation,[],[f3594]) ).

fof(f6943,plain,
    spl38_223,
    inference(avatar_split_clause,[],[f5828,f6940]) ).

fof(f6940,plain,
    ( spl38_223
  <=> sP1(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_223])]) ).

fof(f5828,plain,
    sP1(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(forward_demodulation,[],[f5827,f4029]) ).

fof(f5827,plain,
    sP1(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(forward_demodulation,[],[f5608,f4164]) ).

fof(f5608,plain,
    sP1(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(equality_resolution,[],[f5607]) ).

fof(f5607,plain,
    ! [X1] :
      ( sP1(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
    inference(equality_resolution,[],[f5492]) ).

fof(f5492,plain,
    ! [X0,X1] :
      ( sP1(X0,X1)
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X0
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
    inference(definition_unfolding,[],[f4511,f4035]) ).

fof(f4511,plain,
    ! [X0,X1] :
      ( sP1(X0,X1)
      | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
    inference(cnf_transformation,[],[f3594]) ).

fof(f6938,plain,
    spl38_222,
    inference(avatar_split_clause,[],[f5814,f6935]) ).

fof(f6935,plain,
    ( spl38_222
  <=> sP0(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_222])]) ).

fof(f5814,plain,
    sP0(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(forward_demodulation,[],[f5813,f4029]) ).

fof(f5813,plain,
    sP0(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(forward_demodulation,[],[f5606,f4164]) ).

fof(f5606,plain,
    sP0(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
    inference(equality_resolution,[],[f5605]) ).

fof(f5605,plain,
    ! [X1] :
      ( sP0(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X1 ),
    inference(equality_resolution,[],[f5486]) ).

fof(f5486,plain,
    ! [X0,X1] :
      ( sP0(X0,X1)
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X1 ),
    inference(definition_unfolding,[],[f4502,f4035]) ).

fof(f4502,plain,
    ! [X0,X1] :
      ( sP0(X0,X1)
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
      | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ),
    inference(cnf_transformation,[],[f3591]) ).

fof(f6933,plain,
    spl38_221,
    inference(avatar_split_clause,[],[f5812,f6930]) ).

fof(f6930,plain,
    ( spl38_221
  <=> sP0(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_221])]) ).

fof(f5812,plain,
    sP0(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(forward_demodulation,[],[f5811,f4029]) ).

fof(f5811,plain,
    sP0(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(forward_demodulation,[],[f5604,f4164]) ).

fof(f5604,plain,
    sP0(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(equality_resolution,[],[f5603]) ).

fof(f5603,plain,
    ! [X1] :
      ( sP0(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
    inference(equality_resolution,[],[f5485]) ).

fof(f5485,plain,
    ! [X0,X1] :
      ( sP0(X0,X1)
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X0
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
    inference(definition_unfolding,[],[f4503,f4035]) ).

fof(f4503,plain,
    ! [X0,X1] :
      ( sP0(X0,X1)
      | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
    inference(cnf_transformation,[],[f3591]) ).

fof(f6928,plain,
    spl38_220,
    inference(avatar_split_clause,[],[f4128,f6926]) ).

fof(f4128,plain,
    ! [X0] :
      ( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__semiring__1(X0) ),
    inference(cnf_transformation,[],[f2355]) ).

fof(f2355,plain,
    ! [X0] :
      ( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__semiring__1(X0) ),
    inference(ennf_transformation,[],[f1336]) ).

fof(f1336,plain,
    ! [X0] :
      ( class_Rings_Ocomm__semiring__1(X0)
     => class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1174]) ).

fof(f1174,axiom,
    ! [X90] :
      ( class_Rings_Ocomm__semiring__1(X90)
     => class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__1) ).

fof(f6924,plain,
    spl38_219,
    inference(avatar_split_clause,[],[f4127,f6922]) ).

fof(f6922,plain,
    ( spl38_219
  <=> ! [X0] :
        ( class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Ocomm__semiring__1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_219])]) ).

fof(f4127,plain,
    ! [X0] :
      ( class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__semiring__1(X0) ),
    inference(cnf_transformation,[],[f2354]) ).

fof(f2354,plain,
    ! [X0] :
      ( class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__semiring__1(X0) ),
    inference(ennf_transformation,[],[f1335]) ).

fof(f1335,plain,
    ! [X0] :
      ( class_Rings_Ocomm__semiring__1(X0)
     => class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1183]) ).

fof(f1183,axiom,
    ! [X90] :
      ( class_Rings_Ocomm__semiring__1(X90)
     => class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Omonoid__mult) ).

fof(f6920,plain,
    spl38_218,
    inference(avatar_split_clause,[],[f4126,f6918]) ).

fof(f6918,plain,
    ( spl38_218
  <=> ! [X0] :
        ( class_Power_Opower(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Ocomm__semiring__1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_218])]) ).

fof(f4126,plain,
    ! [X0] :
      ( class_Power_Opower(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__semiring__1(X0) ),
    inference(cnf_transformation,[],[f2353]) ).

fof(f2353,plain,
    ! [X0] :
      ( class_Power_Opower(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__semiring__1(X0) ),
    inference(ennf_transformation,[],[f1334]) ).

fof(f1334,plain,
    ! [X0] :
      ( class_Rings_Ocomm__semiring__1(X0)
     => class_Power_Opower(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1198]) ).

fof(f1198,axiom,
    ! [X90] :
      ( class_Rings_Ocomm__semiring__1(X90)
     => class_Power_Opower(tc_Polynomial_Opoly(X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Power_Opower) ).

fof(f6916,plain,
    spl38_217,
    inference(avatar_split_clause,[],[f4125,f6914]) ).

fof(f6914,plain,
    ( spl38_217
  <=> ! [X0] :
        ( class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Ocomm__semiring__1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_217])]) ).

fof(f4125,plain,
    ! [X0] :
      ( class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__semiring__1(X0) ),
    inference(cnf_transformation,[],[f2352]) ).

fof(f2352,plain,
    ! [X0] :
      ( class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__semiring__1(X0) ),
    inference(ennf_transformation,[],[f1333]) ).

fof(f1333,plain,
    ! [X0] :
      ( class_Rings_Ocomm__semiring__1(X0)
     => class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1167]) ).

fof(f1167,axiom,
    ! [X90] :
      ( class_Rings_Ocomm__semiring__1(X90)
     => class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult) ).

fof(f6912,plain,
    spl38_216,
    inference(avatar_split_clause,[],[f4124,f6910]) ).

fof(f4124,plain,
    ! [X0] :
      ( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__semiring__1(X0) ),
    inference(cnf_transformation,[],[f2351]) ).

fof(f2351,plain,
    ! [X0] :
      ( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__semiring__1(X0) ),
    inference(ennf_transformation,[],[f1332]) ).

fof(f1332,plain,
    ! [X0] :
      ( class_Rings_Ocomm__semiring__1(X0)
     => class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1179]) ).

fof(f1179,axiom,
    ! [X90] :
      ( class_Rings_Ocomm__semiring__1(X90)
     => class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ozero__neq__one) ).

fof(f6908,plain,
    spl38_215,
    inference(avatar_split_clause,[],[f4123,f6906]) ).

fof(f6906,plain,
    ( spl38_215
  <=> ! [X0] :
        ( class_Rings_Odvd(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Ocomm__semiring__1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_215])]) ).

fof(f4123,plain,
    ! [X0] :
      ( class_Rings_Odvd(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__semiring__1(X0) ),
    inference(cnf_transformation,[],[f2350]) ).

fof(f2350,plain,
    ! [X0] :
      ( class_Rings_Odvd(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__semiring__1(X0) ),
    inference(ennf_transformation,[],[f1331]) ).

fof(f1331,plain,
    ! [X0] :
      ( class_Rings_Ocomm__semiring__1(X0)
     => class_Rings_Odvd(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1203]) ).

fof(f1203,axiom,
    ! [X90] :
      ( class_Rings_Ocomm__semiring__1(X90)
     => class_Rings_Odvd(tc_Polynomial_Opoly(X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Odvd) ).

fof(f6904,plain,
    spl38_214,
    inference(avatar_split_clause,[],[f4122,f6902]) ).

fof(f6902,plain,
    ( spl38_214
  <=> ! [X0] :
        ( class_Groups_Oone(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Ocomm__semiring__1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_214])]) ).

fof(f4122,plain,
    ! [X0] :
      ( class_Groups_Oone(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__semiring__1(X0) ),
    inference(cnf_transformation,[],[f2349]) ).

fof(f2349,plain,
    ! [X0] :
      ( class_Groups_Oone(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__semiring__1(X0) ),
    inference(ennf_transformation,[],[f1330]) ).

fof(f1330,plain,
    ! [X0] :
      ( class_Rings_Ocomm__semiring__1(X0)
     => class_Groups_Oone(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1202]) ).

fof(f1202,axiom,
    ! [X90] :
      ( class_Rings_Ocomm__semiring__1(X90)
     => class_Groups_Oone(tc_Polynomial_Opoly(X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oone) ).

fof(f6900,plain,
    spl38_213,
    inference(avatar_split_clause,[],[f4121,f6898]) ).

fof(f6898,plain,
    ( spl38_213
  <=> ! [X0] :
        ( class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Ocomm__semiring__0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_213])]) ).

fof(f4121,plain,
    ! [X0] :
      ( class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__semiring__0(X0) ),
    inference(cnf_transformation,[],[f2348]) ).

fof(f2348,plain,
    ! [X0] :
      ( class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__semiring__0(X0) ),
    inference(ennf_transformation,[],[f1329]) ).

fof(f1329,plain,
    ! [X0] :
      ( class_Rings_Ocomm__semiring__0(X0)
     => class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1175]) ).

fof(f1175,axiom,
    ! [X90] :
      ( class_Rings_Ocomm__semiring__0(X90)
     => class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__0) ).

fof(f6896,plain,
    spl38_212,
    inference(avatar_split_clause,[],[f4120,f6894]) ).

fof(f6894,plain,
    ( spl38_212
  <=> ! [X0] :
        ( class_Rings_Omult__zero(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Ocomm__semiring__0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_212])]) ).

fof(f4120,plain,
    ! [X0] :
      ( class_Rings_Omult__zero(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__semiring__0(X0) ),
    inference(cnf_transformation,[],[f2347]) ).

fof(f2347,plain,
    ! [X0] :
      ( class_Rings_Omult__zero(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__semiring__0(X0) ),
    inference(ennf_transformation,[],[f1328]) ).

fof(f1328,plain,
    ! [X0] :
      ( class_Rings_Ocomm__semiring__0(X0)
     => class_Rings_Omult__zero(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1189]) ).

fof(f1189,axiom,
    ! [X90] :
      ( class_Rings_Ocomm__semiring__0(X90)
     => class_Rings_Omult__zero(tc_Polynomial_Opoly(X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Omult__zero) ).

fof(f6892,plain,
    spl38_211,
    inference(avatar_split_clause,[],[f4119,f6890]) ).

fof(f6890,plain,
    ( spl38_211
  <=> ! [X0] :
        ( class_Rings_Osemiring__0(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Ocomm__semiring__0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_211])]) ).

fof(f4119,plain,
    ! [X0] :
      ( class_Rings_Osemiring__0(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__semiring__0(X0) ),
    inference(cnf_transformation,[],[f2346]) ).

fof(f2346,plain,
    ! [X0] :
      ( class_Rings_Osemiring__0(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__semiring__0(X0) ),
    inference(ennf_transformation,[],[f1327]) ).

fof(f1327,plain,
    ! [X0] :
      ( class_Rings_Ocomm__semiring__0(X0)
     => class_Rings_Osemiring__0(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1186]) ).

fof(f1186,axiom,
    ! [X90] :
      ( class_Rings_Ocomm__semiring__0(X90)
     => class_Rings_Osemiring__0(tc_Polynomial_Opoly(X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Osemiring__0) ).

fof(f6888,plain,
    spl38_210,
    inference(avatar_split_clause,[],[f4118,f6886]) ).

fof(f6886,plain,
    ( spl38_210
  <=> ! [X0] :
        ( class_Rings_Osemiring(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Ocomm__semiring__0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_210])]) ).

fof(f4118,plain,
    ! [X0] :
      ( class_Rings_Osemiring(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__semiring__0(X0) ),
    inference(cnf_transformation,[],[f2345]) ).

fof(f2345,plain,
    ! [X0] :
      ( class_Rings_Osemiring(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__semiring__0(X0) ),
    inference(ennf_transformation,[],[f1326]) ).

fof(f1326,plain,
    ! [X0] :
      ( class_Rings_Ocomm__semiring__0(X0)
     => class_Rings_Osemiring(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1193]) ).

fof(f1193,axiom,
    ! [X90] :
      ( class_Rings_Ocomm__semiring__0(X90)
     => class_Rings_Osemiring(tc_Polynomial_Opoly(X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Osemiring) ).

fof(f6884,plain,
    spl38_209,
    inference(avatar_split_clause,[],[f4117,f6882]) ).

fof(f6882,plain,
    ( spl38_209
  <=> ! [X0] :
        ( class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Ocomm__semiring__0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_209])]) ).

fof(f4117,plain,
    ! [X0] :
      ( class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__semiring__0(X0) ),
    inference(cnf_transformation,[],[f2344]) ).

fof(f2344,plain,
    ! [X0] :
      ( class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__semiring__0(X0) ),
    inference(ennf_transformation,[],[f1325]) ).

fof(f1325,plain,
    ! [X0] :
      ( class_Rings_Ocomm__semiring__0(X0)
     => class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1177]) ).

fof(f1177,axiom,
    ! [X90] :
      ( class_Rings_Ocomm__semiring__0(X90)
     => class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring) ).

fof(f6880,plain,
    spl38_208,
    inference(avatar_split_clause,[],[f4116,f6878]) ).

fof(f6878,plain,
    ( spl38_208
  <=> ! [X0] :
        ( class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Ocomm__semiring__0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_208])]) ).

fof(f4116,plain,
    ! [X0] :
      ( class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__semiring__0(X0) ),
    inference(cnf_transformation,[],[f2343]) ).

fof(f2343,plain,
    ! [X0] :
      ( class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__semiring__0(X0) ),
    inference(ennf_transformation,[],[f1324]) ).

fof(f1324,plain,
    ! [X0] :
      ( class_Rings_Ocomm__semiring__0(X0)
     => class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1166]) ).

fof(f1166,axiom,
    ! [X90] :
      ( class_Rings_Ocomm__semiring__0(X90)
     => class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__semigroup__mult) ).

fof(f6876,plain,
    spl38_207,
    inference(avatar_split_clause,[],[f4113,f6874]) ).

fof(f6874,plain,
    ( spl38_207
  <=> ! [X0] :
        ( class_Groups_Ozero(tc_Polynomial_Opoly(X0))
        | ~ class_Groups_Ozero(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_207])]) ).

fof(f4113,plain,
    ! [X0] :
      ( class_Groups_Ozero(tc_Polynomial_Opoly(X0))
      | ~ class_Groups_Ozero(X0) ),
    inference(cnf_transformation,[],[f2340]) ).

fof(f2340,plain,
    ! [X0] :
      ( class_Groups_Ozero(tc_Polynomial_Opoly(X0))
      | ~ class_Groups_Ozero(X0) ),
    inference(ennf_transformation,[],[f1321]) ).

fof(f1321,plain,
    ! [X0] :
      ( class_Groups_Ozero(X0)
     => class_Groups_Ozero(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1199]) ).

fof(f1199,axiom,
    ! [X90] :
      ( class_Groups_Ozero(X90)
     => class_Groups_Ozero(tc_Polynomial_Opoly(X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ozero) ).

fof(f6872,plain,
    spl38_206,
    inference(avatar_split_clause,[],[f4112,f6870]) ).

fof(f6870,plain,
    ( spl38_206
  <=> ! [X0] :
        ( class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X0))
        | ~ class_Groups_Ocomm__monoid__add(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_206])]) ).

fof(f4112,plain,
    ! [X0] :
      ( class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X0))
      | ~ class_Groups_Ocomm__monoid__add(X0) ),
    inference(cnf_transformation,[],[f2339]) ).

fof(f2339,plain,
    ! [X0] :
      ( class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X0))
      | ~ class_Groups_Ocomm__monoid__add(X0) ),
    inference(ennf_transformation,[],[f1320]) ).

fof(f1320,plain,
    ! [X0] :
      ( class_Groups_Ocomm__monoid__add(X0)
     => class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1171]) ).

fof(f1171,axiom,
    ! [X90] :
      ( class_Groups_Ocomm__monoid__add(X90)
     => class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocomm__monoid__add) ).

fof(f6868,plain,
    spl38_205,
    inference(avatar_split_clause,[],[f4111,f6866]) ).

fof(f6866,plain,
    ( spl38_205
  <=> ! [X0] :
        ( class_Groups_Omonoid__add(tc_Polynomial_Opoly(X0))
        | ~ class_Groups_Ocomm__monoid__add(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_205])]) ).

fof(f4111,plain,
    ! [X0] :
      ( class_Groups_Omonoid__add(tc_Polynomial_Opoly(X0))
      | ~ class_Groups_Ocomm__monoid__add(X0) ),
    inference(cnf_transformation,[],[f2338]) ).

fof(f2338,plain,
    ! [X0] :
      ( class_Groups_Omonoid__add(tc_Polynomial_Opoly(X0))
      | ~ class_Groups_Ocomm__monoid__add(X0) ),
    inference(ennf_transformation,[],[f1319]) ).

fof(f1319,plain,
    ! [X0] :
      ( class_Groups_Ocomm__monoid__add(X0)
     => class_Groups_Omonoid__add(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1185]) ).

fof(f1185,axiom,
    ! [X90] :
      ( class_Groups_Ocomm__monoid__add(X90)
     => class_Groups_Omonoid__add(tc_Polynomial_Opoly(X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Omonoid__add) ).

fof(f6864,plain,
    spl38_204,
    inference(avatar_split_clause,[],[f4110,f6862]) ).

fof(f6862,plain,
    ( spl38_204
  <=> ! [X0] :
        ( class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X0))
        | ~ class_Groups_Ocomm__monoid__add(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_204])]) ).

fof(f4110,plain,
    ! [X0] :
      ( class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X0))
      | ~ class_Groups_Ocomm__monoid__add(X0) ),
    inference(cnf_transformation,[],[f2337]) ).

fof(f2337,plain,
    ! [X0] :
      ( class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X0))
      | ~ class_Groups_Ocomm__monoid__add(X0) ),
    inference(ennf_transformation,[],[f1318]) ).

fof(f1318,plain,
    ! [X0] :
      ( class_Groups_Ocomm__monoid__add(X0)
     => class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1168]) ).

fof(f1168,axiom,
    ! [X90] :
      ( class_Groups_Ocomm__monoid__add(X90)
     => class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__semigroup__add) ).

fof(f6860,plain,
    spl38_203,
    inference(avatar_split_clause,[],[f4106,f6858]) ).

fof(f6858,plain,
    ( spl38_203
  <=> ! [X0] :
        ( class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X0))
        | ~ class_Groups_Ocancel__comm__monoid__add(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_203])]) ).

fof(f4106,plain,
    ! [X0] :
      ( class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X0))
      | ~ class_Groups_Ocancel__comm__monoid__add(X0) ),
    inference(cnf_transformation,[],[f2333]) ).

fof(f2333,plain,
    ! [X0] :
      ( class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X0))
      | ~ class_Groups_Ocancel__comm__monoid__add(X0) ),
    inference(ennf_transformation,[],[f1314]) ).

fof(f1314,plain,
    ! [X0] :
      ( class_Groups_Ocancel__comm__monoid__add(X0)
     => class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1163]) ).

fof(f1163,axiom,
    ! [X90] :
      ( class_Groups_Ocancel__comm__monoid__add(X90)
     => class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add) ).

fof(f6856,plain,
    spl38_202,
    inference(avatar_split_clause,[],[f4105,f6854]) ).

fof(f6854,plain,
    ( spl38_202
  <=> ! [X0] :
        ( class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X0))
        | ~ class_Groups_Ocancel__comm__monoid__add(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_202])]) ).

fof(f4105,plain,
    ! [X0] :
      ( class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X0))
      | ~ class_Groups_Ocancel__comm__monoid__add(X0) ),
    inference(cnf_transformation,[],[f2332]) ).

fof(f2332,plain,
    ! [X0] :
      ( class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X0))
      | ~ class_Groups_Ocancel__comm__monoid__add(X0) ),
    inference(ennf_transformation,[],[f1313]) ).

fof(f1313,plain,
    ! [X0] :
      ( class_Groups_Ocancel__comm__monoid__add(X0)
     => class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f996]) ).

fof(f996,axiom,
    ! [X90] :
      ( class_Groups_Ocancel__comm__monoid__add(X90)
     => class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add) ).

fof(f6852,plain,
    spl38_201,
    inference(avatar_split_clause,[],[f4104,f6850]) ).

fof(f6850,plain,
    ( spl38_201
  <=> ! [X0] :
        ( class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X0))
        | ~ class_Groups_Ocancel__comm__monoid__add(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_201])]) ).

fof(f4104,plain,
    ! [X0] :
      ( class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X0))
      | ~ class_Groups_Ocancel__comm__monoid__add(X0) ),
    inference(cnf_transformation,[],[f2331]) ).

fof(f2331,plain,
    ! [X0] :
      ( class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X0))
      | ~ class_Groups_Ocancel__comm__monoid__add(X0) ),
    inference(ennf_transformation,[],[f1312]) ).

fof(f1312,plain,
    ! [X0] :
      ( class_Groups_Ocancel__comm__monoid__add(X0)
     => class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1155]) ).

fof(f1155,axiom,
    ! [X90] :
      ( class_Groups_Ocancel__comm__monoid__add(X90)
     => class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add) ).

fof(f6848,plain,
    spl38_200,
    inference(avatar_split_clause,[],[f4098,f6846]) ).

fof(f6846,plain,
    ( spl38_200
  <=> ! [X0] :
        ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Oidom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_200])]) ).

fof(f4098,plain,
    ! [X0] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Oidom(X0) ),
    inference(cnf_transformation,[],[f2325]) ).

fof(f2325,plain,
    ! [X0] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Oidom(X0) ),
    inference(ennf_transformation,[],[f1306]) ).

fof(f1306,plain,
    ! [X0] :
      ( class_Rings_Oidom(X0)
     => class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1146]) ).

fof(f1146,axiom,
    ! [X90] :
      ( class_Rings_Oidom(X90)
     => class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).

fof(f6844,plain,
    spl38_199,
    inference(avatar_split_clause,[],[f4097,f6842]) ).

fof(f6842,plain,
    ( spl38_199
  <=> ! [X0] :
        ( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Oidom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_199])]) ).

fof(f4097,plain,
    ! [X0] :
      ( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Oidom(X0) ),
    inference(cnf_transformation,[],[f2324]) ).

fof(f2324,plain,
    ! [X0] :
      ( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Oidom(X0) ),
    inference(ennf_transformation,[],[f1305]) ).

fof(f1305,plain,
    ! [X0] :
      ( class_Rings_Oidom(X0)
     => class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1170]) ).

fof(f1170,axiom,
    ! [X90] :
      ( class_Rings_Oidom(X90)
     => class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ono__zero__divisors) ).

fof(f6840,plain,
    spl38_198,
    inference(avatar_split_clause,[],[f4096,f6838]) ).

fof(f6838,plain,
    ( spl38_198
  <=> ! [X0] :
        ( class_Rings_Oidom(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Oidom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_198])]) ).

fof(f4096,plain,
    ! [X0] :
      ( class_Rings_Oidom(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Oidom(X0) ),
    inference(cnf_transformation,[],[f2323]) ).

fof(f2323,plain,
    ! [X0] :
      ( class_Rings_Oidom(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Oidom(X0) ),
    inference(ennf_transformation,[],[f1304]) ).

fof(f1304,plain,
    ! [X0] :
      ( class_Rings_Oidom(X0)
     => class_Rings_Oidom(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1201]) ).

fof(f1201,axiom,
    ! [X90] :
      ( class_Rings_Oidom(X90)
     => class_Rings_Oidom(tc_Polynomial_Opoly(X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oidom) ).

fof(f6836,plain,
    spl38_197,
    inference(avatar_split_clause,[],[f4095,f6834]) ).

fof(f6834,plain,
    ( spl38_197
  <=> ! [X0] :
        ( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Oidom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_197])]) ).

fof(f4095,plain,
    ! [X0] :
      ( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Oidom(X0) ),
    inference(cnf_transformation,[],[f2322]) ).

fof(f2322,plain,
    ! [X0] :
      ( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Oidom(X0) ),
    inference(ennf_transformation,[],[f1303]) ).

fof(f1303,plain,
    ! [X0] :
      ( class_Rings_Oidom(X0)
     => class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1156]) ).

fof(f1156,axiom,
    ! [X90] :
      ( class_Rings_Oidom(X90)
     => class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors) ).

fof(f6832,plain,
    spl38_196,
    inference(avatar_split_clause,[],[f4094,f6830]) ).

fof(f6830,plain,
    ( spl38_196
  <=> ! [X0] :
        ( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Oidom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_196])]) ).

fof(f4094,plain,
    ! [X0] :
      ( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Oidom(X0) ),
    inference(cnf_transformation,[],[f2321]) ).

fof(f2321,plain,
    ! [X0] :
      ( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Oidom(X0) ),
    inference(ennf_transformation,[],[f1302]) ).

fof(f1302,plain,
    ! [X0] :
      ( class_Rings_Oidom(X0)
     => class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1159]) ).

fof(f1159,axiom,
    ! [X90] :
      ( class_Rings_Oidom(X90)
     => class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors) ).

fof(f6828,plain,
    spl38_195,
    inference(avatar_split_clause,[],[f4091,f6826]) ).

fof(f6826,plain,
    ( spl38_195
  <=> ! [X0] :
        ( class_Groups_Ominus(tc_Polynomial_Opoly(X0))
        | ~ class_Groups_Oab__group__add(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_195])]) ).

fof(f4091,plain,
    ! [X0] :
      ( class_Groups_Ominus(tc_Polynomial_Opoly(X0))
      | ~ class_Groups_Oab__group__add(X0) ),
    inference(cnf_transformation,[],[f2318]) ).

fof(f2318,plain,
    ! [X0] :
      ( class_Groups_Ominus(tc_Polynomial_Opoly(X0))
      | ~ class_Groups_Oab__group__add(X0) ),
    inference(ennf_transformation,[],[f1299]) ).

fof(f1299,plain,
    ! [X0] :
      ( class_Groups_Oab__group__add(X0)
     => class_Groups_Ominus(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1197]) ).

fof(f1197,axiom,
    ! [X90] :
      ( class_Groups_Oab__group__add(X90)
     => class_Groups_Ominus(tc_Polynomial_Opoly(X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ominus) ).

fof(f6824,plain,
    spl38_194,
    inference(avatar_split_clause,[],[f4090,f6822]) ).

fof(f6822,plain,
    ( spl38_194
  <=> ! [X0] :
        ( class_Groups_Ouminus(tc_Polynomial_Opoly(X0))
        | ~ class_Groups_Oab__group__add(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_194])]) ).

fof(f4090,plain,
    ! [X0] :
      ( class_Groups_Ouminus(tc_Polynomial_Opoly(X0))
      | ~ class_Groups_Oab__group__add(X0) ),
    inference(cnf_transformation,[],[f2317]) ).

fof(f2317,plain,
    ! [X0] :
      ( class_Groups_Ouminus(tc_Polynomial_Opoly(X0))
      | ~ class_Groups_Oab__group__add(X0) ),
    inference(ennf_transformation,[],[f1298]) ).

fof(f1298,plain,
    ! [X0] :
      ( class_Groups_Oab__group__add(X0)
     => class_Groups_Ouminus(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1195]) ).

fof(f1195,axiom,
    ! [X90] :
      ( class_Groups_Oab__group__add(X90)
     => class_Groups_Ouminus(tc_Polynomial_Opoly(X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ouminus) ).

fof(f6820,plain,
    spl38_193,
    inference(avatar_split_clause,[],[f4089,f6818]) ).

fof(f6818,plain,
    ( spl38_193
  <=> ! [X0] :
        ( class_Groups_Ogroup__add(tc_Polynomial_Opoly(X0))
        | ~ class_Groups_Oab__group__add(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_193])]) ).

fof(f4089,plain,
    ! [X0] :
      ( class_Groups_Ogroup__add(tc_Polynomial_Opoly(X0))
      | ~ class_Groups_Oab__group__add(X0) ),
    inference(cnf_transformation,[],[f2316]) ).

fof(f2316,plain,
    ! [X0] :
      ( class_Groups_Ogroup__add(tc_Polynomial_Opoly(X0))
      | ~ class_Groups_Oab__group__add(X0) ),
    inference(ennf_transformation,[],[f1297]) ).

fof(f1297,plain,
    ! [X0] :
      ( class_Groups_Oab__group__add(X0)
     => class_Groups_Ogroup__add(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1187]) ).

fof(f1187,axiom,
    ! [X90] :
      ( class_Groups_Oab__group__add(X90)
     => class_Groups_Ogroup__add(tc_Polynomial_Opoly(X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ogroup__add) ).

fof(f6816,plain,
    spl38_192,
    inference(avatar_split_clause,[],[f4088,f6814]) ).

fof(f6814,plain,
    ( spl38_192
  <=> ! [X0] :
        ( class_Groups_Oab__group__add(tc_Polynomial_Opoly(X0))
        | ~ class_Groups_Oab__group__add(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_192])]) ).

fof(f4088,plain,
    ! [X0] :
      ( class_Groups_Oab__group__add(tc_Polynomial_Opoly(X0))
      | ~ class_Groups_Oab__group__add(X0) ),
    inference(cnf_transformation,[],[f2315]) ).

fof(f2315,plain,
    ! [X0] :
      ( class_Groups_Oab__group__add(tc_Polynomial_Opoly(X0))
      | ~ class_Groups_Oab__group__add(X0) ),
    inference(ennf_transformation,[],[f1296]) ).

fof(f1296,plain,
    ! [X0] :
      ( class_Groups_Oab__group__add(X0)
     => class_Groups_Oab__group__add(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1178]) ).

fof(f1178,axiom,
    ! [X90] :
      ( class_Groups_Oab__group__add(X90)
     => class_Groups_Oab__group__add(tc_Polynomial_Opoly(X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__group__add) ).

fof(f6812,plain,
    spl38_191,
    inference(avatar_split_clause,[],[f4087,f6810]) ).

fof(f6810,plain,
    ( spl38_191
  <=> ! [X0] :
        ( class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Ocomm__ring__1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_191])]) ).

fof(f4087,plain,
    ! [X0] :
      ( class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__ring__1(X0) ),
    inference(cnf_transformation,[],[f2314]) ).

fof(f2314,plain,
    ! [X0] :
      ( class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__ring__1(X0) ),
    inference(ennf_transformation,[],[f1295]) ).

fof(f1295,plain,
    ! [X0] :
      ( class_Rings_Ocomm__ring__1(X0)
     => class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1184]) ).

fof(f1184,axiom,
    ! [X90] :
      ( class_Rings_Ocomm__ring__1(X90)
     => class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__ring__1) ).

fof(f6808,plain,
    spl38_190,
    inference(avatar_split_clause,[],[f4086,f6806]) ).

fof(f6806,plain,
    ( spl38_190
  <=> ! [X0] :
        ( class_Rings_Oring__1(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Ocomm__ring__1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_190])]) ).

fof(f4086,plain,
    ! [X0] :
      ( class_Rings_Oring__1(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__ring__1(X0) ),
    inference(cnf_transformation,[],[f2313]) ).

fof(f2313,plain,
    ! [X0] :
      ( class_Rings_Oring__1(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__ring__1(X0) ),
    inference(ennf_transformation,[],[f1294]) ).

fof(f1294,plain,
    ! [X0] :
      ( class_Rings_Ocomm__ring__1(X0)
     => class_Rings_Oring__1(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1196]) ).

fof(f1196,axiom,
    ! [X90] :
      ( class_Rings_Ocomm__ring__1(X90)
     => class_Rings_Oring__1(tc_Polynomial_Opoly(X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__1) ).

fof(f6804,plain,
    spl38_189,
    inference(avatar_split_clause,[],[f4085,f6802]) ).

fof(f6802,plain,
    ( spl38_189
  <=> ! [X0] :
        ( class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Ocomm__ring(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_189])]) ).

fof(f4085,plain,
    ! [X0] :
      ( class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__ring(X0) ),
    inference(cnf_transformation,[],[f2312]) ).

fof(f2312,plain,
    ! [X0] :
      ( class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__ring(X0) ),
    inference(ennf_transformation,[],[f1293]) ).

fof(f1293,plain,
    ! [X0] :
      ( class_Rings_Ocomm__ring(X0)
     => class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1190]) ).

fof(f1190,axiom,
    ! [X90] :
      ( class_Rings_Ocomm__ring(X90)
     => class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__ring) ).

fof(f6800,plain,
    spl38_188,
    inference(avatar_split_clause,[],[f4084,f6798]) ).

fof(f6798,plain,
    ( spl38_188
  <=> ! [X0] :
        ( class_Rings_Oring(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Ocomm__ring(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_188])]) ).

fof(f4084,plain,
    ! [X0] :
      ( class_Rings_Oring(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__ring(X0) ),
    inference(cnf_transformation,[],[f2311]) ).

fof(f2311,plain,
    ! [X0] :
      ( class_Rings_Oring(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__ring(X0) ),
    inference(ennf_transformation,[],[f1292]) ).

fof(f1292,plain,
    ! [X0] :
      ( class_Rings_Ocomm__ring(X0)
     => class_Rings_Oring(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1200]) ).

fof(f1200,axiom,
    ! [X90] :
      ( class_Rings_Ocomm__ring(X90)
     => class_Rings_Oring(tc_Polynomial_Opoly(X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring) ).

fof(f6796,plain,
    spl38_187,
    inference(avatar_split_clause,[],[f4082,f6794]) ).

fof(f6794,plain,
    ( spl38_187
  <=> ! [X0] :
        ( class_Orderings_Oorder(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Olinordered__idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_187])]) ).

fof(f4082,plain,
    ! [X0] :
      ( class_Orderings_Oorder(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(cnf_transformation,[],[f2309]) ).

fof(f2309,plain,
    ! [X0] :
      ( class_Orderings_Oorder(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(ennf_transformation,[],[f1290]) ).

fof(f1290,plain,
    ! [X0] :
      ( class_Rings_Olinordered__idom(X0)
     => class_Orderings_Oorder(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1191]) ).

fof(f1191,axiom,
    ! [X90] :
      ( class_Rings_Olinordered__idom(X90)
     => class_Orderings_Oorder(tc_Polynomial_Opoly(X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Oorder) ).

fof(f6792,plain,
    spl38_186,
    inference(avatar_split_clause,[],[f4081,f6790]) ).

fof(f6790,plain,
    ( spl38_186
  <=> ! [X0] :
        ( class_Orderings_Opreorder(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Olinordered__idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_186])]) ).

fof(f4081,plain,
    ! [X0] :
      ( class_Orderings_Opreorder(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(cnf_transformation,[],[f2308]) ).

fof(f2308,plain,
    ! [X0] :
      ( class_Orderings_Opreorder(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(ennf_transformation,[],[f1289]) ).

fof(f1289,plain,
    ! [X0] :
      ( class_Rings_Olinordered__idom(X0)
     => class_Orderings_Opreorder(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1181]) ).

fof(f1181,axiom,
    ! [X90] :
      ( class_Rings_Olinordered__idom(X90)
     => class_Orderings_Opreorder(tc_Polynomial_Opoly(X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Opreorder) ).

fof(f6788,plain,
    spl38_185,
    inference(avatar_split_clause,[],[f4080,f6786]) ).

fof(f6786,plain,
    ( spl38_185
  <=> ! [X0] :
        ( class_Orderings_Oord(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Olinordered__idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_185])]) ).

fof(f4080,plain,
    ! [X0] :
      ( class_Orderings_Oord(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(cnf_transformation,[],[f2307]) ).

fof(f2307,plain,
    ! [X0] :
      ( class_Orderings_Oord(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(ennf_transformation,[],[f1288]) ).

fof(f1288,plain,
    ! [X0] :
      ( class_Rings_Olinordered__idom(X0)
     => class_Orderings_Oord(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1194]) ).

fof(f1194,axiom,
    ! [X90] :
      ( class_Rings_Olinordered__idom(X90)
     => class_Orderings_Oord(tc_Polynomial_Opoly(X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Oord) ).

fof(f6784,plain,
    spl38_184,
    inference(avatar_split_clause,[],[f4079,f6782]) ).

fof(f6782,plain,
    ( spl38_184
  <=> ! [X0] :
        ( class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Olinordered__idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_184])]) ).

fof(f4079,plain,
    ! [X0] :
      ( class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(cnf_transformation,[],[f2306]) ).

fof(f2306,plain,
    ! [X0] :
      ( class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(ennf_transformation,[],[f1287]) ).

fof(f1287,plain,
    ! [X0] :
      ( class_Rings_Olinordered__idom(X0)
     => class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1165]) ).

fof(f1165,axiom,
    ! [X90] :
      ( class_Rings_Olinordered__idom(X90)
     => class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semidom) ).

fof(f6780,plain,
    spl38_183,
    inference(avatar_split_clause,[],[f4078,f6778]) ).

fof(f6778,plain,
    ( spl38_183
  <=> ! [X0] :
        ( class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Olinordered__idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_183])]) ).

fof(f4078,plain,
    ! [X0] :
      ( class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(cnf_transformation,[],[f2305]) ).

fof(f2305,plain,
    ! [X0] :
      ( class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(ennf_transformation,[],[f1286]) ).

fof(f1286,plain,
    ! [X0] :
      ( class_Rings_Olinordered__idom(X0)
     => class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1151]) ).

fof(f1151,axiom,
    ! [X90] :
      ( class_Rings_Olinordered__idom(X90)
     => class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict) ).

fof(f6776,plain,
    spl38_182,
    inference(avatar_split_clause,[],[f4077,f6774]) ).

fof(f6774,plain,
    ( spl38_182
  <=> ! [X0] :
        ( class_Orderings_Olinorder(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Olinordered__idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_182])]) ).

fof(f4077,plain,
    ! [X0] :
      ( class_Orderings_Olinorder(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(cnf_transformation,[],[f2304]) ).

fof(f2304,plain,
    ! [X0] :
      ( class_Orderings_Olinorder(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(ennf_transformation,[],[f1285]) ).

fof(f1285,plain,
    ! [X0] :
      ( class_Rings_Olinordered__idom(X0)
     => class_Orderings_Olinorder(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1182]) ).

fof(f1182,axiom,
    ! [X90] :
      ( class_Rings_Olinordered__idom(X90)
     => class_Orderings_Olinorder(tc_Polynomial_Opoly(X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Olinorder) ).

fof(f6772,plain,
    spl38_181,
    inference(avatar_split_clause,[],[f4076,f6770]) ).

fof(f6770,plain,
    ( spl38_181
  <=> ! [X0] :
        ( class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Olinordered__idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_181])]) ).

fof(f4076,plain,
    ! [X0] :
      ( class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(cnf_transformation,[],[f2303]) ).

fof(f2303,plain,
    ! [X0] :
      ( class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(ennf_transformation,[],[f1284]) ).

fof(f1284,plain,
    ! [X0] :
      ( class_Rings_Olinordered__idom(X0)
     => class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1153]) ).

fof(f1153,axiom,
    ! [X90] :
      ( class_Rings_Olinordered__idom(X90)
     => class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add) ).

fof(f6768,plain,
    spl38_180,
    inference(avatar_split_clause,[],[f4075,f6766]) ).

fof(f6766,plain,
    ( spl38_180
  <=> ! [X0] :
        ( class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Olinordered__idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_180])]) ).

fof(f4075,plain,
    ! [X0] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(cnf_transformation,[],[f2302]) ).

fof(f2302,plain,
    ! [X0] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(ennf_transformation,[],[f1283]) ).

fof(f1283,plain,
    ! [X0] :
      ( class_Rings_Olinordered__idom(X0)
     => class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1148]) ).

fof(f1148,axiom,
    ! [X90] :
      ( class_Rings_Olinordered__idom(X90)
     => class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le) ).

fof(f6764,plain,
    spl38_179,
    inference(avatar_split_clause,[],[f4074,f6762]) ).

fof(f6762,plain,
    ( spl38_179
  <=> ! [X0] :
        ( class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Olinordered__idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_179])]) ).

fof(f4074,plain,
    ! [X0] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(cnf_transformation,[],[f2301]) ).

fof(f2301,plain,
    ! [X0] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(ennf_transformation,[],[f1282]) ).

fof(f1282,plain,
    ! [X0] :
      ( class_Rings_Olinordered__idom(X0)
     => class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1147]) ).

fof(f1147,axiom,
    ! [X90] :
      ( class_Rings_Olinordered__idom(X90)
     => class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add) ).

fof(f6760,plain,
    spl38_178,
    inference(avatar_split_clause,[],[f4073,f6758]) ).

fof(f6758,plain,
    ( spl38_178
  <=> ! [X0] :
        ( class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Olinordered__idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_178])]) ).

fof(f4073,plain,
    ! [X0] :
      ( class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(cnf_transformation,[],[f2300]) ).

fof(f2300,plain,
    ! [X0] :
      ( class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(ennf_transformation,[],[f1281]) ).

fof(f1281,plain,
    ! [X0] :
      ( class_Rings_Olinordered__idom(X0)
     => class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1157]) ).

fof(f1157,axiom,
    ! [X90] :
      ( class_Rings_Olinordered__idom(X90)
     => class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring) ).

fof(f6756,plain,
    spl38_177,
    inference(avatar_split_clause,[],[f4072,f6754]) ).

fof(f6754,plain,
    ( spl38_177
  <=> ! [X0] :
        ( class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Olinordered__idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_177])]) ).

fof(f4072,plain,
    ! [X0] :
      ( class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(cnf_transformation,[],[f2299]) ).

fof(f2299,plain,
    ! [X0] :
      ( class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(ennf_transformation,[],[f1280]) ).

fof(f1280,plain,
    ! [X0] :
      ( class_Rings_Olinordered__idom(X0)
     => class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1169]) ).

fof(f1169,axiom,
    ! [X90] :
      ( class_Rings_Olinordered__idom(X90)
     => class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__semiring) ).

fof(f6752,plain,
    spl38_176,
    inference(avatar_split_clause,[],[f4071,f6750]) ).

fof(f6750,plain,
    ( spl38_176
  <=> ! [X0] :
        ( class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Olinordered__idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_176])]) ).

fof(f4071,plain,
    ! [X0] :
      ( class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(cnf_transformation,[],[f2298]) ).

fof(f2298,plain,
    ! [X0] :
      ( class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(ennf_transformation,[],[f1279]) ).

fof(f1279,plain,
    ! [X0] :
      ( class_Rings_Olinordered__idom(X0)
     => class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1152]) ).

fof(f1152,axiom,
    ! [X90] :
      ( class_Rings_Olinordered__idom(X90)
     => class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add) ).

fof(f6748,plain,
    spl38_175,
    inference(avatar_split_clause,[],[f4070,f6746]) ).

fof(f6746,plain,
    ( spl38_175
  <=> ! [X0] :
        ( class_Int_Oring__char__0(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Olinordered__idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_175])]) ).

fof(f4070,plain,
    ! [X0] :
      ( class_Int_Oring__char__0(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(cnf_transformation,[],[f2297]) ).

fof(f2297,plain,
    ! [X0] :
      ( class_Int_Oring__char__0(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(ennf_transformation,[],[f1278]) ).

fof(f1278,plain,
    ! [X0] :
      ( class_Rings_Olinordered__idom(X0)
     => class_Int_Oring__char__0(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1192]) ).

fof(f1192,axiom,
    ! [X90] :
      ( class_Rings_Olinordered__idom(X90)
     => class_Int_Oring__char__0(tc_Polynomial_Opoly(X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Int_Oring__char__0) ).

fof(f6744,plain,
    spl38_174,
    inference(avatar_split_clause,[],[f4069,f6742]) ).

fof(f6742,plain,
    ( spl38_174
  <=> ! [X0] :
        ( class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Olinordered__idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_174])]) ).

fof(f4069,plain,
    ! [X0] :
      ( class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(cnf_transformation,[],[f2296]) ).

fof(f2296,plain,
    ! [X0] :
      ( class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(ennf_transformation,[],[f1277]) ).

fof(f1277,plain,
    ! [X0] :
      ( class_Rings_Olinordered__idom(X0)
     => class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1164]) ).

fof(f1164,axiom,
    ! [X90] :
      ( class_Rings_Olinordered__idom(X90)
     => class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring) ).

fof(f6740,plain,
    spl38_173,
    inference(avatar_split_clause,[],[f4068,f6738]) ).

fof(f6738,plain,
    ( spl38_173
  <=> ! [X0] :
        ( class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Olinordered__idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_173])]) ).

fof(f4068,plain,
    ! [X0] :
      ( class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(cnf_transformation,[],[f2295]) ).

fof(f2295,plain,
    ! [X0] :
      ( class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(ennf_transformation,[],[f1276]) ).

fof(f1276,plain,
    ! [X0] :
      ( class_Rings_Olinordered__idom(X0)
     => class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1149]) ).

fof(f1149,axiom,
    ! [X90] :
      ( class_Rings_Olinordered__idom(X90)
     => class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict) ).

fof(f6736,plain,
    spl38_172,
    inference(avatar_split_clause,[],[f4067,f6734]) ).

fof(f6734,plain,
    ( spl38_172
  <=> ! [X0] :
        ( class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Olinordered__idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_172])]) ).

fof(f4067,plain,
    ! [X0] :
      ( class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(cnf_transformation,[],[f2294]) ).

fof(f2294,plain,
    ! [X0] :
      ( class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(ennf_transformation,[],[f1275]) ).

fof(f1275,plain,
    ! [X0] :
      ( class_Rings_Olinordered__idom(X0)
     => class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1160]) ).

fof(f1160,axiom,
    ! [X90] :
      ( class_Rings_Olinordered__idom(X90)
     => class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__comm__semiring) ).

fof(f6732,plain,
    spl38_171,
    inference(avatar_split_clause,[],[f4066,f6730]) ).

fof(f6730,plain,
    ( spl38_171
  <=> ! [X0] :
        ( class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Olinordered__idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_171])]) ).

fof(f4066,plain,
    ! [X0] :
      ( class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(cnf_transformation,[],[f2293]) ).

fof(f2293,plain,
    ! [X0] :
      ( class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(ennf_transformation,[],[f1274]) ).

fof(f1274,plain,
    ! [X0] :
      ( class_Rings_Olinordered__idom(X0)
     => class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1173]) ).

fof(f1173,axiom,
    ! [X90] :
      ( class_Rings_Olinordered__idom(X90)
     => class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__idom) ).

fof(f6728,plain,
    spl38_170,
    inference(avatar_split_clause,[],[f4065,f6726]) ).

fof(f6726,plain,
    ( spl38_170
  <=> ! [X0] :
        ( class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Olinordered__idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_170])]) ).

fof(f4065,plain,
    ! [X0] :
      ( class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(cnf_transformation,[],[f2292]) ).

fof(f2292,plain,
    ! [X0] :
      ( class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(ennf_transformation,[],[f1273]) ).

fof(f1273,plain,
    ! [X0] :
      ( class_Rings_Olinordered__idom(X0)
     => class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1162]) ).

fof(f1162,axiom,
    ! [X90] :
      ( class_Rings_Olinordered__idom(X90)
     => class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__group__add) ).

fof(f6724,plain,
    spl38_169,
    inference(avatar_split_clause,[],[f4064,f6722]) ).

fof(f6722,plain,
    ( spl38_169
  <=> ! [X0] :
        ( class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Olinordered__idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_169])]) ).

fof(f4064,plain,
    ! [X0] :
      ( class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(cnf_transformation,[],[f2291]) ).

fof(f2291,plain,
    ! [X0] :
      ( class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(ennf_transformation,[],[f1272]) ).

fof(f1272,plain,
    ! [X0] :
      ( class_Rings_Olinordered__idom(X0)
     => class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1158]) ).

fof(f1158,axiom,
    ! [X90] :
      ( class_Rings_Olinordered__idom(X90)
     => class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__ring__strict) ).

fof(f6720,plain,
    spl38_168,
    inference(avatar_split_clause,[],[f4063,f6718]) ).

fof(f6718,plain,
    ( spl38_168
  <=> ! [X0] :
        ( class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Olinordered__idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_168])]) ).

fof(f4063,plain,
    ! [X0] :
      ( class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(cnf_transformation,[],[f2290]) ).

fof(f2290,plain,
    ! [X0] :
      ( class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(ennf_transformation,[],[f1271]) ).

fof(f1271,plain,
    ! [X0] :
      ( class_Rings_Olinordered__idom(X0)
     => class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1154]) ).

fof(f1154,axiom,
    ! [X90] :
      ( class_Rings_Olinordered__idom(X90)
     => class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add) ).

fof(f6716,plain,
    spl38_167,
    inference(avatar_split_clause,[],[f4062,f6714]) ).

fof(f6714,plain,
    ( spl38_167
  <=> ! [X0] :
        ( class_Rings_Oordered__ring(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Olinordered__idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_167])]) ).

fof(f4062,plain,
    ! [X0] :
      ( class_Rings_Oordered__ring(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(cnf_transformation,[],[f2289]) ).

fof(f2289,plain,
    ! [X0] :
      ( class_Rings_Oordered__ring(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(ennf_transformation,[],[f1270]) ).

fof(f1270,plain,
    ! [X0] :
      ( class_Rings_Olinordered__idom(X0)
     => class_Rings_Oordered__ring(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1180]) ).

fof(f1180,axiom,
    ! [X90] :
      ( class_Rings_Olinordered__idom(X90)
     => class_Rings_Oordered__ring(tc_Polynomial_Opoly(X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__ring) ).

fof(f6712,plain,
    spl38_166,
    inference(avatar_split_clause,[],[f4061,f6710]) ).

fof(f6710,plain,
    ( spl38_166
  <=> ! [X0] :
        ( class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Olinordered__idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_166])]) ).

fof(f4061,plain,
    ! [X0] :
      ( class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(cnf_transformation,[],[f2288]) ).

fof(f2288,plain,
    ! [X0] :
      ( class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(ennf_transformation,[],[f1269]) ).

fof(f1269,plain,
    ! [X0] :
      ( class_Rings_Olinordered__idom(X0)
     => class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1172]) ).

fof(f1172,axiom,
    ! [X90] :
      ( class_Rings_Olinordered__idom(X90)
     => class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__ring) ).

fof(f6708,plain,
    spl38_165,
    inference(avatar_split_clause,[],[f4060,f6706]) ).

fof(f6706,plain,
    ( spl38_165
  <=> ! [X0] :
        ( class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Olinordered__idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_165])]) ).

fof(f4060,plain,
    ! [X0] :
      ( class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(cnf_transformation,[],[f2287]) ).

fof(f2287,plain,
    ! [X0] :
      ( class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(ennf_transformation,[],[f1268]) ).

fof(f1268,plain,
    ! [X0] :
      ( class_Rings_Olinordered__idom(X0)
     => class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1150]) ).

fof(f1150,axiom,
    ! [X90] :
      ( class_Rings_Olinordered__idom(X90)
     => class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict) ).

fof(f6704,plain,
    spl38_164,
    inference(avatar_split_clause,[],[f4059,f6702]) ).

fof(f6702,plain,
    ( spl38_164
  <=> ! [X0] :
        ( class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Olinordered__idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_164])]) ).

fof(f4059,plain,
    ! [X0] :
      ( class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(cnf_transformation,[],[f2286]) ).

fof(f2286,plain,
    ! [X0] :
      ( class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(ennf_transformation,[],[f1267]) ).

fof(f1267,plain,
    ! [X0] :
      ( class_Rings_Olinordered__idom(X0)
     => class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1161]) ).

fof(f1161,axiom,
    ! [X90] :
      ( class_Rings_Olinordered__idom(X90)
     => class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__1) ).

fof(f6700,plain,
    spl38_163,
    inference(avatar_split_clause,[],[f4057,f6698]) ).

fof(f6698,plain,
    ( spl38_163
  <=> ! [X0] :
        ( class_Divides_Osemiring__div(tc_Polynomial_Opoly(X0))
        | ~ class_Fields_Ofield(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_163])]) ).

fof(f4057,plain,
    ! [X0] :
      ( class_Divides_Osemiring__div(tc_Polynomial_Opoly(X0))
      | ~ class_Fields_Ofield(X0) ),
    inference(cnf_transformation,[],[f2284]) ).

fof(f2284,plain,
    ! [X0] :
      ( class_Divides_Osemiring__div(tc_Polynomial_Opoly(X0))
      | ~ class_Fields_Ofield(X0) ),
    inference(ennf_transformation,[],[f1265]) ).

fof(f1265,plain,
    ! [X0] :
      ( class_Fields_Ofield(X0)
     => class_Divides_Osemiring__div(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1176]) ).

fof(f1176,axiom,
    ! [X90] :
      ( class_Fields_Ofield(X90)
     => class_Divides_Osemiring__div(tc_Polynomial_Opoly(X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Divides_Osemiring__div) ).

fof(f6696,plain,
    spl38_162,
    inference(avatar_split_clause,[],[f4056,f6694]) ).

fof(f6694,plain,
    ( spl38_162
  <=> ! [X0] :
        ( class_Divides_Oring__div(tc_Polynomial_Opoly(X0))
        | ~ class_Fields_Ofield(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_162])]) ).

fof(f4056,plain,
    ! [X0] :
      ( class_Divides_Oring__div(tc_Polynomial_Opoly(X0))
      | ~ class_Fields_Ofield(X0) ),
    inference(cnf_transformation,[],[f2283]) ).

fof(f2283,plain,
    ! [X0] :
      ( class_Divides_Oring__div(tc_Polynomial_Opoly(X0))
      | ~ class_Fields_Ofield(X0) ),
    inference(ennf_transformation,[],[f1264]) ).

fof(f1264,plain,
    ! [X0] :
      ( class_Fields_Ofield(X0)
     => class_Divides_Oring__div(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1188]) ).

fof(f1188,axiom,
    ! [X90] :
      ( class_Fields_Ofield(X90)
     => class_Divides_Oring__div(tc_Polynomial_Opoly(X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Divides_Oring__div) ).

fof(f6692,plain,
    spl38_161,
    inference(avatar_split_clause,[],[f4019,f6690]) ).

fof(f6690,plain,
    ( spl38_161
  <=> ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_161])]) ).

fof(f4019,plain,
    ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0),
    inference(cnf_transformation,[],[f1227]) ).

fof(f1227,plain,
    ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0),
    inference(rectify,[],[f229]) ).

fof(f229,axiom,
    ! [X10] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X10),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le0) ).

fof(f6688,plain,
    spl38_160,
    inference(avatar_split_clause,[],[f4015,f6686]) ).

fof(f6686,plain,
    ( spl38_160
  <=> ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_160])]) ).

fof(f4015,plain,
    ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(cnf_transformation,[],[f1223]) ).

fof(f1223,plain,
    ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(rectify,[],[f338]) ).

fof(f338,axiom,
    ! [X10] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less0) ).

fof(f6684,plain,
    spl38_159,
    inference(avatar_split_clause,[],[f3987,f6681]) ).

fof(f6681,plain,
    ( spl38_159
  <=> v_na____ = c_Polynomial_Odegree(tc_Complex_Ocomplex,v_pa____) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_159])]) ).

fof(f3987,plain,
    v_na____ = c_Polynomial_Odegree(tc_Complex_Ocomplex,v_pa____),
    inference(cnf_transformation,[],[f30]) ).

fof(f30,axiom,
    v_na____ = c_Polynomial_Odegree(tc_Complex_Ocomplex,v_pa____),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dpn) ).

fof(f6679,plain,
    spl38_158,
    inference(avatar_split_clause,[],[f3986,f6676]) ).

fof(f6676,plain,
    ( spl38_158
  <=> v_n = c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_158])]) ).

fof(f3986,plain,
    v_n = c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p),
    inference(cnf_transformation,[],[f26]) ).

fof(f26,axiom,
    v_n = c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_assms_I2_J) ).

fof(f6674,plain,
    ~ spl38_157,
    inference(avatar_split_clause,[],[f3984,f6671]) ).

fof(f6671,plain,
    ( spl38_157
  <=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_157])]) ).

fof(f3984,plain,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
    inference(cnf_transformation,[],[f746]) ).

fof(f746,axiom,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__0__neq__1) ).

fof(f6669,plain,
    spl38_156,
    inference(avatar_split_clause,[],[f5761,f6666]) ).

fof(f6666,plain,
    ( spl38_156
  <=> v_qa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),v_s____))),sK18) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_156])]) ).

fof(f5761,plain,
    v_qa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),v_s____))),sK18),
    inference(forward_demodulation,[],[f4001,f3837]) ).

fof(f4001,plain,
    v_qa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),sK18),
    inference(cnf_transformation,[],[f3480]) ).

fof(f3480,plain,
    v_qa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),sK18),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f2278,f3479]) ).

fof(f3479,plain,
    ( ? [X0] : v_qa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),X0)
   => v_qa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),sK18) ),
    introduced(choice_axiom,[]) ).

fof(f2278,plain,
    ? [X0] : v_qa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),X0),
    inference(ennf_transformation,[],[f1209]) ).

fof(f1209,plain,
    ~ ! [X0] : v_qa____ != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),X0),
    inference(rectify,[],[f226]) ).

fof(f226,axiom,
    ~ ! [X32] : v_qa____ != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),X32),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_Br_O_Aq_A_061_A_091_058_N_Aa_M_A1_058_093_A_K_Ar_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).

fof(f6664,plain,
    spl38_155,
    inference(avatar_split_clause,[],[f5756,f6661]) ).

fof(f6661,plain,
    ( spl38_155
  <=> v_qa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),v_s____))),v_r____) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_155])]) ).

fof(f5756,plain,
    v_qa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),v_s____))),v_r____),
    inference(forward_demodulation,[],[f3996,f3837]) ).

fof(f3996,plain,
    v_qa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_r____),
    inference(cnf_transformation,[],[f67]) ).

fof(f67,axiom,
    v_qa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_r____),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_r) ).

fof(f6659,plain,
    spl38_154,
    inference(avatar_split_clause,[],[f5755,f6656]) ).

fof(f6656,plain,
    ( spl38_154
  <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),v_s____))),v_qa____)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_154])]) ).

fof(f5755,plain,
    hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),v_s____))),v_qa____)),
    inference(forward_demodulation,[],[f3995,f3837]) ).

fof(f3995,plain,
    hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_qa____)),
    inference(cnf_transformation,[],[f68]) ).

fof(f68,axiom,
    hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_qa____)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_091_058_N_Aa_M_A1_058_093_Advd_Aq_096) ).

fof(f6654,plain,
    spl38_153,
    inference(avatar_split_clause,[],[f5590,f6652]) ).

fof(f6652,plain,
    ( spl38_153
  <=> ! [X1] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_153])]) ).

fof(f5590,plain,
    ! [X1] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X1),
    inference(equality_resolution,[],[f4452]) ).

fof(f4452,plain,
    ! [X0,X1] :
      ( X0 != X1
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
    inference(cnf_transformation,[],[f3553]) ).

fof(f6650,plain,
    spl38_152,
    inference(avatar_split_clause,[],[f5546,f6648]) ).

fof(f6648,plain,
    ( spl38_152
  <=> ! [X1] : hBOOL(c_fequal(X1,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_152])]) ).

fof(f5546,plain,
    ! [X1] : hBOOL(c_fequal(X1,X1)),
    inference(equality_resolution,[],[f4184]) ).

fof(f4184,plain,
    ! [X0,X1] :
      ( hBOOL(c_fequal(X1,X0))
      | X0 != X1 ),
    inference(cnf_transformation,[],[f1381]) ).

fof(f1381,plain,
    ! [X0,X1] :
      ( hBOOL(c_fequal(X1,X0))
      | X0 != X1 ),
    inference(rectify,[],[f1205]) ).

fof(f1205,axiom,
    ! [X17,X3] :
      ( hBOOL(c_fequal(X3,X17))
      | X3 != X17 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__2) ).

fof(f6646,plain,
    spl38_151,
    inference(avatar_split_clause,[],[f4008,f6644]) ).

fof(f6644,plain,
    ( spl38_151
  <=> ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_151])]) ).

fof(f4008,plain,
    ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X0),
    inference(cnf_transformation,[],[f1216]) ).

fof(f1216,plain,
    ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X0),
    inference(rectify,[],[f320]) ).

fof(f320,axiom,
    ! [X10] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X10,X10),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__refl) ).

fof(f6642,plain,
    spl38_150,
    inference(avatar_split_clause,[],[f4007,f6640]) ).

fof(f6640,plain,
    ( spl38_150
  <=> ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_150])]) ).

fof(f4007,plain,
    ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X0),
    inference(cnf_transformation,[],[f1215]) ).

fof(f1215,plain,
    ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X0),
    inference(rectify,[],[f730]) ).

fof(f730,axiom,
    ! [X74] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X74,X74),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__refl) ).

fof(f6638,plain,
    spl38_149,
    inference(avatar_split_clause,[],[f4005,f6636]) ).

fof(f6636,plain,
    ( spl38_149
  <=> ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_149])]) ).

fof(f4005,plain,
    ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X0),
    inference(cnf_transformation,[],[f1213]) ).

fof(f1213,plain,
    ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X0),
    inference(rectify,[],[f312]) ).

fof(f312,axiom,
    ! [X10] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,X10),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__irrefl__nat) ).

fof(f6634,plain,
    ~ spl38_148,
    inference(avatar_split_clause,[],[f3982,f6631]) ).

fof(f6631,plain,
    ( spl38_148
  <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v_na____ ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_148])]) ).

fof(f3982,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != v_na____,
    inference(cnf_transformation,[],[f16]) ).

fof(f16,axiom,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != v_na____,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n0) ).

fof(f6629,plain,
    ~ spl38_147,
    inference(avatar_split_clause,[],[f3981,f6626]) ).

fof(f6626,plain,
    ( spl38_147
  <=> v_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_147])]) ).

fof(f3981,plain,
    v_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(cnf_transformation,[],[f7]) ).

fof(f7,axiom,
    v_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_assms_I3_J) ).

fof(f6624,plain,
    spl38_146,
    inference(avatar_split_clause,[],[f3980,f6621]) ).

fof(f6621,plain,
    ( spl38_146
  <=> class_Groups_Ominus(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_146])]) ).

fof(f3980,plain,
    class_Groups_Ominus(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1097]) ).

fof(f1097,axiom,
    class_Groups_Ominus(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ominus) ).

fof(f6619,plain,
    spl38_145,
    inference(avatar_split_clause,[],[f3979,f6616]) ).

fof(f6616,plain,
    ( spl38_145
  <=> class_Groups_Ominus(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_145])]) ).

fof(f3979,plain,
    class_Groups_Ominus(tc_Int_Oint),
    inference(cnf_transformation,[],[f1057]) ).

fof(f1057,axiom,
    class_Groups_Ominus(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ominus) ).

fof(f6614,plain,
    spl38_144,
    inference(avatar_split_clause,[],[f3978,f6611]) ).

fof(f6611,plain,
    ( spl38_144
  <=> class_Groups_Ominus(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_144])]) ).

fof(f3978,plain,
    class_Groups_Ominus(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1138]) ).

fof(f1138,axiom,
    class_Groups_Ominus(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ominus) ).

fof(f6609,plain,
    spl38_143,
    inference(avatar_split_clause,[],[f3977,f6606]) ).

fof(f6606,plain,
    ( spl38_143
  <=> class_Groups_Ominus(tc_HOL_Obool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_143])]) ).

fof(f3977,plain,
    class_Groups_Ominus(tc_HOL_Obool),
    inference(cnf_transformation,[],[f1107]) ).

fof(f1107,axiom,
    class_Groups_Ominus(tc_HOL_Obool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Groups_Ominus) ).

fof(f6604,plain,
    spl38_142,
    inference(avatar_split_clause,[],[f3976,f6601]) ).

fof(f6601,plain,
    ( spl38_142
  <=> class_Orderings_Oorder(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_142])]) ).

fof(f3976,plain,
    class_Orderings_Oorder(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1094]) ).

fof(f1094,axiom,
    class_Orderings_Oorder(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).

fof(f6599,plain,
    spl38_141,
    inference(avatar_split_clause,[],[f3975,f6596]) ).

fof(f6596,plain,
    ( spl38_141
  <=> class_Orderings_Oorder(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_141])]) ).

fof(f3975,plain,
    class_Orderings_Oorder(tc_Int_Oint),
    inference(cnf_transformation,[],[f1051]) ).

fof(f1051,axiom,
    class_Orderings_Oorder(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oorder) ).

fof(f6594,plain,
    spl38_140,
    inference(avatar_split_clause,[],[f3974,f6591]) ).

fof(f6591,plain,
    ( spl38_140
  <=> class_Orderings_Oorder(tc_HOL_Obool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_140])]) ).

fof(f3974,plain,
    class_Orderings_Oorder(tc_HOL_Obool),
    inference(cnf_transformation,[],[f1104]) ).

fof(f1104,axiom,
    class_Orderings_Oorder(tc_HOL_Obool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oorder) ).

fof(f6589,plain,
    spl38_139,
    inference(avatar_split_clause,[],[f3973,f6586]) ).

fof(f6586,plain,
    ( spl38_139
  <=> class_Orderings_Opreorder(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_139])]) ).

fof(f3973,plain,
    class_Orderings_Opreorder(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1088]) ).

fof(f1088,axiom,
    class_Orderings_Opreorder(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).

fof(f6584,plain,
    spl38_138,
    inference(avatar_split_clause,[],[f3972,f6581]) ).

fof(f6581,plain,
    ( spl38_138
  <=> class_Orderings_Opreorder(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_138])]) ).

fof(f3972,plain,
    class_Orderings_Opreorder(tc_Int_Oint),
    inference(cnf_transformation,[],[f1041]) ).

fof(f1041,axiom,
    class_Orderings_Opreorder(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Opreorder) ).

fof(f6579,plain,
    spl38_137,
    inference(avatar_split_clause,[],[f3971,f6576]) ).

fof(f6576,plain,
    ( spl38_137
  <=> class_Orderings_Opreorder(tc_HOL_Obool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_137])]) ).

fof(f3971,plain,
    class_Orderings_Opreorder(tc_HOL_Obool),
    inference(cnf_transformation,[],[f1103]) ).

fof(f1103,axiom,
    class_Orderings_Opreorder(tc_HOL_Obool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Opreorder) ).

fof(f6574,plain,
    spl38_136,
    inference(avatar_split_clause,[],[f3970,f6571]) ).

fof(f6571,plain,
    ( spl38_136
  <=> class_Orderings_Oord(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_136])]) ).

fof(f3970,plain,
    class_Orderings_Oord(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1096]) ).

fof(f1096,axiom,
    class_Orderings_Oord(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).

fof(f6569,plain,
    spl38_135,
    inference(avatar_split_clause,[],[f3969,f6566]) ).

fof(f6566,plain,
    ( spl38_135
  <=> class_Orderings_Oord(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_135])]) ).

fof(f3969,plain,
    class_Orderings_Oord(tc_Int_Oint),
    inference(cnf_transformation,[],[f1054]) ).

fof(f1054,axiom,
    class_Orderings_Oord(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oord) ).

fof(f6564,plain,
    spl38_134,
    inference(avatar_split_clause,[],[f3968,f6561]) ).

fof(f6561,plain,
    ( spl38_134
  <=> class_Orderings_Oord(tc_HOL_Obool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_134])]) ).

fof(f3968,plain,
    class_Orderings_Oord(tc_HOL_Obool),
    inference(cnf_transformation,[],[f1105]) ).

fof(f1105,axiom,
    class_Orderings_Oord(tc_HOL_Obool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oord) ).

fof(f6559,plain,
    spl38_133,
    inference(avatar_split_clause,[],[f3967,f6556]) ).

fof(f6556,plain,
    ( spl38_133
  <=> class_Groups_Ouminus(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_133])]) ).

fof(f3967,plain,
    class_Groups_Ouminus(tc_Int_Oint),
    inference(cnf_transformation,[],[f1055]) ).

fof(f1055,axiom,
    class_Groups_Ouminus(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ouminus) ).

fof(f6554,plain,
    spl38_132,
    inference(avatar_split_clause,[],[f3966,f6551]) ).

fof(f6551,plain,
    ( spl38_132
  <=> class_Groups_Ouminus(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_132])]) ).

fof(f3966,plain,
    class_Groups_Ouminus(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1136]) ).

fof(f1136,axiom,
    class_Groups_Ouminus(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ouminus) ).

fof(f6549,plain,
    spl38_131,
    inference(avatar_split_clause,[],[f3965,f6546]) ).

fof(f6546,plain,
    ( spl38_131
  <=> class_Groups_Ouminus(tc_HOL_Obool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_131])]) ).

fof(f3965,plain,
    class_Groups_Ouminus(tc_HOL_Obool),
    inference(cnf_transformation,[],[f1106]) ).

fof(f1106,axiom,
    class_Groups_Ouminus(tc_HOL_Obool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Groups_Ouminus) ).

fof(f6544,plain,
    spl38_130,
    inference(avatar_split_clause,[],[f3964,f6541]) ).

fof(f6541,plain,
    ( spl38_130
  <=> class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_130])]) ).

fof(f3964,plain,
    class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1083]) ).

fof(f1083,axiom,
    class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).

fof(f6539,plain,
    spl38_129,
    inference(avatar_split_clause,[],[f3963,f6536]) ).

fof(f6536,plain,
    ( spl38_129
  <=> class_Rings_Ocomm__semiring__1(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_129])]) ).

fof(f3963,plain,
    class_Rings_Ocomm__semiring__1(tc_Int_Oint),
    inference(cnf_transformation,[],[f1034]) ).

fof(f1034,axiom,
    class_Rings_Ocomm__semiring__1(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__1) ).

fof(f6534,plain,
    spl38_128,
    inference(avatar_split_clause,[],[f3962,f6531]) ).

fof(f3962,plain,
    class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1121]) ).

fof(f1121,axiom,
    class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).

fof(f6529,plain,
    spl38_127,
    inference(avatar_split_clause,[],[f3961,f6526]) ).

fof(f6526,plain,
    ( spl38_127
  <=> class_Rings_Ocomm__semiring__0(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_127])]) ).

fof(f3961,plain,
    class_Rings_Ocomm__semiring__0(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1084]) ).

fof(f1084,axiom,
    class_Rings_Ocomm__semiring__0(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__0) ).

fof(f6524,plain,
    spl38_126,
    inference(avatar_split_clause,[],[f3960,f6521]) ).

fof(f6521,plain,
    ( spl38_126
  <=> class_Rings_Ocomm__semiring__0(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_126])]) ).

fof(f3960,plain,
    class_Rings_Ocomm__semiring__0(tc_Int_Oint),
    inference(cnf_transformation,[],[f1035]) ).

fof(f1035,axiom,
    class_Rings_Ocomm__semiring__0(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__0) ).

fof(f6519,plain,
    spl38_125,
    inference(avatar_split_clause,[],[f3959,f6516]) ).

fof(f3959,plain,
    class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1122]) ).

fof(f1122,axiom,
    class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__0) ).

fof(f6514,plain,
    spl38_124,
    inference(avatar_split_clause,[],[f3958,f6511]) ).

fof(f6511,plain,
    ( spl38_124
  <=> class_Groups_Ozero(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_124])]) ).

fof(f3958,plain,
    class_Groups_Ozero(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1099]) ).

fof(f1099,axiom,
    class_Groups_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ozero) ).

fof(f6509,plain,
    spl38_123,
    inference(avatar_split_clause,[],[f3957,f6506]) ).

fof(f6506,plain,
    ( spl38_123
  <=> class_Groups_Ozero(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_123])]) ).

fof(f3957,plain,
    class_Groups_Ozero(tc_Int_Oint),
    inference(cnf_transformation,[],[f1059]) ).

fof(f1059,axiom,
    class_Groups_Ozero(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ozero) ).

fof(f6504,plain,
    spl38_122,
    inference(avatar_split_clause,[],[f3956,f6501]) ).

fof(f3956,plain,
    class_Groups_Ozero(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1141]) ).

fof(f1141,axiom,
    class_Groups_Ozero(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ozero) ).

fof(f6499,plain,
    spl38_121,
    inference(avatar_split_clause,[],[f3955,f6496]) ).

fof(f6496,plain,
    ( spl38_121
  <=> class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_121])]) ).

fof(f3955,plain,
    class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1082]) ).

fof(f1082,axiom,
    class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__add) ).

fof(f6494,plain,
    spl38_120,
    inference(avatar_split_clause,[],[f3954,f6491]) ).

fof(f6491,plain,
    ( spl38_120
  <=> class_Groups_Ocomm__monoid__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_120])]) ).

fof(f3954,plain,
    class_Groups_Ocomm__monoid__add(tc_Int_Oint),
    inference(cnf_transformation,[],[f1031]) ).

fof(f1031,axiom,
    class_Groups_Ocomm__monoid__add(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__add) ).

fof(f6489,plain,
    spl38_119,
    inference(avatar_split_clause,[],[f3953,f6486]) ).

fof(f3953,plain,
    class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1120]) ).

fof(f1120,axiom,
    class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocomm__monoid__add) ).

fof(f6484,plain,
    spl38_118,
    inference(avatar_split_clause,[],[f3952,f6481]) ).

fof(f6481,plain,
    ( spl38_118
  <=> class_Groups_Omonoid__mult(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_118])]) ).

fof(f3952,plain,
    class_Groups_Omonoid__mult(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1090]) ).

fof(f1090,axiom,
    class_Groups_Omonoid__mult(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__mult) ).

fof(f6479,plain,
    spl38_117,
    inference(avatar_split_clause,[],[f3951,f6476]) ).

fof(f6476,plain,
    ( spl38_117
  <=> class_Groups_Omonoid__mult(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_117])]) ).

fof(f3951,plain,
    class_Groups_Omonoid__mult(tc_Int_Oint),
    inference(cnf_transformation,[],[f1043]) ).

fof(f1043,axiom,
    class_Groups_Omonoid__mult(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__mult) ).

fof(f6474,plain,
    spl38_116,
    inference(avatar_split_clause,[],[f3950,f6471]) ).

fof(f6471,plain,
    ( spl38_116
  <=> class_Groups_Omonoid__mult(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_116])]) ).

fof(f3950,plain,
    class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1127]) ).

fof(f1127,axiom,
    class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Omonoid__mult) ).

fof(f6469,plain,
    spl38_115,
    inference(avatar_split_clause,[],[f3949,f6466]) ).

fof(f6466,plain,
    ( spl38_115
  <=> class_Power_Opower(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_115])]) ).

fof(f3949,plain,
    class_Power_Opower(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1098]) ).

fof(f1098,axiom,
    class_Power_Opower(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Power_Opower) ).

fof(f6464,plain,
    spl38_114,
    inference(avatar_split_clause,[],[f3948,f6461]) ).

fof(f6461,plain,
    ( spl38_114
  <=> class_Power_Opower(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_114])]) ).

fof(f3948,plain,
    class_Power_Opower(tc_Int_Oint),
    inference(cnf_transformation,[],[f1058]) ).

fof(f1058,axiom,
    class_Power_Opower(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Power_Opower) ).

fof(f6459,plain,
    spl38_113,
    inference(avatar_split_clause,[],[f3947,f6456]) ).

fof(f6456,plain,
    ( spl38_113
  <=> class_Power_Opower(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_113])]) ).

fof(f3947,plain,
    class_Power_Opower(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1140]) ).

fof(f1140,axiom,
    class_Power_Opower(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Power_Opower) ).

fof(f6454,plain,
    spl38_112,
    inference(avatar_split_clause,[],[f3946,f6451]) ).

fof(f6451,plain,
    ( spl38_112
  <=> class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_112])]) ).

fof(f3946,plain,
    class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1074]) ).

fof(f1074,axiom,
    class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).

fof(f6449,plain,
    spl38_111,
    inference(avatar_split_clause,[],[f3945,f6446]) ).

fof(f6446,plain,
    ( spl38_111
  <=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_111])]) ).

fof(f3945,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1064]) ).

fof(f1064,axiom,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).

fof(f6444,plain,
    spl38_110,
    inference(avatar_split_clause,[],[f3944,f6441]) ).

fof(f6441,plain,
    ( spl38_110
  <=> class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_110])]) ).

fof(f3944,plain,
    class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
    inference(cnf_transformation,[],[f1023]) ).

fof(f1023,axiom,
    class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__semigroup__add) ).

fof(f6439,plain,
    spl38_109,
    inference(avatar_split_clause,[],[f3943,f6436]) ).

fof(f6436,plain,
    ( spl38_109
  <=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_109])]) ).

fof(f3943,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
    inference(cnf_transformation,[],[f1006]) ).

fof(f1006,axiom,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).

fof(f6434,plain,
    spl38_108,
    inference(avatar_split_clause,[],[f3942,f6431]) ).

fof(f6431,plain,
    ( spl38_108
  <=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_108])]) ).

fof(f3942,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1108]) ).

fof(f1108,axiom,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).

fof(f6429,plain,
    spl38_107,
    inference(avatar_split_clause,[],[f3941,f6426]) ).

fof(f6426,plain,
    ( spl38_107
  <=> class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_107])]) ).

fof(f3941,plain,
    class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1114]) ).

fof(f1114,axiom,
    class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add) ).

fof(f6424,plain,
    spl38_106,
    inference(avatar_split_clause,[],[f3940,f6421]) ).

fof(f6421,plain,
    ( spl38_106
  <=> class_Rings_Ozero__neq__one(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_106])]) ).

fof(f3940,plain,
    class_Rings_Ozero__neq__one(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1087]) ).

fof(f1087,axiom,
    class_Rings_Ozero__neq__one(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ozero__neq__one) ).

fof(f6419,plain,
    spl38_105,
    inference(avatar_split_clause,[],[f3939,f6416]) ).

fof(f6416,plain,
    ( spl38_105
  <=> class_Rings_Osemiring__0(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_105])]) ).

fof(f3939,plain,
    class_Rings_Osemiring__0(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1092]) ).

fof(f1092,axiom,
    class_Rings_Osemiring__0(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__0) ).

fof(f6414,plain,
    spl38_104,
    inference(avatar_split_clause,[],[f3938,f6411]) ).

fof(f6411,plain,
    ( spl38_104
  <=> class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_104])]) ).

fof(f3938,plain,
    class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat),
    inference(cnf_transformation,[],[f998]) ).

fof(f998,axiom,
    class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__comm__monoid__add) ).

fof(f6409,plain,
    spl38_103,
    inference(avatar_split_clause,[],[f3937,f6406]) ).

fof(f6406,plain,
    ( spl38_103
  <=> class_Rings_Ono__zero__divisors(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_103])]) ).

fof(f3937,plain,
    class_Rings_Ono__zero__divisors(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1081]) ).

fof(f1081,axiom,
    class_Rings_Ono__zero__divisors(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ono__zero__divisors) ).

fof(f6404,plain,
    spl38_102,
    inference(avatar_split_clause,[],[f3936,f6401]) ).

fof(f6401,plain,
    ( spl38_102
  <=> class_Rings_Omult__zero(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_102])]) ).

fof(f3936,plain,
    class_Rings_Omult__zero(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1093]) ).

fof(f1093,axiom,
    class_Rings_Omult__zero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Omult__zero) ).

fof(f6399,plain,
    spl38_101,
    inference(avatar_split_clause,[],[f3935,f6396]) ).

fof(f6396,plain,
    ( spl38_101
  <=> class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_101])]) ).

fof(f3935,plain,
    class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1078]) ).

fof(f1078,axiom,
    class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__mult) ).

fof(f6394,plain,
    spl38_100,
    inference(avatar_split_clause,[],[f3934,f6391]) ).

fof(f6391,plain,
    ( spl38_100
  <=> class_Rings_Ozero__neq__one(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_100])]) ).

fof(f3934,plain,
    class_Rings_Ozero__neq__one(tc_Int_Oint),
    inference(cnf_transformation,[],[f1039]) ).

fof(f1039,axiom,
    class_Rings_Ozero__neq__one(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ozero__neq__one) ).

fof(f6389,plain,
    spl38_99,
    inference(avatar_split_clause,[],[f3933,f6386]) ).

fof(f6386,plain,
    ( spl38_99
  <=> class_Rings_Osemiring__0(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_99])]) ).

fof(f3933,plain,
    class_Rings_Osemiring__0(tc_Int_Oint),
    inference(cnf_transformation,[],[f1046]) ).

fof(f1046,axiom,
    class_Rings_Osemiring__0(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring__0) ).

fof(f6384,plain,
    spl38_98,
    inference(avatar_split_clause,[],[f3932,f6381]) ).

fof(f6381,plain,
    ( spl38_98
  <=> class_Rings_Omult__zero(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_98])]) ).

fof(f3932,plain,
    class_Rings_Omult__zero(tc_Int_Oint),
    inference(cnf_transformation,[],[f1049]) ).

fof(f1049,axiom,
    class_Rings_Omult__zero(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Omult__zero) ).

fof(f6379,plain,
    spl38_97,
    inference(avatar_split_clause,[],[f3931,f6376]) ).

fof(f6376,plain,
    ( spl38_97
  <=> class_Rings_Ono__zero__divisors(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_97])]) ).

fof(f3931,plain,
    class_Rings_Ono__zero__divisors(tc_Int_Oint),
    inference(cnf_transformation,[],[f1030]) ).

fof(f1030,axiom,
    class_Rings_Ono__zero__divisors(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ono__zero__divisors) ).

fof(f6374,plain,
    spl38_96,
    inference(avatar_split_clause,[],[f3930,f6371]) ).

fof(f6371,plain,
    ( spl38_96
  <=> class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_96])]) ).

fof(f3930,plain,
    class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint),
    inference(cnf_transformation,[],[f999]) ).

fof(f999,axiom,
    class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__comm__monoid__add) ).

fof(f6369,plain,
    spl38_95,
    inference(avatar_split_clause,[],[f3929,f6366]) ).

fof(f6366,plain,
    ( spl38_95
  <=> class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_95])]) ).

fof(f3929,plain,
    class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
    inference(cnf_transformation,[],[f1027]) ).

fof(f1027,axiom,
    class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__mult) ).

fof(f6364,plain,
    spl38_94,
    inference(avatar_split_clause,[],[f3928,f6361]) ).

fof(f6361,plain,
    ( spl38_94
  <=> class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_94])]) ).

fof(f3928,plain,
    class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f997]) ).

fof(f997,axiom,
    class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add) ).

fof(f6359,plain,
    spl38_93,
    inference(avatar_split_clause,[],[f3927,f6356]) ).

fof(f6356,plain,
    ( spl38_93
  <=> class_Rings_Osemiring__0(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_93])]) ).

fof(f3927,plain,
    class_Rings_Osemiring__0(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1130]) ).

fof(f1130,axiom,
    class_Rings_Osemiring__0(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring__0) ).

fof(f6354,plain,
    spl38_92,
    inference(avatar_split_clause,[],[f3926,f6351]) ).

fof(f6351,plain,
    ( spl38_92
  <=> class_Rings_Omult__zero(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_92])]) ).

fof(f3926,plain,
    class_Rings_Omult__zero(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1132]) ).

fof(f1132,axiom,
    class_Rings_Omult__zero(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Omult__zero) ).

fof(f6349,plain,
    spl38_91,
    inference(avatar_split_clause,[],[f3925,f6346]) ).

fof(f6346,plain,
    ( spl38_91
  <=> class_Rings_Ozero__neq__one(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_91])]) ).

fof(f3925,plain,
    class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1126]) ).

fof(f1126,axiom,
    class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ozero__neq__one) ).

fof(f6344,plain,
    spl38_90,
    inference(avatar_split_clause,[],[f3924,f6341]) ).

fof(f6341,plain,
    ( spl38_90
  <=> class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_90])]) ).

fof(f3924,plain,
    class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1119]) ).

fof(f1119,axiom,
    class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ono__zero__divisors) ).

fof(f6339,plain,
    spl38_89,
    inference(avatar_split_clause,[],[f3923,f6336]) ).

fof(f6336,plain,
    ( spl38_89
  <=> class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_89])]) ).

fof(f3923,plain,
    class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1117]) ).

fof(f1117,axiom,
    class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult) ).

fof(f6334,plain,
    spl38_88,
    inference(avatar_split_clause,[],[f3922,f6331]) ).

fof(f6331,plain,
    ( spl38_88
  <=> class_Rings_Odvd(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_88])]) ).

fof(f3922,plain,
    class_Rings_Odvd(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1101]) ).

fof(f1101,axiom,
    class_Rings_Odvd(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Odvd) ).

fof(f6329,plain,
    spl38_87,
    inference(avatar_split_clause,[],[f3921,f6326]) ).

fof(f6326,plain,
    ( spl38_87
  <=> class_Groups_Omonoid__add(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_87])]) ).

fof(f3921,plain,
    class_Groups_Omonoid__add(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1091]) ).

fof(f1091,axiom,
    class_Groups_Omonoid__add(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__add) ).

fof(f6324,plain,
    spl38_86,
    inference(avatar_split_clause,[],[f3920,f6321]) ).

fof(f6321,plain,
    ( spl38_86
  <=> class_Rings_Odvd(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_86])]) ).

fof(f3920,plain,
    class_Rings_Odvd(tc_Int_Oint),
    inference(cnf_transformation,[],[f1063]) ).

fof(f1063,axiom,
    class_Rings_Odvd(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Odvd) ).

fof(f6319,plain,
    spl38_85,
    inference(avatar_split_clause,[],[f3919,f6316]) ).

fof(f6316,plain,
    ( spl38_85
  <=> class_Groups_Omonoid__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_85])]) ).

fof(f3919,plain,
    class_Groups_Omonoid__add(tc_Int_Oint),
    inference(cnf_transformation,[],[f1045]) ).

fof(f1045,axiom,
    class_Groups_Omonoid__add(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__add) ).

fof(f6314,plain,
    spl38_84,
    inference(avatar_split_clause,[],[f3918,f6311]) ).

fof(f6311,plain,
    ( spl38_84
  <=> class_Rings_Odvd(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_84])]) ).

fof(f3918,plain,
    class_Rings_Odvd(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1145]) ).

fof(f1145,axiom,
    class_Rings_Odvd(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odvd) ).

fof(f6309,plain,
    spl38_83,
    inference(avatar_split_clause,[],[f3917,f6306]) ).

fof(f6306,plain,
    ( spl38_83
  <=> class_Groups_Omonoid__add(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_83])]) ).

fof(f3917,plain,
    class_Groups_Omonoid__add(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1129]) ).

fof(f1129,axiom,
    class_Groups_Omonoid__add(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Omonoid__add) ).

fof(f6304,plain,
    spl38_82,
    inference(avatar_split_clause,[],[f3916,f6301]) ).

fof(f6301,plain,
    ( spl38_82
  <=> class_Rings_Ocomm__semiring(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_82])]) ).

fof(f3916,plain,
    class_Rings_Ocomm__semiring(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1086]) ).

fof(f1086,axiom,
    class_Rings_Ocomm__semiring(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring) ).

fof(f6299,plain,
    spl38_81,
    inference(avatar_split_clause,[],[f3915,f6296]) ).

fof(f6296,plain,
    ( spl38_81
  <=> class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_81])]) ).

fof(f3915,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1071]) ).

fof(f1071,axiom,
    class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) ).

fof(f6294,plain,
    spl38_80,
    inference(avatar_split_clause,[],[f3914,f6291]) ).

fof(f6291,plain,
    ( spl38_80
  <=> class_Groups_Oab__semigroup__add(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_80])]) ).

fof(f3914,plain,
    class_Groups_Oab__semigroup__add(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1079]) ).

fof(f1079,axiom,
    class_Groups_Oab__semigroup__add(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__add) ).

fof(f6289,plain,
    spl38_79,
    inference(avatar_split_clause,[],[f3913,f6286]) ).

fof(f6286,plain,
    ( spl38_79
  <=> class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_79])]) ).

fof(f3913,plain,
    class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1077]) ).

fof(f1077,axiom,
    class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__mult) ).

fof(f6284,plain,
    spl38_78,
    inference(avatar_split_clause,[],[f3912,f6281]) ).

fof(f6281,plain,
    ( spl38_78
  <=> class_Groups_Oone(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_78])]) ).

fof(f3912,plain,
    class_Groups_Oone(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1100]) ).

fof(f1100,axiom,
    class_Groups_Oone(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oone) ).

fof(f6279,plain,
    spl38_77,
    inference(avatar_split_clause,[],[f3911,f6276]) ).

fof(f6276,plain,
    ( spl38_77
  <=> class_Rings_Osemiring(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_77])]) ).

fof(f3911,plain,
    class_Rings_Osemiring(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1095]) ).

fof(f1095,axiom,
    class_Rings_Osemiring(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring) ).

fof(f6274,plain,
    spl38_76,
    inference(avatar_split_clause,[],[f3910,f6271]) ).

fof(f6271,plain,
    ( spl38_76
  <=> class_Groups_Oab__semigroup__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_76])]) ).

fof(f3910,plain,
    class_Groups_Oab__semigroup__add(tc_Int_Oint),
    inference(cnf_transformation,[],[f1028]) ).

fof(f1028,axiom,
    class_Groups_Oab__semigroup__add(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__add) ).

fof(f6269,plain,
    spl38_75,
    inference(avatar_split_clause,[],[f3909,f6266]) ).

fof(f6266,plain,
    ( spl38_75
  <=> class_Groups_Oone(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_75])]) ).

fof(f3909,plain,
    class_Groups_Oone(tc_Int_Oint),
    inference(cnf_transformation,[],[f1062]) ).

fof(f1062,axiom,
    class_Groups_Oone(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oone) ).

fof(f6264,plain,
    spl38_74,
    inference(avatar_split_clause,[],[f3908,f6261]) ).

fof(f6261,plain,
    ( spl38_74
  <=> class_Rings_Ocomm__semiring(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_74])]) ).

fof(f3908,plain,
    class_Rings_Ocomm__semiring(tc_Int_Oint),
    inference(cnf_transformation,[],[f1037]) ).

fof(f1037,axiom,
    class_Rings_Ocomm__semiring(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring) ).

fof(f6259,plain,
    spl38_73,
    inference(avatar_split_clause,[],[f3907,f6256]) ).

fof(f6256,plain,
    ( spl38_73
  <=> class_Groups_Oab__semigroup__mult(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_73])]) ).

fof(f3907,plain,
    class_Groups_Oab__semigroup__mult(tc_Int_Oint),
    inference(cnf_transformation,[],[f1026]) ).

fof(f1026,axiom,
    class_Groups_Oab__semigroup__mult(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__mult) ).

fof(f6254,plain,
    spl38_72,
    inference(avatar_split_clause,[],[f3906,f6251]) ).

fof(f6251,plain,
    ( spl38_72
  <=> class_Rings_Osemiring(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_72])]) ).

fof(f3906,plain,
    class_Rings_Osemiring(tc_Int_Oint),
    inference(cnf_transformation,[],[f1053]) ).

fof(f1053,axiom,
    class_Rings_Osemiring(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring) ).

fof(f6249,plain,
    spl38_71,
    inference(avatar_split_clause,[],[f3905,f6246]) ).

fof(f6246,plain,
    ( spl38_71
  <=> class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_71])]) ).

fof(f3905,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
    inference(cnf_transformation,[],[f1015]) ).

fof(f1015,axiom,
    class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__ab__semigroup__add) ).

fof(f6244,plain,
    spl38_70,
    inference(avatar_split_clause,[],[f3904,f6241]) ).

fof(f6241,plain,
    ( spl38_70
  <=> class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_70])]) ).

fof(f3904,plain,
    class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1118]) ).

fof(f1118,axiom,
    class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__semigroup__add) ).

fof(f6239,plain,
    spl38_69,
    inference(avatar_split_clause,[],[f3903,f6236]) ).

fof(f6236,plain,
    ( spl38_69
  <=> class_Rings_Ocomm__semiring(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_69])]) ).

fof(f3903,plain,
    class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1124]) ).

fof(f1124,axiom,
    class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring) ).

fof(f6234,plain,
    spl38_68,
    inference(avatar_split_clause,[],[f3902,f6231]) ).

fof(f6231,plain,
    ( spl38_68
  <=> class_Rings_Osemiring(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_68])]) ).

fof(f3902,plain,
    class_Rings_Osemiring(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1135]) ).

fof(f1135,axiom,
    class_Rings_Osemiring(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring) ).

fof(f6229,plain,
    spl38_67,
    inference(avatar_split_clause,[],[f3901,f6226]) ).

fof(f6226,plain,
    ( spl38_67
  <=> class_Groups_Oone(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_67])]) ).

fof(f3901,plain,
    class_Groups_Oone(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1144]) ).

fof(f1144,axiom,
    class_Groups_Oone(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oone) ).

fof(f6224,plain,
    spl38_66,
    inference(avatar_split_clause,[],[f3900,f6221]) ).

fof(f6221,plain,
    ( spl38_66
  <=> class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_66])]) ).

fof(f3900,plain,
    class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1116]) ).

fof(f1116,axiom,
    class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__semigroup__mult) ).

fof(f6219,plain,
    spl38_65,
    inference(avatar_split_clause,[],[f3899,f6216]) ).

fof(f6216,plain,
    ( spl38_65
  <=> class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_65])]) ).

fof(f3899,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1111]) ).

fof(f1111,axiom,
    class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add) ).

fof(f6214,plain,
    spl38_64,
    inference(avatar_split_clause,[],[f3898,f6211]) ).

fof(f6211,plain,
    ( spl38_64
  <=> class_Rings_Olinordered__semidom(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_64])]) ).

fof(f3898,plain,
    class_Rings_Olinordered__semidom(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1076]) ).

fof(f1076,axiom,
    class_Rings_Olinordered__semidom(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semidom) ).

fof(f6209,plain,
    spl38_63,
    inference(avatar_split_clause,[],[f3897,f6206]) ).

fof(f6206,plain,
    ( spl38_63
  <=> class_Rings_Olinordered__semidom(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_63])]) ).

fof(f3897,plain,
    class_Rings_Olinordered__semidom(tc_Int_Oint),
    inference(cnf_transformation,[],[f1025]) ).

fof(f1025,axiom,
    class_Rings_Olinordered__semidom(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semidom) ).

fof(f6204,plain,
    spl38_62,
    inference(avatar_split_clause,[],[f3896,f6201]) ).

fof(f6201,plain,
    ( spl38_62
  <=> class_Divides_Osemiring__div(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_62])]) ).

fof(f3896,plain,
    class_Divides_Osemiring__div(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1085]) ).

fof(f1085,axiom,
    class_Divides_Osemiring__div(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Divides_Osemiring__div) ).

fof(f6199,plain,
    spl38_61,
    inference(avatar_split_clause,[],[f3895,f6196]) ).

fof(f6196,plain,
    ( spl38_61
  <=> class_Divides_Osemiring__div(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_61])]) ).

fof(f3895,plain,
    class_Divides_Osemiring__div(tc_Int_Oint),
    inference(cnf_transformation,[],[f1036]) ).

fof(f1036,axiom,
    class_Divides_Osemiring__div(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Divides_Osemiring__div) ).

fof(f6194,plain,
    spl38_60,
    inference(avatar_split_clause,[],[f3894,f6191]) ).

fof(f6191,plain,
    ( spl38_60
  <=> class_Rings_Oidom(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_60])]) ).

fof(f3894,plain,
    class_Rings_Oidom(tc_Int_Oint),
    inference(cnf_transformation,[],[f1061]) ).

fof(f1061,axiom,
    class_Rings_Oidom(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oidom) ).

fof(f6189,plain,
    spl38_59,
    inference(avatar_split_clause,[],[f3893,f6186]) ).

fof(f6186,plain,
    ( spl38_59
  <=> class_Rings_Oidom(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_59])]) ).

fof(f3893,plain,
    class_Rings_Oidom(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1143]) ).

fof(f1143,axiom,
    class_Rings_Oidom(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oidom) ).

fof(f6184,plain,
    spl38_58,
    inference(avatar_split_clause,[],[f3892,f6181]) ).

fof(f6181,plain,
    ( spl38_58
  <=> class_Groups_Ogroup__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_58])]) ).

fof(f3892,plain,
    class_Groups_Ogroup__add(tc_Int_Oint),
    inference(cnf_transformation,[],[f1047]) ).

fof(f1047,axiom,
    class_Groups_Ogroup__add(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ogroup__add) ).

fof(f6179,plain,
    spl38_57,
    inference(avatar_split_clause,[],[f3891,f6176]) ).

fof(f6176,plain,
    ( spl38_57
  <=> class_Groups_Ogroup__add(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_57])]) ).

fof(f3891,plain,
    class_Groups_Ogroup__add(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1131]) ).

fof(f1131,axiom,
    class_Groups_Ogroup__add(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ogroup__add) ).

fof(f6174,plain,
    spl38_56,
    inference(avatar_split_clause,[],[f3890,f6171]) ).

fof(f6171,plain,
    ( spl38_56
  <=> class_Groups_Oab__group__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_56])]) ).

fof(f3890,plain,
    class_Groups_Oab__group__add(tc_Int_Oint),
    inference(cnf_transformation,[],[f1038]) ).

fof(f1038,axiom,
    class_Groups_Oab__group__add(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__group__add) ).

fof(f6169,plain,
    spl38_55,
    inference(avatar_split_clause,[],[f3889,f6166]) ).

fof(f3889,plain,
    class_Groups_Oab__group__add(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1125]) ).

fof(f1125,axiom,
    class_Groups_Oab__group__add(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__group__add) ).

fof(f6164,plain,
    spl38_54,
    inference(avatar_split_clause,[],[f3888,f6161]) ).

fof(f6161,plain,
    ( spl38_54
  <=> class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_54])]) ).

fof(f3888,plain,
    class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1068]) ).

fof(f1068,axiom,
    class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring__strict) ).

fof(f6159,plain,
    spl38_53,
    inference(avatar_split_clause,[],[f3887,f6156]) ).

fof(f6156,plain,
    ( spl38_53
  <=> class_Orderings_Olinorder(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_53])]) ).

fof(f3887,plain,
    class_Orderings_Olinorder(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1089]) ).

fof(f1089,axiom,
    class_Orderings_Olinorder(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).

fof(f6154,plain,
    spl38_52,
    inference(avatar_split_clause,[],[f3886,f6151]) ).

fof(f6151,plain,
    ( spl38_52
  <=> class_Orderings_Olinorder(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_52])]) ).

fof(f3886,plain,
    class_Orderings_Olinorder(tc_Int_Oint),
    inference(cnf_transformation,[],[f1042]) ).

fof(f1042,axiom,
    class_Orderings_Olinorder(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Olinorder) ).

fof(f6149,plain,
    spl38_51,
    inference(avatar_split_clause,[],[f3885,f6146]) ).

fof(f6146,plain,
    ( spl38_51
  <=> class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_51])]) ).

fof(f3885,plain,
    class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
    inference(cnf_transformation,[],[f1011]) ).

fof(f1011,axiom,
    class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__strict) ).

fof(f6144,plain,
    spl38_50,
    inference(avatar_split_clause,[],[f3884,f6141]) ).

fof(f6141,plain,
    ( spl38_50
  <=> class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_50])]) ).

fof(f3884,plain,
    class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1070]) ).

fof(f1070,axiom,
    class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__comm__monoid__add) ).

fof(f6139,plain,
    spl38_49,
    inference(avatar_split_clause,[],[f3883,f6136]) ).

fof(f6136,plain,
    ( spl38_49
  <=> class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_49])]) ).

fof(f3883,plain,
    class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
    inference(cnf_transformation,[],[f1013]) ).

fof(f1013,axiom,
    class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__comm__monoid__add) ).

fof(f6134,plain,
    spl38_48,
    inference(avatar_split_clause,[],[f3882,f6131]) ).

fof(f6131,plain,
    ( spl38_48
  <=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_48])]) ).

fof(f3882,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1066]) ).

fof(f1066,axiom,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le) ).

fof(f6129,plain,
    spl38_47,
    inference(avatar_split_clause,[],[f3881,f6126]) ).

fof(f6126,plain,
    ( spl38_47
  <=> class_Rings_Ocomm__ring__1(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_47])]) ).

fof(f3881,plain,
    class_Rings_Ocomm__ring__1(tc_Int_Oint),
    inference(cnf_transformation,[],[f1044]) ).

fof(f1044,axiom,
    class_Rings_Ocomm__ring__1(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring__1) ).

fof(f6124,plain,
    spl38_46,
    inference(avatar_split_clause,[],[f3880,f6121]) ).

fof(f6121,plain,
    ( spl38_46
  <=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_46])]) ).

fof(f3880,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
    inference(cnf_transformation,[],[f1008]) ).

fof(f1008,axiom,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le) ).

fof(f6119,plain,
    spl38_45,
    inference(avatar_split_clause,[],[f3879,f6116]) ).

fof(f6116,plain,
    ( spl38_45
  <=> class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_45])]) ).

fof(f3879,plain,
    class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1128]) ).

fof(f1128,axiom,
    class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__ring__1) ).

fof(f6114,plain,
    spl38_44,
    inference(avatar_split_clause,[],[f3878,f6111]) ).

fof(f6111,plain,
    ( spl38_44
  <=> class_Rings_Oring(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_44])]) ).

fof(f3878,plain,
    class_Rings_Oring(tc_Int_Oint),
    inference(cnf_transformation,[],[f1060]) ).

fof(f1060,axiom,
    class_Rings_Oring(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring) ).

fof(f6109,plain,
    spl38_43,
    inference(avatar_split_clause,[],[f3877,f6106]) ).

fof(f6106,plain,
    ( spl38_43
  <=> class_Rings_Ocomm__ring(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_43])]) ).

fof(f3877,plain,
    class_Rings_Ocomm__ring(tc_Int_Oint),
    inference(cnf_transformation,[],[f1050]) ).

fof(f1050,axiom,
    class_Rings_Ocomm__ring(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring) ).

fof(f6104,plain,
    spl38_42,
    inference(avatar_split_clause,[],[f3876,f6101]) ).

fof(f6101,plain,
    ( spl38_42
  <=> class_Rings_Ocomm__ring(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_42])]) ).

fof(f3876,plain,
    class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1133]) ).

fof(f1133,axiom,
    class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__ring) ).

fof(f6099,plain,
    spl38_41,
    inference(avatar_split_clause,[],[f3875,f6096]) ).

fof(f6096,plain,
    ( spl38_41
  <=> class_Rings_Oring(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_41])]) ).

fof(f3875,plain,
    class_Rings_Oring(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1142]) ).

fof(f1142,axiom,
    class_Rings_Oring(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring) ).

fof(f6094,plain,
    spl38_40,
    inference(avatar_split_clause,[],[f3874,f6091]) ).

fof(f6091,plain,
    ( spl38_40
  <=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_40])]) ).

fof(f3874,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1065]) ).

fof(f1065,axiom,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) ).

fof(f6089,plain,
    spl38_39,
    inference(avatar_split_clause,[],[f3873,f6086]) ).

fof(f6086,plain,
    ( spl38_39
  <=> class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_39])]) ).

fof(f3873,plain,
    class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1072]) ).

fof(f1072,axiom,
    class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__cancel__semiring) ).

fof(f6084,plain,
    spl38_38,
    inference(avatar_split_clause,[],[f3872,f6081]) ).

fof(f6081,plain,
    ( spl38_38
  <=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_38])]) ).

fof(f3872,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
    inference(cnf_transformation,[],[f1007]) ).

fof(f1007,axiom,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add) ).

fof(f6079,plain,
    spl38_37,
    inference(avatar_split_clause,[],[f3871,f6076]) ).

fof(f6076,plain,
    ( spl38_37
  <=> class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_37])]) ).

fof(f3871,plain,
    class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
    inference(cnf_transformation,[],[f1017]) ).

fof(f1017,axiom,
    class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__cancel__semiring) ).

fof(f6074,plain,
    spl38_36,
    inference(avatar_split_clause,[],[f3870,f6071]) ).

fof(f6071,plain,
    ( spl38_36
  <=> class_Rings_Oordered__semiring(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_36])]) ).

fof(f3870,plain,
    class_Rings_Oordered__semiring(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1080]) ).

fof(f1080,axiom,
    class_Rings_Oordered__semiring(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__semiring) ).

fof(f6069,plain,
    spl38_35,
    inference(avatar_split_clause,[],[f3869,f6066]) ).

fof(f6066,plain,
    ( spl38_35
  <=> class_Rings_Oordered__semiring(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_35])]) ).

fof(f3869,plain,
    class_Rings_Oordered__semiring(tc_Int_Oint),
    inference(cnf_transformation,[],[f1029]) ).

fof(f1029,axiom,
    class_Rings_Oordered__semiring(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__semiring) ).

fof(f6064,plain,
    spl38_34,
    inference(avatar_split_clause,[],[f3868,f6061]) ).

fof(f6061,plain,
    ( spl38_34
  <=> class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_34])]) ).

fof(f3868,plain,
    class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1069]) ).

fof(f1069,axiom,
    class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) ).

fof(f6059,plain,
    spl38_33,
    inference(avatar_split_clause,[],[f3867,f6056]) ).

fof(f6056,plain,
    ( spl38_33
  <=> class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_33])]) ).

fof(f3867,plain,
    class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
    inference(cnf_transformation,[],[f1012]) ).

fof(f1012,axiom,
    class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add) ).

fof(f6054,plain,
    spl38_32,
    inference(avatar_split_clause,[],[f3866,f6051]) ).

fof(f6051,plain,
    ( spl38_32
  <=> class_Rings_Olinordered__semiring(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_32])]) ).

fof(f3866,plain,
    class_Rings_Olinordered__semiring(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1075]) ).

fof(f1075,axiom,
    class_Rings_Olinordered__semiring(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring) ).

fof(f6049,plain,
    spl38_31,
    inference(avatar_split_clause,[],[f3865,f6046]) ).

fof(f6046,plain,
    ( spl38_31
  <=> class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_31])]) ).

fof(f3865,plain,
    class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
    inference(cnf_transformation,[],[f1016]) ).

fof(f1016,axiom,
    class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1__no__zero__divisors) ).

fof(f6044,plain,
    spl38_30,
    inference(avatar_split_clause,[],[f3864,f6041]) ).

fof(f6041,plain,
    ( spl38_30
  <=> class_Rings_Olinordered__semiring(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_30])]) ).

fof(f3864,plain,
    class_Rings_Olinordered__semiring(tc_Int_Oint),
    inference(cnf_transformation,[],[f1024]) ).

fof(f1024,axiom,
    class_Rings_Olinordered__semiring(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring) ).

fof(f6039,plain,
    spl38_29,
    inference(avatar_split_clause,[],[f3863,f6036]) ).

fof(f6036,plain,
    ( spl38_29
  <=> class_Int_Oring__char__0(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_29])]) ).

fof(f3863,plain,
    class_Int_Oring__char__0(tc_Int_Oint),
    inference(cnf_transformation,[],[f1052]) ).

fof(f1052,axiom,
    class_Int_Oring__char__0(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Int_Oring__char__0) ).

fof(f6034,plain,
    spl38_28,
    inference(avatar_split_clause,[],[f3862,f6031]) ).

fof(f6031,plain,
    ( spl38_28
  <=> class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_28])]) ).

fof(f3862,plain,
    class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1112]) ).

fof(f1112,axiom,
    class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors) ).

fof(f6029,plain,
    spl38_27,
    inference(avatar_split_clause,[],[f3861,f6026]) ).

fof(f6026,plain,
    ( spl38_27
  <=> class_Int_Oring__char__0(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_27])]) ).

fof(f3861,plain,
    class_Int_Oring__char__0(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1134]) ).

fof(f1134,axiom,
    class_Int_Oring__char__0(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Int_Oring__char__0) ).

fof(f6024,plain,
    spl38_26,
    inference(avatar_split_clause,[],[f3860,f6021]) ).

fof(f6021,plain,
    ( spl38_26
  <=> class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_26])]) ).

fof(f3860,plain,
    class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1067]) ).

fof(f1067,axiom,
    class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict) ).

fof(f6019,plain,
    spl38_25,
    inference(avatar_split_clause,[],[f3859,f6016]) ).

fof(f6016,plain,
    ( spl38_25
  <=> class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_25])]) ).

fof(f3859,plain,
    class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1073]) ).

fof(f1073,axiom,
    class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__comm__semiring) ).

fof(f6014,plain,
    spl38_24,
    inference(avatar_split_clause,[],[f3858,f6011]) ).

fof(f6011,plain,
    ( spl38_24
  <=> class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_24])]) ).

fof(f3858,plain,
    class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
    inference(cnf_transformation,[],[f1019]) ).

fof(f1019,axiom,
    class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__no__zero__divisors) ).

fof(f6009,plain,
    spl38_23,
    inference(avatar_split_clause,[],[f3857,f6006]) ).

fof(f6006,plain,
    ( spl38_23
  <=> class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_23])]) ).

fof(f3857,plain,
    class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
    inference(cnf_transformation,[],[f1009]) ).

fof(f1009,axiom,
    class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__comm__semiring__strict) ).

fof(f6004,plain,
    spl38_22,
    inference(avatar_split_clause,[],[f3856,f6001]) ).

fof(f6001,plain,
    ( spl38_22
  <=> class_Rings_Oordered__comm__semiring(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_22])]) ).

fof(f3856,plain,
    class_Rings_Oordered__comm__semiring(tc_Int_Oint),
    inference(cnf_transformation,[],[f1020]) ).

fof(f1020,axiom,
    class_Rings_Oordered__comm__semiring(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__comm__semiring) ).

fof(f5999,plain,
    spl38_21,
    inference(avatar_split_clause,[],[f3855,f5996]) ).

fof(f5996,plain,
    ( spl38_21
  <=> class_Rings_Oring__1(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_21])]) ).

fof(f3855,plain,
    class_Rings_Oring__1(tc_Int_Oint),
    inference(cnf_transformation,[],[f1056]) ).

fof(f1056,axiom,
    class_Rings_Oring__1(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1) ).

fof(f5994,plain,
    spl38_20,
    inference(avatar_split_clause,[],[f3854,f5991]) ).

fof(f5991,plain,
    ( spl38_20
  <=> class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_20])]) ).

fof(f3854,plain,
    class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1113]) ).

fof(f1113,axiom,
    class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors) ).

fof(f5989,plain,
    spl38_19,
    inference(avatar_split_clause,[],[f3853,f5986]) ).

fof(f5986,plain,
    ( spl38_19
  <=> class_Rings_Oring__1(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_19])]) ).

fof(f3853,plain,
    class_Rings_Oring__1(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1137]) ).

fof(f1137,axiom,
    class_Rings_Oring__1(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__1) ).

fof(f5984,plain,
    spl38_18,
    inference(avatar_split_clause,[],[f3852,f5981]) ).

fof(f5981,plain,
    ( spl38_18
  <=> class_Rings_Olinordered__idom(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_18])]) ).

fof(f3852,plain,
    class_Rings_Olinordered__idom(tc_Int_Oint),
    inference(cnf_transformation,[],[f1033]) ).

fof(f1033,axiom,
    class_Rings_Olinordered__idom(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__idom) ).

fof(f5979,plain,
    spl38_17,
    inference(avatar_split_clause,[],[f3851,f5976]) ).

fof(f5976,plain,
    ( spl38_17
  <=> class_Groups_Oordered__ab__group__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_17])]) ).

fof(f3851,plain,
    class_Groups_Oordered__ab__group__add(tc_Int_Oint),
    inference(cnf_transformation,[],[f1022]) ).

fof(f1022,axiom,
    class_Groups_Oordered__ab__group__add(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__group__add) ).

fof(f5974,plain,
    spl38_16,
    inference(avatar_split_clause,[],[f3850,f5971]) ).

fof(f5971,plain,
    ( spl38_16
  <=> class_Rings_Olinordered__ring__strict(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_16])]) ).

fof(f3850,plain,
    class_Rings_Olinordered__ring__strict(tc_Int_Oint),
    inference(cnf_transformation,[],[f1018]) ).

fof(f1018,axiom,
    class_Rings_Olinordered__ring__strict(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring__strict) ).

fof(f5969,plain,
    spl38_15,
    inference(avatar_split_clause,[],[f3849,f5966]) ).

fof(f5966,plain,
    ( spl38_15
  <=> class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_15])]) ).

fof(f3849,plain,
    class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
    inference(cnf_transformation,[],[f1014]) ).

fof(f1014,axiom,
    class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Olinordered__ab__group__add) ).

fof(f5964,plain,
    spl38_14,
    inference(avatar_split_clause,[],[f3848,f5961]) ).

fof(f5961,plain,
    ( spl38_14
  <=> class_Rings_Oordered__ring(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_14])]) ).

fof(f3848,plain,
    class_Rings_Oordered__ring(tc_Int_Oint),
    inference(cnf_transformation,[],[f1040]) ).

fof(f1040,axiom,
    class_Rings_Oordered__ring(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring) ).

fof(f5959,plain,
    spl38_13,
    inference(avatar_split_clause,[],[f3847,f5956]) ).

fof(f5956,plain,
    ( spl38_13
  <=> class_Divides_Oring__div(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_13])]) ).

fof(f3847,plain,
    class_Divides_Oring__div(tc_Int_Oint),
    inference(cnf_transformation,[],[f1048]) ).

fof(f1048,axiom,
    class_Divides_Oring__div(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Divides_Oring__div) ).

fof(f5954,plain,
    spl38_12,
    inference(avatar_split_clause,[],[f3846,f5951]) ).

fof(f5951,plain,
    ( spl38_12
  <=> class_Lattices_Oboolean__algebra(tc_HOL_Obool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_12])]) ).

fof(f3846,plain,
    class_Lattices_Oboolean__algebra(tc_HOL_Obool),
    inference(cnf_transformation,[],[f1102]) ).

fof(f1102,axiom,
    class_Lattices_Oboolean__algebra(tc_HOL_Obool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Oboolean__algebra) ).

fof(f5949,plain,
    spl38_11,
    inference(avatar_split_clause,[],[f3845,f5946]) ).

fof(f5946,plain,
    ( spl38_11
  <=> class_Rings_Olinordered__ring(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_11])]) ).

fof(f3845,plain,
    class_Rings_Olinordered__ring(tc_Int_Oint),
    inference(cnf_transformation,[],[f1032]) ).

fof(f1032,axiom,
    class_Rings_Olinordered__ring(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring) ).

fof(f5944,plain,
    spl38_10,
    inference(avatar_split_clause,[],[f3844,f5941]) ).

fof(f5941,plain,
    ( spl38_10
  <=> class_Rings_Olinordered__semiring__1(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_10])]) ).

fof(f3844,plain,
    class_Rings_Olinordered__semiring__1(tc_Int_Oint),
    inference(cnf_transformation,[],[f1021]) ).

fof(f1021,axiom,
    class_Rings_Olinordered__semiring__1(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1) ).

fof(f5939,plain,
    spl38_9,
    inference(avatar_split_clause,[],[f3843,f5936]) ).

fof(f5936,plain,
    ( spl38_9
  <=> class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_9])]) ).

fof(f3843,plain,
    class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
    inference(cnf_transformation,[],[f1010]) ).

fof(f1010,axiom,
    class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1__strict) ).

fof(f5934,plain,
    spl38_8,
    inference(avatar_split_clause,[],[f3842,f5931]) ).

fof(f3842,plain,
    class_Fields_Ofield(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1139]) ).

fof(f1139,axiom,
    class_Fields_Ofield(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Fields_Ofield) ).

fof(f5929,plain,
    spl38_7,
    inference(avatar_split_clause,[],[f3841,f5926]) ).

fof(f5926,plain,
    ( spl38_7
  <=> class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_7])]) ).

fof(f3841,plain,
    class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1110]) ).

fof(f1110,axiom,
    class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).

fof(f5924,plain,
    spl38_6,
    inference(avatar_split_clause,[],[f3840,f5921]) ).

fof(f5921,plain,
    ( spl38_6
  <=> class_Rings_Odivision__ring(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_6])]) ).

fof(f3840,plain,
    class_Rings_Odivision__ring(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1123]) ).

fof(f1123,axiom,
    class_Rings_Odivision__ring(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odivision__ring) ).

fof(f5919,plain,
    spl38_5,
    inference(avatar_split_clause,[],[f3839,f5916]) ).

fof(f5916,plain,
    ( spl38_5
  <=> class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_5])]) ).

fof(f3839,plain,
    class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1109]) ).

fof(f1109,axiom,
    class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero) ).

fof(f5914,plain,
    spl38_4,
    inference(avatar_split_clause,[],[f3838,f5911]) ).

fof(f5911,plain,
    ( spl38_4
  <=> class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_4])]) ).

fof(f3838,plain,
    class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1115]) ).

fof(f1115,axiom,
    class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Fields_Ofield__inverse__zero) ).

fof(f5909,plain,
    spl38_3,
    inference(avatar_split_clause,[],[f3837,f5906]) ).

fof(f5904,plain,
    ~ spl38_2,
    inference(avatar_split_clause,[],[f5754,f5901]) ).

fof(f5901,plain,
    ( spl38_2
  <=> v_qa____ = v_s____ ),
    introduced(avatar_definition,[new_symbols(naming,[spl38_2])]) ).

fof(f5754,plain,
    v_qa____ != v_s____,
    inference(forward_demodulation,[],[f3985,f3837]) ).

fof(f3985,plain,
    c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_qa____,
    inference(cnf_transformation,[],[f3]) ).

fof(f3,axiom,
    c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_qa____,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_q0) ).

fof(f5899,plain,
    ~ spl38_1,
    inference(avatar_split_clause,[],[f5753,f5896]) ).

fof(f5753,plain,
    v_pa____ != v_s____,
    inference(forward_demodulation,[],[f3983,f3837]) ).

fof(f3983,plain,
    v_pa____ != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
    inference(cnf_transformation,[],[f2]) ).

fof(f2,axiom,
    v_pa____ != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pne) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.14  % Problem    : SWW272+1 : TPTP v8.1.2. Released v5.2.0.
% 0.03/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.36  % Computer : n011.cluster.edu
% 0.13/0.36  % Model    : x86_64 x86_64
% 0.13/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36  % Memory   : 8042.1875MB
% 0.13/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36  % CPULimit   : 300
% 0.13/0.36  % WCLimit    : 300
% 0.13/0.36  % DateTime   : Fri May  3 19:42:08 EDT 2024
% 0.13/0.36  % CPUTime    : 
% 0.13/0.37  % (7779)Running in auto input_syntax mode. Trying TPTP
% 0.19/0.45  % (7782)WARNING: value z3 for option sas not known
% 0.19/0.45  % (7780)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.19/0.45  % (7786)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)
% 0.19/0.45  % (7783)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.19/0.45  % (7782)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)
% 0.19/0.45  % (7785)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.19/0.45  % (7784)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)
% 0.19/0.45  % (7781)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.95/0.60  % (7784)First to succeed.
% 0.95/0.64  % (7784)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-7779"
% 0.95/0.64  % (7784)Refutation found. Thanks to Tanya!
% 0.95/0.64  % SZS status Theorem for theBenchmark
% 0.95/0.64  % SZS output start Proof for theBenchmark
% See solution above
% 1.61/0.67  % (7784)------------------------------
% 1.61/0.67  % (7784)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 1.61/0.67  % (7784)Termination reason: Refutation
% 1.61/0.67  
% 1.61/0.67  % (7784)Memory used [KB]: 5592
% 1.61/0.67  % (7784)Time elapsed: 0.190 s
% 1.61/0.67  % (7784)Instructions burned: 427 (million)
% 1.61/0.67  % (7779)Success in time 0.292 s
%------------------------------------------------------------------------------