TSTP Solution File: SWW258+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SWW258+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n017.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue May 21 07:19:48 EDT 2024

% Result   : Theorem 6.94s 1.42s
% Output   : Refutation 7.34s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      : 2084
% Syntax   : Number of formulae    : 6290 (1866 unt;   0 def)
%            Number of atoms       : 15383 (3279 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives : 14327 (5234   ~;5316   |; 695   &)
%                                         (1618 <=>;1464  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    8 (   1 avg)
%            Number of predicates  : 1249 (1247 usr;1157 prp; 0-4 aty)
%            Number of functors    :   67 (  67 usr;  24 con; 0-3 aty)
%            Number of variables   : 10104 (9993   !; 111   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f25722,plain,
    $false,
    inference(avatar_sat_refutation,[],[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,f6639,f6644,f6649,f6654,f6659,f6664,f6669,f6674,f6679,f6684,f6689,f6694,f6699,f6704,f6709,f6714,f6719,f6724,f6729,f6734,f6739,f6744,f6749,f6754,f6759,f6764,f6769,f6774,f6779,f6784,f6789,f6794,f6799,f6804,f6809,f6814,f6819,f6824,f6829,f6834,f6839,f6844,f6849,f6854,f6859,f6864,f6869,f6874,f6879,f6884,f6889,f6894,f6899,f6904,f6909,f6914,f6919,f6924,f6929,f6934,f6939,f6944,f6949,f6954,f6959,f6964,f6969,f6974,f6979,f6984,f6989,f6994,f6999,f7004,f7009,f7014,f7019,f7024,f7029,f7034,f7039,f7044,f7049,f7054,f7059,f7064,f7069,f7074,f7079,f7084,f7089,f7094,f7099,f7104,f7109,f7114,f7119,f7124,f7129,f7134,f7138,f7142,f7146,f7150,f7154,f7159,f7164,f7168,f7172,f7177,f7182,f7187,f7192,f7196,f7200,f7204,f7208,f7212,f7216,f7220,f7224,f7228,f7232,f7236,f7240,f7244,f7248,f7252,f7256,f7260,f7264,f7268,f7272,f7276,f7280,f7284,f7288,f7292,f7296,f7300,f7304,f7308,f7312,f7316,f7320,f7324,f7328,f7332,f7336,f7340,f7344,f7348,f7352,f7356,f7360,f7364,f7368,f7372,f7376,f7380,f7384,f7388,f7392,f7396,f7400,f7404,f7408,f7412,f7416,f7420,f7424,f7428,f7432,f7437,f7441,f7446,f7451,f7456,f7461,f7466,f7472,f7477,f7482,f7487,f7492,f7497,f7501,f7505,f7509,f7513,f7517,f7521,f7525,f7529,f7533,f7537,f7541,f7545,f7549,f7553,f7558,f7563,f7568,f7573,f7579,f7584,f7589,f7593,f7597,f7601,f7605,f7609,f7613,f7617,f7621,f7625,f7629,f7633,f7637,f7641,f7645,f7649,f7653,f7657,f7661,f7665,f7669,f7674,f7679,f7683,f7688,f7693,f7710,f7715,f7719,f7723,f7727,f7731,f7735,f7739,f7743,f7747,f7751,f7755,f7759,f7763,f7767,f7771,f7775,f7779,f7783,f7787,f7819,f7824,f7830,f7834,f7838,f7842,f7846,f7850,f7854,f7858,f7862,f7866,f7870,f7875,f7879,f7883,f7887,f7891,f7895,f7899,f7903,f7907,f7911,f7915,f7920,f7924,f7928,f7932,f7936,f7940,f7944,f7948,f7952,f7956,f7960,f7964,f7968,f7972,f7976,f7980,f7984,f7988,f7992,f7996,f8000,f8004,f8008,f8012,f8016,f8020,f8024,f8028,f8033,f8053,f8156,f8206,f8229,f8234,f8238,f8243,f8247,f8251,f8255,f8259,f8263,f8267,f8271,f8275,f8279,f8283,f8288,f8292,f8296,f8300,f8304,f8308,f8312,f8316,f8320,f8324,f8328,f8333,f8337,f8341,f8345,f8349,f8353,f8357,f8361,f8365,f8369,f8373,f8378,f8383,f8424,f8549,f8662,f8666,f8670,f8674,f8678,f8682,f8687,f8691,f8695,f8699,f8703,f8707,f8711,f8715,f8719,f8723,f8727,f8733,f8737,f8741,f8745,f8749,f8753,f8757,f8761,f8765,f8769,f8774,f8778,f8782,f8786,f8790,f8794,f8798,f8802,f8806,f8810,f8814,f8819,f8823,f8827,f8831,f8835,f8839,f8843,f8847,f8851,f8855,f8859,f8864,f8868,f8872,f8876,f8880,f8884,f8888,f8892,f8896,f8900,f8904,f8909,f8913,f8917,f8921,f8925,f8929,f8933,f8937,f8941,f8945,f8949,f8954,f8958,f8962,f8966,f8970,f8974,f8978,f8982,f8987,f8991,f8995,f8999,f9003,f9007,f9011,f9015,f9019,f9023,f9027,f9031,f9035,f9041,f9122,f9172,f9254,f9643,f9729,f9733,f9737,f9741,f9745,f9749,f9753,f9757,f9761,f9765,f9769,f9773,f9777,f9781,f9785,f9789,f9793,f9797,f9804,f9808,f9812,f9816,f9820,f9824,f9828,f9832,f9836,f9840,f9845,f9849,f9853,f9857,f9861,f9865,f9869,f9873,f9877,f9881,f9885,f9889,f9893,f9897,f9901,f9905,f9909,f9913,f9917,f9921,f9925,f9929,f9933,f9937,f9941,f9945,f9949,f9953,f9957,f9961,f9965,f9969,f9973,f9982,f9986,f9990,f9994,f9998,f10002,f10006,f10010,f10014,f10018,f10027,f10032,f10036,f10040,f10044,f10048,f10052,f10141,f10273,f10380,f10475,f10730,f10738,f10742,f10746,f10750,f10754,f10758,f10762,f10766,f10770,f10774,f10778,f10782,f10786,f10790,f10794,f10798,f10802,f10806,f10810,f10814,f10818,f10822,f10826,f10830,f10834,f10838,f10842,f10846,f10850,f10854,f10863,f10867,f10871,f10875,f10879,f10883,f10887,f10891,f10895,f10899,f10903,f10907,f10911,f10915,f10919,f10923,f10927,f10931,f10935,f10939,f10943,f10947,f10951,f10955,f10959,f11059,f11201,f11401,f11851,f11890,f11894,f11898,f11902,f11906,f11910,f11914,f11918,f11922,f11926,f11930,f11934,f11938,f11942,f11946,f11950,f11954,f11958,f11962,f11966,f11970,f11974,f11978,f11982,f11986,f11990,f11994,f11998,f12002,f12006,f12010,f12014,f12018,f12022,f12026,f12030,f12034,f12038,f12042,f12046,f12050,f12054,f12058,f12062,f12066,f12070,f12074,f12078,f12082,f12086,f12090,f12094,f12098,f12102,f12106,f12110,f12114,f12118,f12122,f12126,f12130,f12134,f12138,f12142,f12146,f12150,f12154,f12158,f12162,f12166,f12170,f12174,f12178,f12182,f12186,f12190,f12194,f12198,f12202,f12206,f12210,f12214,f12218,f12222,f12226,f12230,f12234,f12238,f12242,f12246,f12250,f12254,f12258,f12262,f12266,f12270,f12274,f12278,f12282,f12286,f12290,f12294,f12298,f12302,f12306,f12310,f12314,f12318,f12322,f12326,f12330,f12334,f12338,f12342,f12346,f12354,f12358,f12362,f12366,f12370,f12374,f12378,f12382,f12386,f12390,f12399,f12403,f12407,f12411,f12415,f12419,f12423,f12427,f12431,f12435,f12446,f12453,f12742,f13073,f13309,f13599,f14002,f14891,f15106,f15279,f15283,f15287,f15291,f15295,f15299,f15303,f15307,f15311,f15315,f15319,f15324,f15328,f15332,f15336,f15340,f15344,f15348,f15352,f15356,f15360,f15364,f15369,f15373,f15377,f15381,f15385,f15389,f15393,f15397,f15401,f15405,f15409,f15421,f15425,f15429,f15433,f15437,f15441,f15445,f15449,f15453,f15457,f15481,f15485,f15489,f15493,f15497,f15501,f15505,f15509,f15513,f15517,f15521,f15525,f15529,f15534,f15538,f15962,f16788,f17117,f17122,f17126,f17130,f17135,f17139,f17143,f17147,f17151,f17155,f17159,f17170,f17174,f17178,f17182,f17186,f17190,f17194,f17198,f17202,f17206,f17210,f17214,f17218,f17222,f17226,f17230,f17234,f17238,f17242,f17246,f17250,f17266,f17270,f17274,f17278,f17283,f17288,f17317,f17340,f18138,f18785,f18876,f18880,f18884,f18888,f18893,f18898,f18902,f18906,f18910,f18914,f18918,f18922,f18926,f18930,f18934,f18938,f18942,f18954,f18958,f18962,f18966,f18970,f18974,f18978,f18982,f18986,f18990,f18994,f18998,f19002,f19006,f19010,f19014,f19018,f19022,f19026,f19030,f19034,f19057,f19061,f19065,f19069,f19073,f19077,f19151,f19155,f19159,f20126,f20131,f20136,f20140,f20144,f20148,f20152,f20156,f20160,f20164,f20168,f20177,f20181,f20185,f20189,f20193,f20197,f20201,f20205,f20209,f20213,f20218,f20222,f20226,f20230,f20234,f20238,f20242,f20246,f20250,f20254,f20258,f20267,f20271,f20275,f20279,f20283,f20287,f20291,f20295,f20299,f20303,f20308,f20312,f20316,f20320,f20324,f20328,f20332,f20336,f20340,f20345,f20350,f22151,f22199,f22203,f22207,f22211,f22215,f22219,f22223,f22227,f22231,f22235,f22244,f22248,f22252,f22256,f22260,f22264,f22268,f22272,f22276,f22280,f22327,f22331,f22335,f22339,f22343,f22347,f22351,f22355,f22359,f22363,f22367,f22371,f22375,f22379,f22383,f22387,f22391,f22395,f22399,f22403,f22407,f22411,f22415,f22419,f22423,f22427,f22432,f22436,f22440,f22444,f22448,f22452,f22772,f23215,f23795,f23799,f23803,f23807,f23811,f23815,f23819,f23823,f23827,f23881,f23885,f23889,f23893,f23897,f23901,f23905,f23909,f23913,f23917,f23944,f23948,f23952,f23956,f23960,f23964,f23968,f23972,f23976,f23980,f24003,f24007,f24011,f24189,f25031,f25643,f25647,f25651,f25655,f25659,f25684,f25688,f25692,f25696,f25700,f25704,f25708,f25712,f25716,f25720,f25721]) ).

fof(f25721,plain,
    ( ~ spl50_48
    | spl50_213
    | ~ spl50_888
    | ~ spl50_1141 ),
    inference(avatar_split_clause,[],[f25677,f25028,f15435,f7111,f6286]) ).

fof(f6286,plain,
    ( spl50_48
  <=> class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_48])]) ).

fof(f7111,plain,
    ( spl50_213
  <=> v_w____ = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_213])]) ).

fof(f15435,plain,
    ( spl50_888
  <=> ! [X2,X0,X1] :
        ( c_Groups_Ozero__class_Ozero(X2) != hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)
        | c_Groups_Ozero__class_Ozero(X2) = X1
        | ~ class_Rings_Oring__1__no__zero__divisors(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_888])]) ).

fof(f25028,plain,
    ( spl50_1141
  <=> c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1141])]) ).

fof(f25677,plain,
    ( v_w____ = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
    | ~ class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex)
    | ~ spl50_888
    | ~ spl50_1141 ),
    inference(trivial_inequality_removal,[],[f25661]) ).

fof(f25661,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
    | v_w____ = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
    | ~ class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex)
    | ~ spl50_888
    | ~ spl50_1141 ),
    inference(superposition,[],[f15436,f25030]) ).

fof(f25030,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | ~ spl50_1141 ),
    inference(avatar_component_clause,[],[f25028]) ).

fof(f15436,plain,
    ( ! [X2,X0,X1] :
        ( c_Groups_Ozero__class_Ozero(X2) != hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)
        | c_Groups_Ozero__class_Ozero(X2) = X1
        | ~ class_Rings_Oring__1__no__zero__divisors(X2) )
    | ~ spl50_888 ),
    inference(avatar_component_clause,[],[f15435]) ).

fof(f25720,plain,
    spl50_1156,
    inference(avatar_split_clause,[],[f5398,f25718]) ).

fof(f25718,plain,
    ( spl50_1156
  <=> ! [X0,X3,X2,X1] :
        ( c_Polynomial_Osmult(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X0),c_Polynomial_Osmult(X3,X1,X0))
        | ~ class_Rings_Ocomm__semiring__0(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1156])]) ).

fof(f5398,plain,
    ! [X2,X3,X0,X1] :
      ( c_Polynomial_Osmult(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X0),c_Polynomial_Osmult(X3,X1,X0))
      | ~ class_Rings_Ocomm__semiring__0(X3) ),
    inference(cnf_transformation,[],[f3243]) ).

fof(f3243,plain,
    ! [X0,X1,X2,X3] :
      ( c_Polynomial_Osmult(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X0),c_Polynomial_Osmult(X3,X1,X0))
      | ~ class_Rings_Ocomm__semiring__0(X3) ),
    inference(ennf_transformation,[],[f2162]) ).

fof(f2162,plain,
    ! [X0,X1,X2,X3] :
      ( class_Rings_Ocomm__semiring__0(X3)
     => c_Polynomial_Osmult(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X0),c_Polynomial_Osmult(X3,X1,X0)) ),
    inference(rectify,[],[f652]) ).

fof(f652,axiom,
    ! [X54,X13,X4,X5] :
      ( class_Rings_Ocomm__semiring__0(X5)
     => c_Polynomial_Osmult(X5,c_Groups_Oplus__class_Oplus(X5,X4,X13),X54) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X5),c_Polynomial_Osmult(X5,X4,X54),c_Polynomial_Osmult(X5,X13,X54)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__add__left) ).

fof(f25716,plain,
    spl50_1155,
    inference(avatar_split_clause,[],[f5397,f25714]) ).

fof(f25714,plain,
    ( spl50_1155
  <=> ! [X0,X3,X2,X1] :
        ( c_Polynomial_Osynthetic__div(X3,c_Polynomial_OpCons(X3,X2,X1),X0) = c_Polynomial_OpCons(X3,hAPP(c_Polynomial_Opoly(X3,X1),X0),c_Polynomial_Osynthetic__div(X3,X1,X0))
        | ~ class_Rings_Ocomm__semiring__0(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1155])]) ).

fof(f5397,plain,
    ! [X2,X3,X0,X1] :
      ( c_Polynomial_Osynthetic__div(X3,c_Polynomial_OpCons(X3,X2,X1),X0) = c_Polynomial_OpCons(X3,hAPP(c_Polynomial_Opoly(X3,X1),X0),c_Polynomial_Osynthetic__div(X3,X1,X0))
      | ~ class_Rings_Ocomm__semiring__0(X3) ),
    inference(cnf_transformation,[],[f3242]) ).

fof(f3242,plain,
    ! [X0,X1,X2,X3] :
      ( c_Polynomial_Osynthetic__div(X3,c_Polynomial_OpCons(X3,X2,X1),X0) = c_Polynomial_OpCons(X3,hAPP(c_Polynomial_Opoly(X3,X1),X0),c_Polynomial_Osynthetic__div(X3,X1,X0))
      | ~ class_Rings_Ocomm__semiring__0(X3) ),
    inference(ennf_transformation,[],[f2161]) ).

fof(f2161,plain,
    ! [X0,X1,X2,X3] :
      ( class_Rings_Ocomm__semiring__0(X3)
     => c_Polynomial_Osynthetic__div(X3,c_Polynomial_OpCons(X3,X2,X1),X0) = c_Polynomial_OpCons(X3,hAPP(c_Polynomial_Opoly(X3,X1),X0),c_Polynomial_Osynthetic__div(X3,X1,X0)) ),
    inference(rectify,[],[f691]) ).

fof(f691,axiom,
    ! [X23,X54,X4,X5] :
      ( class_Rings_Ocomm__semiring__0(X5)
     => c_Polynomial_Osynthetic__div(X5,c_Polynomial_OpCons(X5,X4,X54),X23) = c_Polynomial_OpCons(X5,hAPP(c_Polynomial_Opoly(X5,X54),X23),c_Polynomial_Osynthetic__div(X5,X54,X23)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_synthetic__div__pCons) ).

fof(f25712,plain,
    spl50_1154,
    inference(avatar_split_clause,[],[f5389,f25710]) ).

fof(f25710,plain,
    ( spl50_1154
  <=> ! [X0,X3,X2,X1] :
        ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Omonom(X3,X2,X1),c_Polynomial_Omonom(X3,X0,X1)) = c_Polynomial_Omonom(X3,c_Groups_Oplus__class_Oplus(X3,X2,X0),X1)
        | ~ class_Groups_Ocomm__monoid__add(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1154])]) ).

fof(f5389,plain,
    ! [X2,X3,X0,X1] :
      ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Omonom(X3,X2,X1),c_Polynomial_Omonom(X3,X0,X1)) = c_Polynomial_Omonom(X3,c_Groups_Oplus__class_Oplus(X3,X2,X0),X1)
      | ~ class_Groups_Ocomm__monoid__add(X3) ),
    inference(cnf_transformation,[],[f3235]) ).

fof(f3235,plain,
    ! [X0,X1,X2,X3] :
      ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Omonom(X3,X2,X1),c_Polynomial_Omonom(X3,X0,X1)) = c_Polynomial_Omonom(X3,c_Groups_Oplus__class_Oplus(X3,X2,X0),X1)
      | ~ class_Groups_Ocomm__monoid__add(X3) ),
    inference(ennf_transformation,[],[f2154]) ).

fof(f2154,plain,
    ! [X0,X1,X2,X3] :
      ( class_Groups_Ocomm__monoid__add(X3)
     => c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Omonom(X3,X2,X1),c_Polynomial_Omonom(X3,X0,X1)) = c_Polynomial_Omonom(X3,c_Groups_Oplus__class_Oplus(X3,X2,X0),X1) ),
    inference(rectify,[],[f665]) ).

fof(f665,axiom,
    ! [X13,X3,X4,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X5),c_Polynomial_Omonom(X5,X4,X3),c_Polynomial_Omonom(X5,X13,X3)) = c_Polynomial_Omonom(X5,c_Groups_Oplus__class_Oplus(X5,X4,X13),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__monom) ).

fof(f25708,plain,
    spl50_1153,
    inference(avatar_split_clause,[],[f5357,f25706]) ).

fof(f25706,plain,
    ( spl50_1153
  <=> ! [X0,X3,X2,X1] :
        ( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),c_Polynomial_Omonom(X3,X2,X1),c_Polynomial_Omonom(X3,X0,X1)) = c_Polynomial_Omonom(X3,c_Groups_Ominus__class_Ominus(X3,X2,X0),X1)
        | ~ class_Groups_Oab__group__add(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1153])]) ).

fof(f5357,plain,
    ! [X2,X3,X0,X1] :
      ( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),c_Polynomial_Omonom(X3,X2,X1),c_Polynomial_Omonom(X3,X0,X1)) = c_Polynomial_Omonom(X3,c_Groups_Ominus__class_Ominus(X3,X2,X0),X1)
      | ~ class_Groups_Oab__group__add(X3) ),
    inference(cnf_transformation,[],[f3188]) ).

fof(f3188,plain,
    ! [X0,X1,X2,X3] :
      ( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),c_Polynomial_Omonom(X3,X2,X1),c_Polynomial_Omonom(X3,X0,X1)) = c_Polynomial_Omonom(X3,c_Groups_Ominus__class_Ominus(X3,X2,X0),X1)
      | ~ class_Groups_Oab__group__add(X3) ),
    inference(ennf_transformation,[],[f2127]) ).

fof(f2127,plain,
    ! [X0,X1,X2,X3] :
      ( class_Groups_Oab__group__add(X3)
     => c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),c_Polynomial_Omonom(X3,X2,X1),c_Polynomial_Omonom(X3,X0,X1)) = c_Polynomial_Omonom(X3,c_Groups_Ominus__class_Ominus(X3,X2,X0),X1) ),
    inference(rectify,[],[f667]) ).

fof(f667,axiom,
    ! [X13,X3,X4,X5] :
      ( class_Groups_Oab__group__add(X5)
     => c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X5),c_Polynomial_Omonom(X5,X4,X3),c_Polynomial_Omonom(X5,X13,X3)) = c_Polynomial_Omonom(X5,c_Groups_Ominus__class_Ominus(X5,X4,X13),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__monom) ).

fof(f25704,plain,
    spl50_1152,
    inference(avatar_split_clause,[],[f5338,f25702]) ).

fof(f25702,plain,
    ( spl50_1152
  <=> ! [X0,X3,X2,X1] :
        ( c_Polynomial_Osmult(X3,c_Groups_Ominus__class_Ominus(X3,X2,X1),X0) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X0),c_Polynomial_Osmult(X3,X1,X0))
        | ~ class_Rings_Ocomm__ring(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1152])]) ).

fof(f5338,plain,
    ! [X2,X3,X0,X1] :
      ( c_Polynomial_Osmult(X3,c_Groups_Ominus__class_Ominus(X3,X2,X1),X0) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X0),c_Polynomial_Osmult(X3,X1,X0))
      | ~ class_Rings_Ocomm__ring(X3) ),
    inference(cnf_transformation,[],[f3163]) ).

fof(f3163,plain,
    ! [X0,X1,X2,X3] :
      ( c_Polynomial_Osmult(X3,c_Groups_Ominus__class_Ominus(X3,X2,X1),X0) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X0),c_Polynomial_Osmult(X3,X1,X0))
      | ~ class_Rings_Ocomm__ring(X3) ),
    inference(ennf_transformation,[],[f2112]) ).

fof(f2112,plain,
    ! [X0,X1,X2,X3] :
      ( class_Rings_Ocomm__ring(X3)
     => c_Polynomial_Osmult(X3,c_Groups_Ominus__class_Ominus(X3,X2,X1),X0) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X0),c_Polynomial_Osmult(X3,X1,X0)) ),
    inference(rectify,[],[f654]) ).

fof(f654,axiom,
    ! [X54,X13,X4,X5] :
      ( class_Rings_Ocomm__ring(X5)
     => c_Polynomial_Osmult(X5,c_Groups_Ominus__class_Ominus(X5,X4,X13),X54) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X5),c_Polynomial_Osmult(X5,X4,X54),c_Polynomial_Osmult(X5,X13,X54)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__diff__left) ).

fof(f25700,plain,
    spl50_1151,
    inference(avatar_split_clause,[],[f5183,f25698]) ).

fof(f25698,plain,
    ( spl50_1151
  <=> ! [X2,X0,X1] :
        ( c_Groups_Ozero__class_Ozero(X2) = X1
        | c_Groups_Ozero__class_Ozero(X2) != hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)
        | ~ class_Rings_Ozero__neq__one(X2)
        | ~ class_Rings_Ono__zero__divisors(X2)
        | ~ class_Rings_Omult__zero(X2)
        | ~ class_Power_Opower(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1151])]) ).

fof(f5183,plain,
    ! [X2,X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X2) = X1
      | c_Groups_Ozero__class_Ozero(X2) != hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)
      | ~ class_Rings_Ozero__neq__one(X2)
      | ~ class_Rings_Ono__zero__divisors(X2)
      | ~ class_Rings_Omult__zero(X2)
      | ~ class_Power_Opower(X2) ),
    inference(cnf_transformation,[],[f3754]) ).

fof(f3754,plain,
    ! [X0,X1,X2] :
      ( ( ( c_Groups_Ozero__class_Ozero(X2) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)
          | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
          | c_Groups_Ozero__class_Ozero(X2) != X1 )
        & ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
            & c_Groups_Ozero__class_Ozero(X2) = X1 )
          | c_Groups_Ozero__class_Ozero(X2) != hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0) ) )
      | ~ class_Rings_Ozero__neq__one(X2)
      | ~ class_Rings_Ono__zero__divisors(X2)
      | ~ class_Rings_Omult__zero(X2)
      | ~ class_Power_Opower(X2) ),
    inference(flattening,[],[f3753]) ).

fof(f3753,plain,
    ! [X0,X1,X2] :
      ( ( ( c_Groups_Ozero__class_Ozero(X2) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)
          | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
          | c_Groups_Ozero__class_Ozero(X2) != X1 )
        & ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
            & c_Groups_Ozero__class_Ozero(X2) = X1 )
          | c_Groups_Ozero__class_Ozero(X2) != hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0) ) )
      | ~ class_Rings_Ozero__neq__one(X2)
      | ~ class_Rings_Ono__zero__divisors(X2)
      | ~ class_Rings_Omult__zero(X2)
      | ~ class_Power_Opower(X2) ),
    inference(nnf_transformation,[],[f3080]) ).

fof(f3080,plain,
    ! [X0,X1,X2] :
      ( ( c_Groups_Ozero__class_Ozero(X2) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)
      <=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
          & c_Groups_Ozero__class_Ozero(X2) = X1 ) )
      | ~ class_Rings_Ozero__neq__one(X2)
      | ~ class_Rings_Ono__zero__divisors(X2)
      | ~ class_Rings_Omult__zero(X2)
      | ~ class_Power_Opower(X2) ),
    inference(flattening,[],[f3079]) ).

fof(f3079,plain,
    ! [X0,X1,X2] :
      ( ( c_Groups_Ozero__class_Ozero(X2) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)
      <=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
          & c_Groups_Ozero__class_Ozero(X2) = X1 ) )
      | ~ class_Rings_Ozero__neq__one(X2)
      | ~ class_Rings_Ono__zero__divisors(X2)
      | ~ class_Rings_Omult__zero(X2)
      | ~ class_Power_Opower(X2) ),
    inference(ennf_transformation,[],[f2041]) ).

fof(f2041,plain,
    ! [X0,X1,X2] :
      ( ( class_Rings_Ozero__neq__one(X2)
        & class_Rings_Ono__zero__divisors(X2)
        & class_Rings_Omult__zero(X2)
        & class_Power_Opower(X2) )
     => ( c_Groups_Ozero__class_Ozero(X2) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)
      <=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
          & c_Groups_Ozero__class_Ozero(X2) = X1 ) ) ),
    inference(rectify,[],[f108]) ).

fof(f108,axiom,
    ! [X16,X24,X5] :
      ( ( class_Rings_Ozero__neq__one(X5)
        & class_Rings_Ono__zero__divisors(X5)
        & class_Rings_Omult__zero(X5)
        & class_Power_Opower(X5) )
     => ( c_Groups_Ozero__class_Ozero(X5) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),X24),X16)
      <=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X16
          & c_Groups_Ozero__class_Ozero(X5) = X24 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__eq__0__iff) ).

fof(f25696,plain,
    spl50_1150,
    inference(avatar_split_clause,[],[f5157,f25694]) ).

fof(f25694,plain,
    ( spl50_1150
  <=> ! [X2,X0,X1] :
        ( X0 = X1
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1150])]) ).

fof(f5157,plain,
    ! [X2,X0,X1] :
      ( X0 = X1
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
    inference(cnf_transformation,[],[f3743]) ).

fof(f3743,plain,
    ! [X0,X1,X2] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)
          | X0 != X1 )
        & ( X0 = X1
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0) ) )
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
    inference(nnf_transformation,[],[f3051]) ).

fof(f3051,plain,
    ! [X0,X1,X2] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)
      <=> X0 = X1 )
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
    inference(ennf_transformation,[],[f2023]) ).

fof(f2023,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)
      <=> X0 = X1 ) ),
    inference(rectify,[],[f431]) ).

fof(f431,axiom,
    ! [X16,X32,X36] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X36)
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X32) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X16)
      <=> X16 = X32 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel1) ).

fof(f25692,plain,
    spl50_1149,
    inference(avatar_split_clause,[],[f4890,f25690]) ).

fof(f25690,plain,
    ( spl50_1149
  <=> ! [X2,X0,X1] :
        ( c_Groups_Osgn__class_Osgn(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Osgn__class_Osgn(X2,X1)),c_Groups_Osgn__class_Osgn(X2,X0))
        | ~ class_Rings_Olinordered__idom(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1149])]) ).

fof(f4890,plain,
    ! [X2,X0,X1] :
      ( c_Groups_Osgn__class_Osgn(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Osgn__class_Osgn(X2,X1)),c_Groups_Osgn__class_Osgn(X2,X0))
      | ~ class_Rings_Olinordered__idom(X2) ),
    inference(cnf_transformation,[],[f2757]) ).

fof(f2757,plain,
    ! [X0,X1,X2] :
      ( c_Groups_Osgn__class_Osgn(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Osgn__class_Osgn(X2,X1)),c_Groups_Osgn__class_Osgn(X2,X0))
      | ~ class_Rings_Olinordered__idom(X2) ),
    inference(ennf_transformation,[],[f1825]) ).

fof(f1825,plain,
    ! [X0,X1,X2] :
      ( class_Rings_Olinordered__idom(X2)
     => c_Groups_Osgn__class_Osgn(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Osgn__class_Osgn(X2,X1)),c_Groups_Osgn__class_Osgn(X2,X0)) ),
    inference(rectify,[],[f822]) ).

fof(f822,axiom,
    ! [X13,X4,X5] :
      ( class_Rings_Olinordered__idom(X5)
     => c_Groups_Osgn__class_Osgn(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X13)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Osgn__class_Osgn(X5,X4)),c_Groups_Osgn__class_Osgn(X5,X13)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__times) ).

fof(f25688,plain,
    spl50_1148,
    inference(avatar_split_clause,[],[f4816,f25686]) ).

fof(f25686,plain,
    ( spl50_1148
  <=> ! [X2,X0,X1] :
        ( c_RealVector_Onorm__class_Onorm(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2,X1)),c_RealVector_Onorm__class_Onorm(X2,X0))
        | ~ class_RealVector_Oreal__normed__div__algebra(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1148])]) ).

fof(f4816,plain,
    ! [X2,X0,X1] :
      ( c_RealVector_Onorm__class_Onorm(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2,X1)),c_RealVector_Onorm__class_Onorm(X2,X0))
      | ~ class_RealVector_Oreal__normed__div__algebra(X2) ),
    inference(cnf_transformation,[],[f2701]) ).

fof(f2701,plain,
    ! [X0,X1,X2] :
      ( c_RealVector_Onorm__class_Onorm(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2,X1)),c_RealVector_Onorm__class_Onorm(X2,X0))
      | ~ class_RealVector_Oreal__normed__div__algebra(X2) ),
    inference(ennf_transformation,[],[f1783]) ).

fof(f1783,plain,
    ! [X0,X1,X2] :
      ( class_RealVector_Oreal__normed__div__algebra(X2)
     => c_RealVector_Onorm__class_Onorm(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2,X1)),c_RealVector_Onorm__class_Onorm(X2,X0)) ),
    inference(rectify,[],[f170]) ).

fof(f170,axiom,
    ! [X7,X9,X5] :
      ( class_RealVector_Oreal__normed__div__algebra(X5)
     => c_RealVector_Onorm__class_Onorm(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X9),X7)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5,X9)),c_RealVector_Onorm__class_Onorm(X5,X7)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__mult) ).

fof(f25684,plain,
    spl50_1147,
    inference(avatar_split_clause,[],[f4815,f25682]) ).

fof(f25682,plain,
    ( spl50_1147
  <=> ! [X2,X0,X1] :
        ( c_Groups_Osgn__class_Osgn(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Osgn__class_Osgn(X2,X1)),c_Groups_Osgn__class_Osgn(X2,X0))
        | ~ class_RealVector_Oreal__normed__div__algebra(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1147])]) ).

fof(f4815,plain,
    ! [X2,X0,X1] :
      ( c_Groups_Osgn__class_Osgn(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Osgn__class_Osgn(X2,X1)),c_Groups_Osgn__class_Osgn(X2,X0))
      | ~ class_RealVector_Oreal__normed__div__algebra(X2) ),
    inference(cnf_transformation,[],[f2700]) ).

fof(f2700,plain,
    ! [X0,X1,X2] :
      ( c_Groups_Osgn__class_Osgn(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Osgn__class_Osgn(X2,X1)),c_Groups_Osgn__class_Osgn(X2,X0))
      | ~ class_RealVector_Oreal__normed__div__algebra(X2) ),
    inference(ennf_transformation,[],[f1782]) ).

fof(f1782,plain,
    ! [X0,X1,X2] :
      ( class_RealVector_Oreal__normed__div__algebra(X2)
     => c_Groups_Osgn__class_Osgn(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Osgn__class_Osgn(X2,X1)),c_Groups_Osgn__class_Osgn(X2,X0)) ),
    inference(rectify,[],[f821]) ).

fof(f821,axiom,
    ! [X7,X9,X5] :
      ( class_RealVector_Oreal__normed__div__algebra(X5)
     => c_Groups_Osgn__class_Osgn(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X9),X7)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Osgn__class_Osgn(X5,X9)),c_Groups_Osgn__class_Osgn(X5,X7)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__mult) ).

fof(f25659,plain,
    spl50_1146,
    inference(avatar_split_clause,[],[f4808,f25657]) ).

fof(f25657,plain,
    ( spl50_1146
  <=> ! [X2,X0,X1] :
        ( c_Rings_Oinverse__class_Oinverse(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Rings_Oinverse__class_Oinverse(X2,X1)),c_Rings_Oinverse__class_Oinverse(X2,X0))
        | ~ class_Fields_Ofield__inverse__zero(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1146])]) ).

fof(f4808,plain,
    ! [X2,X0,X1] :
      ( c_Rings_Oinverse__class_Oinverse(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Rings_Oinverse__class_Oinverse(X2,X1)),c_Rings_Oinverse__class_Oinverse(X2,X0))
      | ~ class_Fields_Ofield__inverse__zero(X2) ),
    inference(cnf_transformation,[],[f2694]) ).

fof(f2694,plain,
    ! [X0,X1,X2] :
      ( c_Rings_Oinverse__class_Oinverse(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Rings_Oinverse__class_Oinverse(X2,X1)),c_Rings_Oinverse__class_Oinverse(X2,X0))
      | ~ class_Fields_Ofield__inverse__zero(X2) ),
    inference(ennf_transformation,[],[f1777]) ).

fof(f1777,plain,
    ! [X0,X1,X2] :
      ( class_Fields_Ofield__inverse__zero(X2)
     => c_Rings_Oinverse__class_Oinverse(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Rings_Oinverse__class_Oinverse(X2,X1)),c_Rings_Oinverse__class_Oinverse(X2,X0)) ),
    inference(rectify,[],[f119]) ).

fof(f119,axiom,
    ! [X13,X4,X5] :
      ( class_Fields_Ofield__inverse__zero(X5)
     => c_Rings_Oinverse__class_Oinverse(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X13)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Rings_Oinverse__class_Oinverse(X5,X4)),c_Rings_Oinverse__class_Oinverse(X5,X13)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__mult__distrib) ).

fof(f25655,plain,
    spl50_1145,
    inference(avatar_split_clause,[],[f4770,f25653]) ).

fof(f25653,plain,
    ( spl50_1145
  <=> ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X0
        | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1145])]) ).

fof(f4770,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X0
      | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),X0)) ),
    inference(cnf_transformation,[],[f3650]) ).

fof(f3650,plain,
    ! [X0,X1] :
      ( ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),X0))
        | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X0
        | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X1 )
      & ( ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X0
          & c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X1 )
        | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),X0)) ) ),
    inference(flattening,[],[f3649]) ).

fof(f3649,plain,
    ! [X0,X1] :
      ( ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),X0))
        | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X0
        | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X1 )
      & ( ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X0
          & c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X1 )
        | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),X0)) ) ),
    inference(nnf_transformation,[],[f1742]) ).

fof(f1742,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),X0))
    <=> ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X0
        & c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X1 ) ),
    inference(rectify,[],[f239]) ).

fof(f239,axiom,
    ! [X20,X12] :
      ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X12),X12),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X20),X20))
    <=> ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X20
        & c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X12 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__two__squares__add__zero__iff) ).

fof(f25651,plain,
    spl50_1144,
    inference(avatar_split_clause,[],[f4769,f25649]) ).

fof(f25649,plain,
    ( spl50_1144
  <=> ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X1
        | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1144])]) ).

fof(f4769,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X1
      | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),X0)) ),
    inference(cnf_transformation,[],[f3650]) ).

fof(f25647,plain,
    spl50_1143,
    inference(avatar_split_clause,[],[f4590,f25645]) ).

fof(f25645,plain,
    ( spl50_1143
  <=> ! [X0,X1] :
        ( X0 = X1
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,X1)
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X0)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1143])]) ).

fof(f4590,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,X1)
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(cnf_transformation,[],[f2620]) ).

fof(f2620,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,X1)
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(flattening,[],[f2619]) ).

fof(f2619,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,X1)
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(ennf_transformation,[],[f1658]) ).

fof(f1658,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_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
       => ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X0)
         => ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,X1)
           => X0 = X1 ) ) ) ),
    inference(rectify,[],[f867]) ).

fof(f867,axiom,
    ! [X3,X17] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X17)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
       => ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X17,X3)
         => ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X3,X17)
           => X3 = X17 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__antisym__nonneg) ).

fof(f25643,plain,
    spl50_1142,
    inference(avatar_split_clause,[],[f4468,f25641]) ).

fof(f25641,plain,
    ( spl50_1142
  <=> ! [X0,X1] :
        ( 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) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1142])]) ).

fof(f4468,plain,
    ! [X0,X1] :
      ( 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(cnf_transformation,[],[f3538]) ).

fof(f3538,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,[],[f3537]) ).

fof(f3537,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,[],[f2493]) ).

fof(f2493,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,[],[f1551]) ).

fof(f1551,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,[],[f343]) ).

fof(f343,axiom,
    ! [X12,X5] :
      ( class_Rings_Oring__1__no__zero__divisors(X5)
     => ( c_Groups_Oone__class_Oone(X5) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X12),X12)
      <=> ( c_Groups_Ouminus__class_Ouminus(X5,c_Groups_Oone__class_Oone(X5)) = X12
          | c_Groups_Oone__class_Oone(X5) = X12 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_square__eq__1__iff) ).

fof(f25031,plain,
    ( ~ spl50_16
    | spl50_1141
    | ~ spl50_656
    | spl50_1140 ),
    inference(avatar_split_clause,[],[f24647,f24186,f10772,f25028,f6126]) ).

fof(f6126,plain,
    ( spl50_16
  <=> class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_16])]) ).

fof(f10772,plain,
    ( spl50_656
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X0))
        | c_Groups_Ozero__class_Ozero(X1) = X0
        | ~ class_RealVector_Oreal__normed__vector(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_656])]) ).

fof(f24186,plain,
    ( spl50_1140
  <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1140])]) ).

fof(f24647,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
    | ~ spl50_656
    | spl50_1140 ),
    inference(resolution,[],[f24188,f10773]) ).

fof(f10773,plain,
    ( ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X0))
        | c_Groups_Ozero__class_Ozero(X1) = X0
        | ~ class_RealVector_Oreal__normed__vector(X1) )
    | ~ spl50_656 ),
    inference(avatar_component_clause,[],[f10772]) ).

fof(f24188,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))
    | spl50_1140 ),
    inference(avatar_component_clause,[],[f24186]) ).

fof(f24189,plain,
    ( ~ spl50_229
    | ~ spl50_1140
    | ~ spl50_9
    | spl50_843
    | ~ spl50_1069
    | ~ spl50_1110 ),
    inference(avatar_split_clause,[],[f24063,f23801,f22262,f12739,f6091,f24186,f7184]) ).

fof(f7184,plain,
    ( spl50_229
  <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_229])]) ).

fof(f6091,plain,
    ( spl50_9
  <=> class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_9])]) ).

fof(f12739,plain,
    ( spl50_843
  <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_843])]) ).

fof(f22262,plain,
    ( spl50_1069
  <=> ! [X2,X0,X1] :
        ( c_RealVector_Onorm__class_Onorm(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2,X1)),X0)
        | ~ class_RealVector_Oreal__normed__div__algebra(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1069])]) ).

fof(f23801,plain,
    ( spl50_1110
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X0))
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1110])]) ).

fof(f24063,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____)
    | ~ spl50_9
    | spl50_843
    | ~ spl50_1069
    | ~ spl50_1110 ),
    inference(forward_demodulation,[],[f24040,f22935]) ).

fof(f22935,plain,
    ( ! [X0,X1] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),X1)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0)),X1)
    | ~ spl50_9
    | ~ spl50_1069 ),
    inference(resolution,[],[f22263,f6093]) ).

fof(f6093,plain,
    ( class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex)
    | ~ spl50_9 ),
    inference(avatar_component_clause,[],[f6091]) ).

fof(f22263,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_RealVector_Oreal__normed__div__algebra(X2)
        | c_RealVector_Onorm__class_Onorm(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2,X1)),X0) )
    | ~ spl50_1069 ),
    inference(avatar_component_clause,[],[f22262]) ).

fof(f24040,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____)
    | spl50_843
    | ~ spl50_1110 ),
    inference(resolution,[],[f23802,f12741]) ).

fof(f12741,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))
    | spl50_843 ),
    inference(avatar_component_clause,[],[f12739]) ).

fof(f23802,plain,
    ( ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X0))
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) )
    | ~ spl50_1110 ),
    inference(avatar_component_clause,[],[f23801]) ).

fof(f24011,plain,
    spl50_1139,
    inference(avatar_split_clause,[],[f5963,f24009]) ).

fof(f24009,plain,
    ( spl50_1139
  <=> ! [X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1139])]) ).

fof(f5963,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)) ),
    inference(forward_demodulation,[],[f5962,f4161]) ).

fof(f4161,plain,
    ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
    inference(cnf_transformation,[],[f1309]) ).

fof(f1309,plain,
    ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
    inference(rectify,[],[f380]) ).

fof(f380,axiom,
    ! [X17] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X17,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).

fof(f5962,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(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)),X1)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)) ),
    inference(forward_demodulation,[],[f5961,f4313]) ).

fof(f4313,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,[],[f1444]) ).

fof(f1444,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,[],[f364]) ).

fof(f364,axiom,
    ! [X3,X17] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X3) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X17),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__commute) ).

fof(f5961,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
      | ~ c_Orderings_Oord__class_Oless(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)),X1) ),
    inference(forward_demodulation,[],[f5960,f4161]) ).

fof(f5960,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(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)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
      | ~ c_Orderings_Oord__class_Oless(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)),X1) ),
    inference(forward_demodulation,[],[f5959,f4313]) ).

fof(f5959,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
      | ~ c_Orderings_Oord__class_Oless(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)
      | ~ c_Orderings_Oord__class_Oless(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)),X1) ),
    inference(forward_demodulation,[],[f5958,f4161]) ).

fof(f5958,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(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)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
      | ~ c_Orderings_Oord__class_Oless(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)
      | ~ c_Orderings_Oord__class_Oless(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)),X1) ),
    inference(forward_demodulation,[],[f5620,f4313]) ).

fof(f5620,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(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)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
      | ~ c_Orderings_Oord__class_Oless(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)
      | ~ c_Orderings_Oord__class_Oless(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)),X1) ),
    inference(definition_unfolding,[],[f4611,f4164,f4164,f4164]) ).

fof(f4164,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,[],[f1312]) ).

fof(f1312,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,[],[f942]) ).

fof(f942,axiom,
    ! [X3] : c_Nat_OSuc(X3) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).

fof(f4611,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ),
    inference(cnf_transformation,[],[f2646]) ).

fof(f2646,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ),
    inference(flattening,[],[f2645]) ).

fof(f2645,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ),
    inference(ennf_transformation,[],[f1675]) ).

fof(f1675,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)) ) ),
    inference(rectify,[],[f993]) ).

fof(f993,axiom,
    ! [X17,X3] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X3)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__less__mult) ).

fof(f24007,plain,
    spl50_1138,
    inference(avatar_split_clause,[],[f5598,f24005]) ).

fof(f24005,plain,
    ( spl50_1138
  <=> ! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(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,[spl50_1138])]) ).

fof(f5598,plain,
    ! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X0),
    inference(definition_unfolding,[],[f4335,f4164]) ).

fof(f4335,plain,
    ! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X1)),X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)),
    inference(cnf_transformation,[],[f1466]) ).

fof(f1466,plain,
    ! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X1)),X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)),
    inference(rectify,[],[f945]) ).

fof(f945,axiom,
    ! [X3,X17] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X17)),X3) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__Suc) ).

fof(f24003,plain,
    spl50_1137,
    inference(avatar_split_clause,[],[f5597,f24001]) ).

fof(f24001,plain,
    ( spl50_1137
  <=> ! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(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,[spl50_1137])]) ).

fof(f5597,plain,
    ! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
    inference(definition_unfolding,[],[f4334,f4164]) ).

fof(f4334,plain,
    ! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Nat_OSuc(X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)),
    inference(cnf_transformation,[],[f1465]) ).

fof(f1465,plain,
    ! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Nat_OSuc(X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)),
    inference(rectify,[],[f944]) ).

fof(f944,axiom,
    ! [X3,X17] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),c_Nat_OSuc(X3)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__Suc__right) ).

fof(f23980,plain,
    spl50_1136,
    inference(avatar_split_clause,[],[f5488,f23978]) ).

fof(f23978,plain,
    ( spl50_1136
  <=> ! [X4,X0,X3,X2,X1] :
        ( c_Orderings_Oord__class_Oless(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0))
        | ~ c_Orderings_Oord__class_Oless(X4,X1,X0)
        | ~ c_Orderings_Oord__class_Oless(X4,X3,X2)
        | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1136])]) ).

fof(f5488,plain,
    ! [X2,X3,X0,X1,X4] :
      ( c_Orderings_Oord__class_Oless(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0))
      | ~ c_Orderings_Oord__class_Oless(X4,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(X4,X3,X2)
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X4) ),
    inference(cnf_transformation,[],[f3372]) ).

fof(f3372,plain,
    ! [X0,X1,X2,X3,X4] :
      ( c_Orderings_Oord__class_Oless(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0))
      | ~ c_Orderings_Oord__class_Oless(X4,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(X4,X3,X2)
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X4) ),
    inference(flattening,[],[f3371]) ).

fof(f3371,plain,
    ! [X0,X1,X2,X3,X4] :
      ( c_Orderings_Oord__class_Oless(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0))
      | ~ c_Orderings_Oord__class_Oless(X4,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(X4,X3,X2)
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X4) ),
    inference(ennf_transformation,[],[f2244]) ).

fof(f2244,plain,
    ! [X0,X1,X2,X3,X4] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(X4)
     => ( c_Orderings_Oord__class_Oless(X4,X3,X2)
       => ( c_Orderings_Oord__class_Oless(X4,X1,X0)
         => c_Orderings_Oord__class_Oless(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0)) ) ) ),
    inference(rectify,[],[f228]) ).

fof(f228,axiom,
    ! [X22,X23,X13,X4,X5] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(X5)
     => ( c_Orderings_Oord__class_Oless(X5,X4,X13)
       => ( c_Orderings_Oord__class_Oless(X5,X23,X22)
         => c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,X4,X23),c_Groups_Oplus__class_Oplus(X5,X13,X22)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__mono) ).

fof(f23976,plain,
    spl50_1135,
    inference(avatar_split_clause,[],[f5487,f23974]) ).

fof(f23974,plain,
    ( spl50_1135
  <=> ! [X4,X0,X3,X2,X1] :
        ( c_Orderings_Oord__class_Oless(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0))
        | ~ c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
        | ~ c_Orderings_Oord__class_Oless(X4,X3,X2)
        | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1135])]) ).

fof(f5487,plain,
    ! [X2,X3,X0,X1,X4] :
      ( c_Orderings_Oord__class_Oless(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0))
      | ~ c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(X4,X3,X2)
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X4) ),
    inference(cnf_transformation,[],[f3370]) ).

fof(f3370,plain,
    ! [X0,X1,X2,X3,X4] :
      ( c_Orderings_Oord__class_Oless(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0))
      | ~ c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(X4,X3,X2)
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X4) ),
    inference(flattening,[],[f3369]) ).

fof(f3369,plain,
    ! [X0,X1,X2,X3,X4] :
      ( c_Orderings_Oord__class_Oless(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0))
      | ~ c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(X4,X3,X2)
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X4) ),
    inference(ennf_transformation,[],[f2243]) ).

fof(f2243,plain,
    ! [X0,X1,X2,X3,X4] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(X4)
     => ( c_Orderings_Oord__class_Oless(X4,X3,X2)
       => ( c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
         => c_Orderings_Oord__class_Oless(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0)) ) ) ),
    inference(rectify,[],[f252]) ).

fof(f252,axiom,
    ! [X22,X23,X13,X4,X5] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(X5)
     => ( c_Orderings_Oord__class_Oless(X5,X4,X13)
       => ( c_Orderings_Oord__class_Oless__eq(X5,X23,X22)
         => c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,X4,X23),c_Groups_Oplus__class_Oplus(X5,X13,X22)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__le__mono) ).

fof(f23972,plain,
    spl50_1134,
    inference(avatar_split_clause,[],[f5486,f23970]) ).

fof(f23970,plain,
    ( spl50_1134
  <=> ! [X4,X0,X3,X2,X1] :
        ( c_Orderings_Oord__class_Oless(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0))
        | ~ c_Orderings_Oord__class_Oless(X4,X1,X0)
        | ~ c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
        | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1134])]) ).

fof(f5486,plain,
    ! [X2,X3,X0,X1,X4] :
      ( c_Orderings_Oord__class_Oless(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0))
      | ~ c_Orderings_Oord__class_Oless(X4,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X4) ),
    inference(cnf_transformation,[],[f3368]) ).

fof(f3368,plain,
    ! [X0,X1,X2,X3,X4] :
      ( c_Orderings_Oord__class_Oless(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0))
      | ~ c_Orderings_Oord__class_Oless(X4,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X4) ),
    inference(flattening,[],[f3367]) ).

fof(f3367,plain,
    ! [X0,X1,X2,X3,X4] :
      ( c_Orderings_Oord__class_Oless(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0))
      | ~ c_Orderings_Oord__class_Oless(X4,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X4) ),
    inference(ennf_transformation,[],[f2242]) ).

fof(f2242,plain,
    ! [X0,X1,X2,X3,X4] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(X4)
     => ( c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
       => ( c_Orderings_Oord__class_Oless(X4,X1,X0)
         => c_Orderings_Oord__class_Oless(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0)) ) ) ),
    inference(rectify,[],[f253]) ).

fof(f253,axiom,
    ! [X22,X23,X13,X4,X5] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(X5)
     => ( c_Orderings_Oord__class_Oless__eq(X5,X4,X13)
       => ( c_Orderings_Oord__class_Oless(X5,X23,X22)
         => c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,X4,X23),c_Groups_Oplus__class_Oplus(X5,X13,X22)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__less__mono) ).

fof(f23968,plain,
    spl50_1133,
    inference(avatar_split_clause,[],[f5483,f23966]) ).

fof(f23966,plain,
    ( spl50_1133
  <=> ! [X4,X0,X3,X2,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0))
        | ~ c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
        | ~ c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
        | ~ class_Groups_Oordered__ab__semigroup__add(X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1133])]) ).

fof(f5483,plain,
    ! [X2,X3,X0,X1,X4] :
      ( c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0))
      | ~ c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
      | ~ class_Groups_Oordered__ab__semigroup__add(X4) ),
    inference(cnf_transformation,[],[f3362]) ).

fof(f3362,plain,
    ! [X0,X1,X2,X3,X4] :
      ( c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0))
      | ~ c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
      | ~ class_Groups_Oordered__ab__semigroup__add(X4) ),
    inference(flattening,[],[f3361]) ).

fof(f3361,plain,
    ! [X0,X1,X2,X3,X4] :
      ( c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0))
      | ~ c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
      | ~ class_Groups_Oordered__ab__semigroup__add(X4) ),
    inference(ennf_transformation,[],[f2239]) ).

fof(f2239,plain,
    ! [X0,X1,X2,X3,X4] :
      ( class_Groups_Oordered__ab__semigroup__add(X4)
     => ( c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
       => ( c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
         => c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0)) ) ) ),
    inference(rectify,[],[f221]) ).

fof(f221,axiom,
    ! [X22,X23,X13,X4,X5] :
      ( class_Groups_Oordered__ab__semigroup__add(X5)
     => ( c_Orderings_Oord__class_Oless__eq(X5,X4,X13)
       => ( c_Orderings_Oord__class_Oless__eq(X5,X23,X22)
         => c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,X4,X23),c_Groups_Oplus__class_Oplus(X5,X13,X22)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__mono) ).

fof(f23964,plain,
    spl50_1132,
    inference(avatar_split_clause,[],[f5448,f23962]) ).

fof(f23962,plain,
    ( spl50_1132
  <=> ! [X0,X3,X2,X1] :
        ( c_Orderings_Oord__class_Oless(tc_fun(X2,X3),X1,X0)
        | c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X0,X1)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0)
        | ~ class_Orderings_Oord(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1132])]) ).

fof(f5448,plain,
    ! [X2,X3,X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_fun(X2,X3),X1,X0)
      | c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X0,X1)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0)
      | ~ class_Orderings_Oord(X3) ),
    inference(cnf_transformation,[],[f3838]) ).

fof(f3838,plain,
    ! [X0,X1,X2,X3] :
      ( ( ( c_Orderings_Oord__class_Oless(tc_fun(X2,X3),X1,X0)
          | c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X0,X1)
          | ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0) )
        & ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X0,X1)
            & c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0) )
          | ~ c_Orderings_Oord__class_Oless(tc_fun(X2,X3),X1,X0) ) )
      | ~ class_Orderings_Oord(X3) ),
    inference(flattening,[],[f3837]) ).

fof(f3837,plain,
    ! [X0,X1,X2,X3] :
      ( ( ( c_Orderings_Oord__class_Oless(tc_fun(X2,X3),X1,X0)
          | c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X0,X1)
          | ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0) )
        & ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X0,X1)
            & c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0) )
          | ~ c_Orderings_Oord__class_Oless(tc_fun(X2,X3),X1,X0) ) )
      | ~ class_Orderings_Oord(X3) ),
    inference(nnf_transformation,[],[f3306]) ).

fof(f3306,plain,
    ! [X0,X1,X2,X3] :
      ( ( c_Orderings_Oord__class_Oless(tc_fun(X2,X3),X1,X0)
      <=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X0,X1)
          & c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0) ) )
      | ~ class_Orderings_Oord(X3) ),
    inference(ennf_transformation,[],[f2209]) ).

fof(f2209,plain,
    ! [X0,X1,X2,X3] :
      ( class_Orderings_Oord(X3)
     => ( c_Orderings_Oord__class_Oless(tc_fun(X2,X3),X1,X0)
      <=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X0,X1)
          & c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0) ) ) ),
    inference(rectify,[],[f773]) ).

fof(f773,axiom,
    ! [X0,X1,X5,X46] :
      ( class_Orderings_Oord(X46)
     => ( c_Orderings_Oord__class_Oless(tc_fun(X5,X46),X1,X0)
      <=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X46),X0,X1)
          & c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X46),X1,X0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__fun__def) ).

fof(f23960,plain,
    spl50_1131,
    inference(avatar_split_clause,[],[f5432,f23958]) ).

fof(f23958,plain,
    ( spl50_1131
  <=> ! [X0,X3,X2,X1] :
        ( c_Rings_Odvd__class_Odvd(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0))
        | ~ c_Rings_Odvd__class_Odvd(X3,X2,X1)
        | ~ class_Rings_Ocomm__semiring__1(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1131])]) ).

fof(f5432,plain,
    ! [X2,X3,X0,X1] :
      ( c_Rings_Odvd__class_Odvd(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0))
      | ~ c_Rings_Odvd__class_Odvd(X3,X2,X1)
      | ~ class_Rings_Ocomm__semiring__1(X3) ),
    inference(cnf_transformation,[],[f3283]) ).

fof(f3283,plain,
    ! [X0,X1,X2,X3] :
      ( c_Rings_Odvd__class_Odvd(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0))
      | ~ c_Rings_Odvd__class_Odvd(X3,X2,X1)
      | ~ class_Rings_Ocomm__semiring__1(X3) ),
    inference(flattening,[],[f3282]) ).

fof(f3282,plain,
    ! [X0,X1,X2,X3] :
      ( c_Rings_Odvd__class_Odvd(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0))
      | ~ c_Rings_Odvd__class_Odvd(X3,X2,X1)
      | ~ class_Rings_Ocomm__semiring__1(X3) ),
    inference(ennf_transformation,[],[f2196]) ).

fof(f2196,plain,
    ! [X0,X1,X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => ( c_Rings_Odvd__class_Odvd(X3,X2,X1)
       => c_Rings_Odvd__class_Odvd(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0)) ) ),
    inference(rectify,[],[f823]) ).

fof(f823,axiom,
    ! [X3,X7,X9,X5] :
      ( class_Rings_Ocomm__semiring__1(X5)
     => ( c_Rings_Odvd__class_Odvd(X5,X9,X7)
       => c_Rings_Odvd__class_Odvd(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X9),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),X3)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__power__same) ).

fof(f23956,plain,
    spl50_1130,
    inference(avatar_split_clause,[],[f5429,f23954]) ).

fof(f23954,plain,
    ( spl50_1130
  <=> ! [X0,X3,X2,X1] :
        ( c_Rings_Odvd__class_Odvd(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
        | ~ class_Rings_Ocomm__semiring__1(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1130])]) ).

fof(f5429,plain,
    ! [X2,X3,X0,X1] :
      ( c_Rings_Odvd__class_Odvd(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
      | ~ class_Rings_Ocomm__semiring__1(X3) ),
    inference(cnf_transformation,[],[f3277]) ).

fof(f3277,plain,
    ! [X0,X1,X2,X3] :
      ( c_Rings_Odvd__class_Odvd(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
      | ~ class_Rings_Ocomm__semiring__1(X3) ),
    inference(flattening,[],[f3276]) ).

fof(f3276,plain,
    ! [X0,X1,X2,X3] :
      ( c_Rings_Odvd__class_Odvd(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
      | ~ class_Rings_Ocomm__semiring__1(X3) ),
    inference(ennf_transformation,[],[f2193]) ).

fof(f2193,plain,
    ! [X0,X1,X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
       => c_Rings_Odvd__class_Odvd(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1)) ) ),
    inference(rectify,[],[f839]) ).

fof(f839,axiom,
    ! [X4,X3,X17,X5] :
      ( class_Rings_Ocomm__semiring__1(X5)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X3)
       => c_Rings_Odvd__class_Odvd(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X17),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X3)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__power__dvd) ).

fof(f23952,plain,
    spl50_1129,
    inference(avatar_split_clause,[],[f5396,f23950]) ).

fof(f23950,plain,
    ( spl50_1129
  <=> ! [X0,X3,X2,X1] :
        ( hAPP(c_Polynomial_Opoly(X3,c_Polynomial_Opcompose(X3,X2,X1)),X0) = hAPP(c_Polynomial_Opoly(X3,X2),hAPP(c_Polynomial_Opoly(X3,X1),X0))
        | ~ class_Rings_Ocomm__semiring__0(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1129])]) ).

fof(f5396,plain,
    ! [X2,X3,X0,X1] :
      ( hAPP(c_Polynomial_Opoly(X3,c_Polynomial_Opcompose(X3,X2,X1)),X0) = hAPP(c_Polynomial_Opoly(X3,X2),hAPP(c_Polynomial_Opoly(X3,X1),X0))
      | ~ class_Rings_Ocomm__semiring__0(X3) ),
    inference(cnf_transformation,[],[f3241]) ).

fof(f3241,plain,
    ! [X0,X1,X2,X3] :
      ( hAPP(c_Polynomial_Opoly(X3,c_Polynomial_Opcompose(X3,X2,X1)),X0) = hAPP(c_Polynomial_Opoly(X3,X2),hAPP(c_Polynomial_Opoly(X3,X1),X0))
      | ~ class_Rings_Ocomm__semiring__0(X3) ),
    inference(ennf_transformation,[],[f2160]) ).

fof(f2160,plain,
    ! [X0,X1,X2,X3] :
      ( class_Rings_Ocomm__semiring__0(X3)
     => hAPP(c_Polynomial_Opoly(X3,c_Polynomial_Opcompose(X3,X2,X1)),X0) = hAPP(c_Polynomial_Opoly(X3,X2),hAPP(c_Polynomial_Opoly(X3,X1),X0)) ),
    inference(rectify,[],[f704]) ).

fof(f704,axiom,
    ! [X9,X53,X54,X5] :
      ( class_Rings_Ocomm__semiring__0(X5)
     => hAPP(c_Polynomial_Opoly(X5,c_Polynomial_Opcompose(X5,X54,X53)),X9) = hAPP(c_Polynomial_Opoly(X5,X54),hAPP(c_Polynomial_Opoly(X5,X53),X9)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__pcompose) ).

fof(f23948,plain,
    spl50_1128,
    inference(avatar_split_clause,[],[f5356,f23946]) ).

fof(f23946,plain,
    ( spl50_1128
  <=> ! [X0,X3,X2,X1] :
        ( c_Rings_Odvd__class_Odvd(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
        | ~ c_Rings_Odvd__class_Odvd(X3,X1,X0)
        | ~ class_Rings_Oidom(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1128])]) ).

fof(f5356,plain,
    ! [X2,X3,X0,X1] :
      ( c_Rings_Odvd__class_Odvd(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
      | ~ c_Rings_Odvd__class_Odvd(X3,X1,X0)
      | ~ class_Rings_Oidom(X3) ),
    inference(cnf_transformation,[],[f3826]) ).

fof(f3826,plain,
    ! [X0,X1,X2,X3] :
      ( ( ( c_Rings_Odvd__class_Odvd(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
          | ( ~ c_Rings_Odvd__class_Odvd(X3,X1,X0)
            & c_Groups_Ozero__class_Ozero(X3) != X2 ) )
        & ( c_Rings_Odvd__class_Odvd(X3,X1,X0)
          | c_Groups_Ozero__class_Ozero(X3) = X2
          | ~ c_Rings_Odvd__class_Odvd(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)) ) )
      | ~ class_Rings_Oidom(X3) ),
    inference(flattening,[],[f3825]) ).

fof(f3825,plain,
    ! [X0,X1,X2,X3] :
      ( ( ( c_Rings_Odvd__class_Odvd(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
          | ( ~ c_Rings_Odvd__class_Odvd(X3,X1,X0)
            & c_Groups_Ozero__class_Ozero(X3) != X2 ) )
        & ( c_Rings_Odvd__class_Odvd(X3,X1,X0)
          | c_Groups_Ozero__class_Ozero(X3) = X2
          | ~ c_Rings_Odvd__class_Odvd(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)) ) )
      | ~ class_Rings_Oidom(X3) ),
    inference(nnf_transformation,[],[f3187]) ).

fof(f3187,plain,
    ! [X0,X1,X2,X3] :
      ( ( c_Rings_Odvd__class_Odvd(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
      <=> ( c_Rings_Odvd__class_Odvd(X3,X1,X0)
          | c_Groups_Ozero__class_Ozero(X3) = X2 ) )
      | ~ class_Rings_Oidom(X3) ),
    inference(ennf_transformation,[],[f2126]) ).

fof(f2126,plain,
    ! [X0,X1,X2,X3] :
      ( class_Rings_Oidom(X3)
     => ( c_Rings_Odvd__class_Odvd(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
      <=> ( c_Rings_Odvd__class_Odvd(X3,X1,X0)
          | c_Groups_Ozero__class_Ozero(X3) = X2 ) ) ),
    inference(rectify,[],[f819]) ).

fof(f819,axiom,
    ! [X21,X24,X25,X5] :
      ( class_Rings_Oidom(X5)
     => ( c_Rings_Odvd__class_Odvd(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X25),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X25),X21))
      <=> ( c_Rings_Odvd__class_Odvd(X5,X24,X21)
          | c_Groups_Ozero__class_Ozero(X5) = X25 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult__cancel__left) ).

fof(f23944,plain,
    spl50_1127,
    inference(avatar_split_clause,[],[f5353,f23942]) ).

fof(f23942,plain,
    ( spl50_1127
  <=> ! [X0,X3,X2,X1] :
        ( c_Rings_Odvd__class_Odvd(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
        | ~ c_Rings_Odvd__class_Odvd(X3,X2,X0)
        | ~ class_Rings_Oidom(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1127])]) ).

fof(f5353,plain,
    ! [X2,X3,X0,X1] :
      ( c_Rings_Odvd__class_Odvd(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
      | ~ c_Rings_Odvd__class_Odvd(X3,X2,X0)
      | ~ class_Rings_Oidom(X3) ),
    inference(cnf_transformation,[],[f3824]) ).

fof(f3824,plain,
    ! [X0,X1,X2,X3] :
      ( ( ( c_Rings_Odvd__class_Odvd(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
          | ( ~ c_Rings_Odvd__class_Odvd(X3,X2,X0)
            & c_Groups_Ozero__class_Ozero(X3) != X1 ) )
        & ( c_Rings_Odvd__class_Odvd(X3,X2,X0)
          | c_Groups_Ozero__class_Ozero(X3) = X1
          | ~ c_Rings_Odvd__class_Odvd(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1)) ) )
      | ~ class_Rings_Oidom(X3) ),
    inference(flattening,[],[f3823]) ).

fof(f3823,plain,
    ! [X0,X1,X2,X3] :
      ( ( ( c_Rings_Odvd__class_Odvd(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
          | ( ~ c_Rings_Odvd__class_Odvd(X3,X2,X0)
            & c_Groups_Ozero__class_Ozero(X3) != X1 ) )
        & ( c_Rings_Odvd__class_Odvd(X3,X2,X0)
          | c_Groups_Ozero__class_Ozero(X3) = X1
          | ~ c_Rings_Odvd__class_Odvd(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1)) ) )
      | ~ class_Rings_Oidom(X3) ),
    inference(nnf_transformation,[],[f3186]) ).

fof(f3186,plain,
    ! [X0,X1,X2,X3] :
      ( ( c_Rings_Odvd__class_Odvd(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
      <=> ( c_Rings_Odvd__class_Odvd(X3,X2,X0)
          | c_Groups_Ozero__class_Ozero(X3) = X1 ) )
      | ~ class_Rings_Oidom(X3) ),
    inference(ennf_transformation,[],[f2125]) ).

fof(f2125,plain,
    ! [X0,X1,X2,X3] :
      ( class_Rings_Oidom(X3)
     => ( c_Rings_Odvd__class_Odvd(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
      <=> ( c_Rings_Odvd__class_Odvd(X3,X2,X0)
          | c_Groups_Ozero__class_Ozero(X3) = X1 ) ) ),
    inference(rectify,[],[f820]) ).

fof(f820,axiom,
    ! [X21,X25,X24,X5] :
      ( class_Rings_Oidom(X5)
     => ( c_Rings_Odvd__class_Odvd(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X24),X25),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X21),X25))
      <=> ( c_Rings_Odvd__class_Odvd(X5,X24,X21)
          | c_Groups_Ozero__class_Ozero(X5) = X25 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult__cancel__right) ).

fof(f23917,plain,
    spl50_1126,
    inference(avatar_split_clause,[],[f5233,f23915]) ).

fof(f23915,plain,
    ( spl50_1126
  <=> ! [X2,X0,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2
        | X0 = X1
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1126])]) ).

fof(f5233,plain,
    ! [X2,X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2
      | X0 = X1
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0) ),
    inference(cnf_transformation,[],[f3783]) ).

fof(f3783,plain,
    ! [X0,X1,X2] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)
        | ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2
          & X0 != X1 ) )
      & ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2
        | X0 = X1
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0) ) ),
    inference(flattening,[],[f3782]) ).

fof(f3782,plain,
    ! [X0,X1,X2] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)
        | ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2
          & X0 != X1 ) )
      & ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2
        | X0 = X1
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0) ) ),
    inference(nnf_transformation,[],[f2057]) ).

fof(f2057,plain,
    ! [X0,X1,X2] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)
    <=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2
        | X0 = X1 ) ),
    inference(rectify,[],[f388]) ).

fof(f388,axiom,
    ! [X16,X32,X36] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X32) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X16)
    <=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X36
        | X16 = X32 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__cancel1) ).

fof(f23913,plain,
    spl50_1125,
    inference(avatar_split_clause,[],[f5230,f23911]) ).

fof(f23911,plain,
    ( spl50_1125
  <=> ! [X2,X0,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
        | X0 = X2
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1125])]) ).

fof(f5230,plain,
    ! [X2,X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
      | X0 = X2
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) ),
    inference(cnf_transformation,[],[f3781]) ).

fof(f3781,plain,
    ! [X0,X1,X2] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)
        | ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
          & X0 != X2 ) )
      & ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
        | X0 = X2
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) ) ),
    inference(flattening,[],[f3780]) ).

fof(f3780,plain,
    ! [X0,X1,X2] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)
        | ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
          & X0 != X2 ) )
      & ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
        | X0 = X2
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) ) ),
    inference(nnf_transformation,[],[f2056]) ).

fof(f2056,plain,
    ! [X0,X1,X2] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)
    <=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
        | X0 = X2 ) ),
    inference(rectify,[],[f389]) ).

fof(f389,axiom,
    ! [X16,X36,X32] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X32),X36) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16),X36)
    <=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X36
        | X16 = X32 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__cancel2) ).

fof(f23909,plain,
    spl50_1124,
    inference(avatar_split_clause,[],[f5181,f23907]) ).

fof(f23907,plain,
    ( spl50_1124
  <=> ! [X0,X6,X2,X1] :
        ( hBOOL(hAPP(X1,sK37(X0,X1,X2)))
        | ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X6)))
        | ~ class_Rings_Osemiring__0(X2)
        | ~ class_Rings_Odvd(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1124])]) ).

fof(f5181,plain,
    ! [X2,X0,X1,X6] :
      ( hBOOL(hAPP(X1,sK37(X0,X1,X2)))
      | ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X6)))
      | ~ class_Rings_Osemiring__0(X2)
      | ~ class_Rings_Odvd(X2) ),
    inference(cnf_transformation,[],[f3752]) ).

fof(f3752,plain,
    ! [X0,X1,X2] :
      ( ( ( hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),sK36(X0,X1,X2))))
          | ! [X4] :
              ( ~ hBOOL(hAPP(X1,X4))
              | ~ c_Rings_Odvd__class_Odvd(X2,X0,c_Groups_Oplus__class_Oplus(X2,X4,c_Groups_Ozero__class_Ozero(X2))) ) )
        & ( ( hBOOL(hAPP(X1,sK37(X0,X1,X2)))
            & c_Rings_Odvd__class_Odvd(X2,X0,c_Groups_Oplus__class_Oplus(X2,sK37(X0,X1,X2),c_Groups_Ozero__class_Ozero(X2))) )
          | ! [X6] : ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X6))) ) )
      | ~ class_Rings_Osemiring__0(X2)
      | ~ class_Rings_Odvd(X2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK36,sK37])],[f3749,f3751,f3750]) ).

fof(f3750,plain,
    ! [X0,X1,X2] :
      ( ? [X3] : hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X3)))
     => hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),sK36(X0,X1,X2)))) ),
    introduced(choice_axiom,[]) ).

fof(f3751,plain,
    ! [X0,X1,X2] :
      ( ? [X5] :
          ( hBOOL(hAPP(X1,X5))
          & c_Rings_Odvd__class_Odvd(X2,X0,c_Groups_Oplus__class_Oplus(X2,X5,c_Groups_Ozero__class_Ozero(X2))) )
     => ( hBOOL(hAPP(X1,sK37(X0,X1,X2)))
        & c_Rings_Odvd__class_Odvd(X2,X0,c_Groups_Oplus__class_Oplus(X2,sK37(X0,X1,X2),c_Groups_Ozero__class_Ozero(X2))) ) ),
    introduced(choice_axiom,[]) ).

fof(f3749,plain,
    ! [X0,X1,X2] :
      ( ( ( ? [X3] : hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X3)))
          | ! [X4] :
              ( ~ hBOOL(hAPP(X1,X4))
              | ~ c_Rings_Odvd__class_Odvd(X2,X0,c_Groups_Oplus__class_Oplus(X2,X4,c_Groups_Ozero__class_Ozero(X2))) ) )
        & ( ? [X5] :
              ( hBOOL(hAPP(X1,X5))
              & c_Rings_Odvd__class_Odvd(X2,X0,c_Groups_Oplus__class_Oplus(X2,X5,c_Groups_Ozero__class_Ozero(X2))) )
          | ! [X6] : ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X6))) ) )
      | ~ class_Rings_Osemiring__0(X2)
      | ~ class_Rings_Odvd(X2) ),
    inference(rectify,[],[f3748]) ).

fof(f3748,plain,
    ! [X0,X1,X2] :
      ( ( ( ? [X3] : hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X3)))
          | ! [X4] :
              ( ~ hBOOL(hAPP(X1,X4))
              | ~ c_Rings_Odvd__class_Odvd(X2,X0,c_Groups_Oplus__class_Oplus(X2,X4,c_Groups_Ozero__class_Ozero(X2))) ) )
        & ( ? [X4] :
              ( hBOOL(hAPP(X1,X4))
              & c_Rings_Odvd__class_Odvd(X2,X0,c_Groups_Oplus__class_Oplus(X2,X4,c_Groups_Ozero__class_Ozero(X2))) )
          | ! [X3] : ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X3))) ) )
      | ~ class_Rings_Osemiring__0(X2)
      | ~ class_Rings_Odvd(X2) ),
    inference(nnf_transformation,[],[f3078]) ).

fof(f3078,plain,
    ! [X0,X1,X2] :
      ( ( ? [X3] : hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X3)))
      <=> ? [X4] :
            ( hBOOL(hAPP(X1,X4))
            & c_Rings_Odvd__class_Odvd(X2,X0,c_Groups_Oplus__class_Oplus(X2,X4,c_Groups_Ozero__class_Ozero(X2))) ) )
      | ~ class_Rings_Osemiring__0(X2)
      | ~ class_Rings_Odvd(X2) ),
    inference(flattening,[],[f3077]) ).

fof(f3077,plain,
    ! [X0,X1,X2] :
      ( ( ? [X3] : hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X3)))
      <=> ? [X4] :
            ( hBOOL(hAPP(X1,X4))
            & c_Rings_Odvd__class_Odvd(X2,X0,c_Groups_Oplus__class_Oplus(X2,X4,c_Groups_Ozero__class_Ozero(X2))) ) )
      | ~ class_Rings_Osemiring__0(X2)
      | ~ class_Rings_Odvd(X2) ),
    inference(ennf_transformation,[],[f2040]) ).

fof(f2040,plain,
    ! [X0,X1,X2] :
      ( ( class_Rings_Osemiring__0(X2)
        & class_Rings_Odvd(X2) )
     => ( ? [X3] : hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X3)))
      <=> ? [X4] :
            ( hBOOL(hAPP(X1,X4))
            & c_Rings_Odvd__class_Odvd(X2,X0,c_Groups_Oplus__class_Oplus(X2,X4,c_Groups_Ozero__class_Ozero(X2))) ) ) ),
    inference(rectify,[],[f883]) ).

fof(f883,axiom,
    ! [X35,X49,X5] :
      ( ( class_Rings_Osemiring__0(X5)
        & class_Rings_Odvd(X5) )
     => ( ? [X2] : hBOOL(hAPP(X49,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X35),X2)))
      <=> ? [X2] :
            ( hBOOL(hAPP(X49,X2))
            & c_Rings_Odvd__class_Odvd(X5,X35,c_Groups_Oplus__class_Oplus(X5,X2,c_Groups_Ozero__class_Ozero(X5))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_unity__coeff__ex) ).

fof(f23905,plain,
    spl50_1123,
    inference(avatar_split_clause,[],[f5122,f23903]) ).

fof(f23903,plain,
    ( spl50_1123
  <=> ! [X2,X0,X1] :
        ( X0 = X1
        | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1123])]) ).

fof(f5122,plain,
    ! [X2,X0,X1] :
      ( X0 = X1
      | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    inference(cnf_transformation,[],[f3733]) ).

fof(f3733,plain,
    ! [X0,X1,X2] :
      ( ( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)
          | X0 != X1 )
        & ( X0 = X1
          | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) ) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    inference(nnf_transformation,[],[f3012]) ).

fof(f3012,plain,
    ! [X0,X1,X2] :
      ( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)
      <=> X0 = X1 )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    inference(flattening,[],[f3011]) ).

fof(f3011,plain,
    ! [X0,X1,X2] :
      ( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)
      <=> X0 = X1 )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    inference(ennf_transformation,[],[f1997]) ).

fof(f1997,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,X0)
       => ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)
        <=> X0 = X1 ) ) ),
    inference(rectify,[],[f461]) ).

fof(f461,axiom,
    ! [X16,X32,X36] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,X32)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,X16)
       => ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X32,X36) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X16,X36)
        <=> X16 = X32 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__diff__iff) ).

fof(f23901,plain,
    spl50_1122,
    inference(avatar_split_clause,[],[f5092,f23899]) ).

fof(f23899,plain,
    ( spl50_1122
  <=> ! [X2,X0,X1] :
        ( X0 = X1
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),X2)
        | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1122])]) ).

fof(f5092,plain,
    ! [X2,X0,X1] :
      ( X0 = X1
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),X2)
      | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X2 ),
    inference(cnf_transformation,[],[f3731]) ).

fof(f3731,plain,
    ! [X0,X1,X2] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),X2)
          | X0 != X1 )
        & ( X0 = X1
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),X2) ) )
      | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X2 ),
    inference(nnf_transformation,[],[f2976]) ).

fof(f2976,plain,
    ! [X0,X1,X2] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),X2)
      <=> X0 = X1 )
      | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X2 ),
    inference(ennf_transformation,[],[f1970]) ).

fof(f1970,plain,
    ! [X0,X1,X2] :
      ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X2
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),X2)
      <=> X0 = X1 ) ),
    inference(rectify,[],[f237]) ).

fof(f237,axiom,
    ! [X21,X24,X25] :
      ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X25
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X24),X25) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X21),X25)
      <=> X21 = X24 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__right__cancel) ).

fof(f23897,plain,
    spl50_1121,
    inference(avatar_split_clause,[],[f5090,f23895]) ).

fof(f23895,plain,
    ( spl50_1121
  <=> ! [X2,X0,X1] :
        ( X0 = X1
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X0)
        | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1121])]) ).

fof(f5090,plain,
    ! [X2,X0,X1] :
      ( X0 = X1
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X0)
      | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X2 ),
    inference(cnf_transformation,[],[f3730]) ).

fof(f3730,plain,
    ! [X0,X1,X2] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X0)
          | X0 != X1 )
        & ( X0 = X1
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X0) ) )
      | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X2 ),
    inference(nnf_transformation,[],[f2975]) ).

fof(f2975,plain,
    ! [X0,X1,X2] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X0)
      <=> X0 = X1 )
      | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X2 ),
    inference(ennf_transformation,[],[f1969]) ).

fof(f1969,plain,
    ! [X0,X1,X2] :
      ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X2
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X0)
      <=> X0 = X1 ) ),
    inference(rectify,[],[f238]) ).

fof(f238,axiom,
    ! [X21,X24,X25] :
      ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X25
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X25),X24) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X25),X21)
      <=> X21 = X24 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__left__cancel) ).

fof(f23893,plain,
    spl50_1120,
    inference(avatar_split_clause,[],[f4939,f23891]) ).

fof(f23891,plain,
    ( spl50_1120
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oplus__class_Oplus(X2,X1,X0))
        | ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X0)
        | ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
        | ~ class_Groups_Oordered__comm__monoid__add(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1120])]) ).

fof(f4939,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oplus__class_Oplus(X2,X1,X0))
      | ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X0)
      | ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
      | ~ class_Groups_Oordered__comm__monoid__add(X2) ),
    inference(cnf_transformation,[],[f2813]) ).

fof(f2813,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oplus__class_Oplus(X2,X1,X0))
      | ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X0)
      | ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
      | ~ class_Groups_Oordered__comm__monoid__add(X2) ),
    inference(flattening,[],[f2812]) ).

fof(f2812,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oplus__class_Oplus(X2,X1,X0))
      | ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X0)
      | ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
      | ~ class_Groups_Oordered__comm__monoid__add(X2) ),
    inference(ennf_transformation,[],[f1861]) ).

fof(f1861,plain,
    ! [X0,X1,X2] :
      ( class_Groups_Oordered__comm__monoid__add(X2)
     => ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
       => ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X0)
         => c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oplus__class_Oplus(X2,X1,X0)) ) ) ),
    inference(rectify,[],[f250]) ).

fof(f250,axiom,
    ! [X13,X4,X5] :
      ( class_Groups_Oordered__comm__monoid__add(X5)
     => ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X4)
       => ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X13)
         => c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),c_Groups_Oplus__class_Oplus(X5,X4,X13)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__pos__pos) ).

fof(f23889,plain,
    spl50_1119,
    inference(avatar_split_clause,[],[f4937,f23887]) ).

fof(f23887,plain,
    ( spl50_1119
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2))
        | ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
        | ~ c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ozero__class_Ozero(X2))
        | ~ class_Groups_Oordered__comm__monoid__add(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1119])]) ).

fof(f4937,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2))
      | ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
      | ~ c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ozero__class_Ozero(X2))
      | ~ class_Groups_Oordered__comm__monoid__add(X2) ),
    inference(cnf_transformation,[],[f2809]) ).

fof(f2809,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2))
      | ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
      | ~ c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ozero__class_Ozero(X2))
      | ~ class_Groups_Oordered__comm__monoid__add(X2) ),
    inference(flattening,[],[f2808]) ).

fof(f2808,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2))
      | ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
      | ~ c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ozero__class_Ozero(X2))
      | ~ class_Groups_Oordered__comm__monoid__add(X2) ),
    inference(ennf_transformation,[],[f1859]) ).

fof(f1859,plain,
    ! [X0,X1,X2] :
      ( class_Groups_Oordered__comm__monoid__add(X2)
     => ( c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ozero__class_Ozero(X2))
       => ( c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
         => c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2)) ) ) ),
    inference(rectify,[],[f251]) ).

fof(f251,axiom,
    ! [X13,X4,X5] :
      ( class_Groups_Oordered__comm__monoid__add(X5)
     => ( c_Orderings_Oord__class_Oless(X5,X4,c_Groups_Ozero__class_Ozero(X5))
       => ( c_Orderings_Oord__class_Oless(X5,X13,c_Groups_Ozero__class_Ozero(X5))
         => c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,X4,X13),c_Groups_Ozero__class_Ozero(X5)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__neg__neg) ).

fof(f23885,plain,
    spl50_1118,
    inference(avatar_split_clause,[],[f4936,f23883]) ).

fof(f23883,plain,
    ( spl50_1118
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),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(X2,X1,c_Groups_Ozero__class_Ozero(X2))
        | ~ class_Groups_Oordered__comm__monoid__add(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1118])]) ).

fof(f4936,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),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(X2,X1,c_Groups_Ozero__class_Ozero(X2))
      | ~ class_Groups_Oordered__comm__monoid__add(X2) ),
    inference(cnf_transformation,[],[f2807]) ).

fof(f2807,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),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(X2,X1,c_Groups_Ozero__class_Ozero(X2))
      | ~ class_Groups_Oordered__comm__monoid__add(X2) ),
    inference(flattening,[],[f2806]) ).

fof(f2806,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),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(X2,X1,c_Groups_Ozero__class_Ozero(X2))
      | ~ class_Groups_Oordered__comm__monoid__add(X2) ),
    inference(ennf_transformation,[],[f1858]) ).

fof(f1858,plain,
    ! [X0,X1,X2] :
      ( class_Groups_Oordered__comm__monoid__add(X2)
     => ( c_Orderings_Oord__class_Oless(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(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2)) ) ) ),
    inference(rectify,[],[f189]) ).

fof(f189,axiom,
    ! [X13,X4,X5] :
      ( class_Groups_Oordered__comm__monoid__add(X5)
     => ( c_Orderings_Oord__class_Oless(X5,X4,c_Groups_Ozero__class_Ozero(X5))
       => ( c_Orderings_Oord__class_Oless__eq(X5,X13,c_Groups_Ozero__class_Ozero(X5))
         => c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,X4,X13),c_Groups_Ozero__class_Ozero(X5)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__neg__nonpos) ).

fof(f23881,plain,
    spl50_1117,
    inference(avatar_split_clause,[],[f4930,f23879]) ).

fof(f23879,plain,
    ( spl50_1117
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2))
        | ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
        | ~ c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2))
        | ~ class_Groups_Oordered__comm__monoid__add(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1117])]) ).

fof(f4930,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2))
      | ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
      | ~ c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2))
      | ~ class_Groups_Oordered__comm__monoid__add(X2) ),
    inference(cnf_transformation,[],[f2799]) ).

fof(f2799,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2))
      | ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
      | ~ c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2))
      | ~ class_Groups_Oordered__comm__monoid__add(X2) ),
    inference(flattening,[],[f2798]) ).

fof(f2798,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2))
      | ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
      | ~ c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2))
      | ~ class_Groups_Oordered__comm__monoid__add(X2) ),
    inference(ennf_transformation,[],[f1854]) ).

fof(f1854,plain,
    ! [X0,X1,X2] :
      ( class_Groups_Oordered__comm__monoid__add(X2)
     => ( c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2))
       => ( c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
         => c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2)) ) ) ),
    inference(rectify,[],[f188]) ).

fof(f188,axiom,
    ! [X13,X4,X5] :
      ( class_Groups_Oordered__comm__monoid__add(X5)
     => ( c_Orderings_Oord__class_Oless__eq(X5,X4,c_Groups_Ozero__class_Ozero(X5))
       => ( c_Orderings_Oord__class_Oless(X5,X13,c_Groups_Ozero__class_Ozero(X5))
         => c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,X4,X13),c_Groups_Ozero__class_Ozero(X5)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonpos__neg) ).

fof(f23827,plain,
    spl50_1116,
    inference(avatar_split_clause,[],[f4929,f23825]) ).

fof(f23825,plain,
    ( spl50_1116
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),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,X1,c_Groups_Ozero__class_Ozero(X2))
        | ~ class_Groups_Oordered__comm__monoid__add(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1116])]) ).

fof(f4929,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),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,X1,c_Groups_Ozero__class_Ozero(X2))
      | ~ class_Groups_Oordered__comm__monoid__add(X2) ),
    inference(cnf_transformation,[],[f2797]) ).

fof(f2797,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),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,X1,c_Groups_Ozero__class_Ozero(X2))
      | ~ class_Groups_Oordered__comm__monoid__add(X2) ),
    inference(flattening,[],[f2796]) ).

fof(f2796,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),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,X1,c_Groups_Ozero__class_Ozero(X2))
      | ~ class_Groups_Oordered__comm__monoid__add(X2) ),
    inference(ennf_transformation,[],[f1853]) ).

fof(f1853,plain,
    ! [X0,X1,X2] :
      ( class_Groups_Oordered__comm__monoid__add(X2)
     => ( 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_Oplus__class_Oplus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2)) ) ) ),
    inference(rectify,[],[f247]) ).

fof(f247,axiom,
    ! [X13,X4,X5] :
      ( class_Groups_Oordered__comm__monoid__add(X5)
     => ( c_Orderings_Oord__class_Oless__eq(X5,X4,c_Groups_Ozero__class_Ozero(X5))
       => ( c_Orderings_Oord__class_Oless__eq(X5,X13,c_Groups_Ozero__class_Ozero(X5))
         => c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,X4,X13),c_Groups_Ozero__class_Ozero(X5)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonpos__nonpos) ).

fof(f23823,plain,
    spl50_1115,
    inference(avatar_split_clause,[],[f4841,f23821]) ).

fof(f23821,plain,
    ( spl50_1115
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0)))
        | ~ class_Rings_Olinordered__ring(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1115])]) ).

fof(f4841,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0)))
      | ~ class_Rings_Olinordered__ring(X2) ),
    inference(cnf_transformation,[],[f2735]) ).

fof(f2735,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0)))
      | ~ class_Rings_Olinordered__ring(X2) ),
    inference(ennf_transformation,[],[f1807]) ).

fof(f1807,plain,
    ! [X0,X1,X2] :
      ( class_Rings_Olinordered__ring(X2)
     => c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0))) ),
    inference(rectify,[],[f187]) ).

fof(f187,axiom,
    ! [X7,X9,X5] :
      ( class_Rings_Olinordered__ring(X5)
     => c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X9),X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X7),X7))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__squares__ge__zero) ).

fof(f23819,plain,
    spl50_1114,
    inference(avatar_split_clause,[],[f4840,f23817]) ).

fof(f23817,plain,
    ( spl50_1114
  <=> ! [X2,X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0)),c_Groups_Ozero__class_Ozero(X2))
        | ~ class_Rings_Olinordered__ring(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1114])]) ).

fof(f4840,plain,
    ! [X2,X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0)),c_Groups_Ozero__class_Ozero(X2))
      | ~ class_Rings_Olinordered__ring(X2) ),
    inference(cnf_transformation,[],[f2734]) ).

fof(f2734,plain,
    ! [X0,X1,X2] :
      ( ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0)),c_Groups_Ozero__class_Ozero(X2))
      | ~ class_Rings_Olinordered__ring(X2) ),
    inference(ennf_transformation,[],[f1806]) ).

fof(f1806,plain,
    ! [X0,X1,X2] :
      ( class_Rings_Olinordered__ring(X2)
     => ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0)),c_Groups_Ozero__class_Ozero(X2)) ),
    inference(rectify,[],[f185]) ).

fof(f185,axiom,
    ! [X7,X9,X5] :
      ( class_Rings_Olinordered__ring(X5)
     => ~ c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X9),X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X7),X7)),c_Groups_Ozero__class_Ozero(X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__sum__squares__lt__zero) ).

fof(f23815,plain,
    spl50_1113,
    inference(avatar_split_clause,[],[f4828,f23813]) ).

fof(f23813,plain,
    ( spl50_1113
  <=> ! [X2,X0,X1] :
        ( X0 = X1
        | c_Groups_Ozero__class_Ozero(X2) = X0
        | c_Groups_Ozero__class_Ozero(X2) = X1
        | c_Rings_Oinverse__class_Oinverse(X2,X0) != c_Rings_Oinverse__class_Oinverse(X2,X1)
        | ~ class_Rings_Odivision__ring(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1113])]) ).

fof(f4828,plain,
    ! [X2,X0,X1] :
      ( X0 = X1
      | c_Groups_Ozero__class_Ozero(X2) = X0
      | c_Groups_Ozero__class_Ozero(X2) = X1
      | c_Rings_Oinverse__class_Oinverse(X2,X0) != c_Rings_Oinverse__class_Oinverse(X2,X1)
      | ~ class_Rings_Odivision__ring(X2) ),
    inference(cnf_transformation,[],[f2721]) ).

fof(f2721,plain,
    ! [X0,X1,X2] :
      ( X0 = X1
      | c_Groups_Ozero__class_Ozero(X2) = X0
      | c_Groups_Ozero__class_Ozero(X2) = X1
      | c_Rings_Oinverse__class_Oinverse(X2,X0) != c_Rings_Oinverse__class_Oinverse(X2,X1)
      | ~ class_Rings_Odivision__ring(X2) ),
    inference(flattening,[],[f2720]) ).

fof(f2720,plain,
    ! [X0,X1,X2] :
      ( X0 = X1
      | c_Groups_Ozero__class_Ozero(X2) = X0
      | c_Groups_Ozero__class_Ozero(X2) = X1
      | c_Rings_Oinverse__class_Oinverse(X2,X0) != c_Rings_Oinverse__class_Oinverse(X2,X1)
      | ~ class_Rings_Odivision__ring(X2) ),
    inference(ennf_transformation,[],[f1794]) ).

fof(f1794,plain,
    ! [X0,X1,X2] :
      ( class_Rings_Odivision__ring(X2)
     => ( c_Rings_Oinverse__class_Oinverse(X2,X0) = c_Rings_Oinverse__class_Oinverse(X2,X1)
       => ( c_Groups_Ozero__class_Ozero(X2) != X1
         => ( c_Groups_Ozero__class_Ozero(X2) != X0
           => X0 = X1 ) ) ) ),
    inference(rectify,[],[f112]) ).

fof(f112,axiom,
    ! [X13,X4,X5] :
      ( class_Rings_Odivision__ring(X5)
     => ( c_Rings_Oinverse__class_Oinverse(X5,X4) = c_Rings_Oinverse__class_Oinverse(X5,X13)
       => ( c_Groups_Ozero__class_Ozero(X5) != X4
         => ( c_Groups_Ozero__class_Ozero(X5) != X13
           => X4 = X13 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__inverse__eq__imp__eq) ).

fof(f23811,plain,
    spl50_1112,
    inference(avatar_split_clause,[],[f4807,f23809]) ).

fof(f23809,plain,
    ( spl50_1112
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2,X1)),X0))
        | ~ class_RealVector_Oreal__normed__algebra__1(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1112])]) ).

fof(f4807,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2,X1)),X0))
      | ~ class_RealVector_Oreal__normed__algebra__1(X2) ),
    inference(cnf_transformation,[],[f2693]) ).

fof(f2693,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2,X1)),X0))
      | ~ class_RealVector_Oreal__normed__algebra__1(X2) ),
    inference(ennf_transformation,[],[f1776]) ).

fof(f1776,plain,
    ! [X0,X1,X2] :
      ( class_RealVector_Oreal__normed__algebra__1(X2)
     => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2,X1)),X0)) ),
    inference(rectify,[],[f80]) ).

fof(f80,axiom,
    ! [X3,X9,X5] :
      ( class_RealVector_Oreal__normed__algebra__1(X5)
     => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X9),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5,X9)),X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__power__ineq) ).

fof(f23807,plain,
    spl50_1111,
    inference(avatar_split_clause,[],[f4768,f23805]) ).

fof(f23805,plain,
    ( spl50_1111
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,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) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1111])]) ).

fof(f4768,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,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) ),
    inference(cnf_transformation,[],[f3648]) ).

fof(f3648,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,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_Orderings_Oord__class_Oless(tc_Nat_Onat,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_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ) ),
    inference(flattening,[],[f3647]) ).

fof(f3647,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,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_Orderings_Oord__class_Oless(tc_Nat_Onat,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_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ) ),
    inference(nnf_transformation,[],[f1741]) ).

fof(f1741,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
    <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,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) ) ),
    inference(rectify,[],[f428]) ).

fof(f428,axiom,
    ! [X16,X32] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X32),X16))
    <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X16)
        & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X32) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__0__less__mult__iff) ).

fof(f23803,plain,
    spl50_1110,
    inference(avatar_split_clause,[],[f4591,f23801]) ).

fof(f4591,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X0))
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
    inference(cnf_transformation,[],[f2622]) ).

fof(f2622,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X0))
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
    inference(flattening,[],[f2621]) ).

fof(f2621,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X0))
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
    inference(ennf_transformation,[],[f1659]) ).

fof(f1659,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
     => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
       => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X0)) ) ),
    inference(rectify,[],[f256]) ).

fof(f256,axiom,
    ! [X7,X9] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X9)
     => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X7)
       => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X9),X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__order) ).

fof(f23799,plain,
    spl50_1109,
    inference(avatar_split_clause,[],[f4589,f23797]) ).

fof(f23797,plain,
    ( spl50_1109
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1109])]) ).

fof(f4589,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(cnf_transformation,[],[f2618]) ).

fof(f2618,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(flattening,[],[f2617]) ).

fof(f2617,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(ennf_transformation,[],[f1657]) ).

fof(f1657,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_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
       => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0)) ) ),
    inference(rectify,[],[f697]) ).

fof(f697,axiom,
    ! [X7,X9] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X9)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X7)
       => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X9),X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) ).

fof(f23795,plain,
    spl50_1108,
    inference(avatar_split_clause,[],[f4121,f23792]) ).

fof(f23792,plain,
    ( spl50_1108
  <=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1108])]) ).

fof(f4121,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),
    inference(cnf_transformation,[],[f662]) ).

fof(f662,axiom,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_th02) ).

fof(f23215,plain,
    ( ~ spl50_166
    | spl50_1107
    | ~ spl50_427
    | ~ spl50_544 ),
    inference(avatar_split_clause,[],[f9652,f8980,f8232,f23213,f6876]) ).

fof(f6876,plain,
    ( spl50_166
  <=> class_Rings_Odvd(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_166])]) ).

fof(f23213,plain,
    ( spl50_1107
  <=> ! [X0] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1107])]) ).

fof(f8232,plain,
    ( spl50_427
  <=> ! [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,[spl50_427])]) ).

fof(f8980,plain,
    ( spl50_544
  <=> ! [X0,X1,X3] :
        ( c_Rings_Odvd__class_Odvd(X3,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0))
        | ~ class_Rings_Odvd(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_544])]) ).

fof(f9652,plain,
    ( ! [X0] :
        ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ class_Rings_Odvd(tc_Nat_Onat) )
    | ~ spl50_427
    | ~ spl50_544 ),
    inference(superposition,[],[f8981,f8233]) ).

fof(f8233,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))
    | ~ spl50_427 ),
    inference(avatar_component_clause,[],[f8232]) ).

fof(f8981,plain,
    ( ! [X3,X0,X1] :
        ( c_Rings_Odvd__class_Odvd(X3,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0))
        | ~ class_Rings_Odvd(X3) )
    | ~ spl50_544 ),
    inference(avatar_component_clause,[],[f8980]) ).

fof(f22772,plain,
    ( ~ spl50_162
    | spl50_1106
    | ~ spl50_377
    | ~ spl50_544 ),
    inference(avatar_split_clause,[],[f9649,f8980,f7848,f22770,f6856]) ).

fof(f6856,plain,
    ( spl50_162
  <=> class_Rings_Odvd(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_162])]) ).

fof(f22770,plain,
    ( spl50_1106
  <=> ! [X0] : c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1106])]) ).

fof(f7848,plain,
    ( spl50_377
  <=> ! [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,[spl50_377])]) ).

fof(f9649,plain,
    ( ! [X0] :
        ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)
        | ~ class_Rings_Odvd(tc_Int_Oint) )
    | ~ spl50_377
    | ~ spl50_544 ),
    inference(superposition,[],[f8981,f7849]) ).

fof(f7849,plain,
    ( ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X0) = X0
    | ~ spl50_377 ),
    inference(avatar_component_clause,[],[f7848]) ).

fof(f22452,plain,
    spl50_1105,
    inference(avatar_split_clause,[],[f5957,f22450]) ).

fof(f22450,plain,
    ( spl50_1105
  <=> ! [X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1105])]) ).

fof(f5957,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ),
    inference(forward_demodulation,[],[f5956,f4161]) ).

fof(f5956,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(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)),X1)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ),
    inference(forward_demodulation,[],[f5955,f4313]) ).

fof(f5955,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
      | ~ c_Orderings_Oord__class_Oless(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)),X1) ),
    inference(forward_demodulation,[],[f5954,f4161]) ).

fof(f5954,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(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)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
      | ~ c_Orderings_Oord__class_Oless(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)),X1) ),
    inference(forward_demodulation,[],[f5619,f4313]) ).

fof(f5619,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
      | ~ c_Orderings_Oord__class_Oless(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)
      | ~ c_Orderings_Oord__class_Oless(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)),X1) ),
    inference(definition_unfolding,[],[f4610,f4164,f4164]) ).

fof(f4610,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ),
    inference(cnf_transformation,[],[f2644]) ).

fof(f2644,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ),
    inference(flattening,[],[f2643]) ).

fof(f2643,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ),
    inference(ennf_transformation,[],[f1674]) ).

fof(f1674,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ) ),
    inference(rectify,[],[f994]) ).

fof(f994,axiom,
    ! [X17,X3] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X17)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__less__n__mult__m) ).

fof(f22448,plain,
    spl50_1104,
    inference(avatar_split_clause,[],[f5953,f22446]) ).

fof(f22446,plain,
    ( spl50_1104
  <=> ! [X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1104])]) ).

fof(f5953,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)) ),
    inference(forward_demodulation,[],[f5952,f4161]) ).

fof(f5952,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(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)),X1)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)) ),
    inference(forward_demodulation,[],[f5951,f4313]) ).

fof(f5951,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
      | ~ c_Orderings_Oord__class_Oless(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)),X1) ),
    inference(forward_demodulation,[],[f5950,f4161]) ).

fof(f5950,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(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)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
      | ~ c_Orderings_Oord__class_Oless(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)),X1) ),
    inference(forward_demodulation,[],[f5618,f4313]) ).

fof(f5618,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
      | ~ c_Orderings_Oord__class_Oless(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)
      | ~ c_Orderings_Oord__class_Oless(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)),X1) ),
    inference(definition_unfolding,[],[f4609,f4164,f4164]) ).

fof(f4609,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ),
    inference(cnf_transformation,[],[f2642]) ).

fof(f2642,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ),
    inference(flattening,[],[f2641]) ).

fof(f2641,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ),
    inference(ennf_transformation,[],[f1673]) ).

fof(f1673,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)) ) ),
    inference(rectify,[],[f995]) ).

fof(f995,axiom,
    ! [X17,X3] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X3)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__less__m__mult__n) ).

fof(f22444,plain,
    spl50_1103,
    inference(avatar_split_clause,[],[f5814,f22442]) ).

fof(f22442,plain,
    ( spl50_1103
  <=> ! [X2,X0] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ouminus__class_Ouminus(X2,X0)),c_Groups_Ouminus__class_Ouminus(X2,X0))
        | ~ class_Rings_Oidom(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1103])]) ).

fof(f5814,plain,
    ! [X2,X0] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ouminus__class_Ouminus(X2,X0)),c_Groups_Ouminus__class_Ouminus(X2,X0))
      | ~ class_Rings_Oidom(X2) ),
    inference(equality_resolution,[],[f4985]) ).

fof(f4985,plain,
    ! [X2,X0,X1] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0)
      | c_Groups_Ouminus__class_Ouminus(X2,X0) != X1
      | ~ class_Rings_Oidom(X2) ),
    inference(cnf_transformation,[],[f3706]) ).

fof(f3706,plain,
    ! [X0,X1,X2] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0)
          | ( c_Groups_Ouminus__class_Ouminus(X2,X0) != X1
            & X0 != X1 ) )
        & ( c_Groups_Ouminus__class_Ouminus(X2,X0) = X1
          | X0 = X1
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0) ) )
      | ~ class_Rings_Oidom(X2) ),
    inference(flattening,[],[f3705]) ).

fof(f3705,plain,
    ! [X0,X1,X2] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0)
          | ( c_Groups_Ouminus__class_Ouminus(X2,X0) != X1
            & X0 != X1 ) )
        & ( c_Groups_Ouminus__class_Ouminus(X2,X0) = X1
          | X0 = X1
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0) ) )
      | ~ class_Rings_Oidom(X2) ),
    inference(nnf_transformation,[],[f2862]) ).

fof(f2862,plain,
    ! [X0,X1,X2] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0)
      <=> ( c_Groups_Ouminus__class_Ouminus(X2,X0) = X1
          | X0 = X1 ) )
      | ~ class_Rings_Oidom(X2) ),
    inference(ennf_transformation,[],[f1890]) ).

fof(f1890,plain,
    ! [X0,X1,X2] :
      ( class_Rings_Oidom(X2)
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0)
      <=> ( c_Groups_Ouminus__class_Ouminus(X2,X0) = X1
          | X0 = X1 ) ) ),
    inference(rectify,[],[f307]) ).

fof(f307,axiom,
    ! [X21,X24,X5] :
      ( class_Rings_Oidom(X5)
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X24),X24) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X21),X21)
      <=> ( c_Groups_Ouminus__class_Ouminus(X5,X21) = X24
          | X21 = X24 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_square__eq__iff) ).

fof(f22440,plain,
    spl50_1102,
    inference(avatar_split_clause,[],[f5613,f22438]) ).

fof(f22438,plain,
    ( spl50_1102
  <=> ! [X0,X1] :
        ( 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)
        | ~ c_Orderings_Oord__class_Oless__eq(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,[spl50_1102])]) ).

fof(f5613,plain,
    ! [X0,X1] :
      ( 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)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(definition_unfolding,[],[f4603,f4164,f4164]) ).

fof(f4603,plain,
    ! [X0,X1] :
      ( c_Nat_OSuc(X0) = X1
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) ),
    inference(cnf_transformation,[],[f2635]) ).

fof(f2635,plain,
    ! [X0,X1] :
      ( c_Nat_OSuc(X0) = X1
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) ),
    inference(flattening,[],[f2634]) ).

fof(f2634,plain,
    ! [X0,X1] :
      ( c_Nat_OSuc(X0) = X1
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) ),
    inference(ennf_transformation,[],[f1667]) ).

fof(f1667,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
     => ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
       => c_Nat_OSuc(X0) = X1 ) ),
    inference(rectify,[],[f950]) ).

fof(f950,axiom,
    ! [X3,X17] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,c_Nat_OSuc(X3))
     => ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X3)
       => c_Nat_OSuc(X3) = X17 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__SucE) ).

fof(f22436,plain,
    spl50_1101,
    inference(avatar_split_clause,[],[f5610,f22434]) ).

fof(f22434,plain,
    ( spl50_1101
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)
        | 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,[spl50_1101])]) ).

fof(f5610,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)
      | 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,[],[f4584,f4164,f4164]) ).

fof(f4584,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),X0)
      | c_Nat_OSuc(X1) = X0
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
    inference(cnf_transformation,[],[f2610]) ).

fof(f2610,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),X0)
      | c_Nat_OSuc(X1) = X0
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
    inference(flattening,[],[f2609]) ).

fof(f2609,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),X0)
      | c_Nat_OSuc(X1) = X0
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
    inference(ennf_transformation,[],[f1652]) ).

fof(f1652,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
     => ( c_Nat_OSuc(X1) != X0
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),X0) ) ),
    inference(rectify,[],[f968]) ).

fof(f968,axiom,
    ! [X3,X17] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X3)
     => ( c_Nat_OSuc(X17) != X3
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X17),X3) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__lessI) ).

fof(f22432,plain,
    spl50_1100,
    inference(avatar_split_clause,[],[f5557,f22429]) ).

fof(f22429,plain,
    ( spl50_1100
  <=> c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),sK44) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1100])]) ).

fof(f5557,plain,
    c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),sK44),
    inference(cnf_transformation,[],[f3867]) ).

fof(f3867,plain,
    c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),sK44),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK44])],[f2292,f3866]) ).

fof(f3866,plain,
    ( ? [X0] : c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),X0)
   => c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),sK44) ),
    introduced(choice_axiom,[]) ).

fof(f2292,plain,
    ? [X0] : c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),X0),
    inference(rectify,[],[f687]) ).

fof(f687,axiom,
    ? [X34] : c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),X34),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096EX_Az_O_Apoly_A_IpCons_A1_A_Imonom_Aa_A_Ik_A_N_A1_J_J_J_Az_A_061_A0_096) ).

fof(f22427,plain,
    spl50_1099,
    inference(avatar_split_clause,[],[f5521,f22425]) ).

fof(f22425,plain,
    ( spl50_1099
  <=> ! [X4,X0,X3,X2,X1] :
        ( hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,X4),X2,X1),X0) = c_Groups_Ominus__class_Ominus(X4,hAPP(X2,X0),hAPP(X1,X0))
        | ~ class_Groups_Ominus(X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1099])]) ).

fof(f5521,plain,
    ! [X2,X3,X0,X1,X4] :
      ( hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,X4),X2,X1),X0) = c_Groups_Ominus__class_Ominus(X4,hAPP(X2,X0),hAPP(X1,X0))
      | ~ class_Groups_Ominus(X4) ),
    inference(cnf_transformation,[],[f3408]) ).

fof(f3408,plain,
    ! [X0,X1,X2,X3,X4] :
      ( hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,X4),X2,X1),X0) = c_Groups_Ominus__class_Ominus(X4,hAPP(X2,X0),hAPP(X1,X0))
      | ~ class_Groups_Ominus(X4) ),
    inference(ennf_transformation,[],[f2269]) ).

fof(f2269,plain,
    ! [X0,X1,X2,X3,X4] :
      ( class_Groups_Ominus(X4)
     => hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,X4),X2,X1),X0) = c_Groups_Ominus__class_Ominus(X4,hAPP(X2,X0),hAPP(X1,X0)) ),
    inference(rectify,[],[f799]) ).

fof(f799,axiom,
    ! [X12,X78,X79,X46,X5] :
      ( class_Groups_Ominus(X5)
     => hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X46,X5),X79,X78),X12) = c_Groups_Ominus__class_Ominus(X5,hAPP(X79,X12),hAPP(X78,X12)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__apply) ).

fof(f22423,plain,
    spl50_1098,
    inference(avatar_split_clause,[],[f5482,f22421]) ).

fof(f22421,plain,
    ( spl50_1098
  <=> ! [X4,X0,X3,X2,X1] :
        ( c_Orderings_Oord__class_Oless(X4,X3,X2)
        | ~ c_Orderings_Oord__class_Oless(X4,X1,X0)
        | c_Groups_Ominus__class_Ominus(X4,X3,X2) != c_Groups_Ominus__class_Ominus(X4,X1,X0)
        | ~ class_Groups_Oordered__ab__group__add(X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1098])]) ).

fof(f5482,plain,
    ! [X2,X3,X0,X1,X4] :
      ( c_Orderings_Oord__class_Oless(X4,X3,X2)
      | ~ c_Orderings_Oord__class_Oless(X4,X1,X0)
      | c_Groups_Ominus__class_Ominus(X4,X3,X2) != c_Groups_Ominus__class_Ominus(X4,X1,X0)
      | ~ class_Groups_Oordered__ab__group__add(X4) ),
    inference(cnf_transformation,[],[f3845]) ).

fof(f3845,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ( ( c_Orderings_Oord__class_Oless(X4,X3,X2)
          | ~ c_Orderings_Oord__class_Oless(X4,X1,X0) )
        & ( c_Orderings_Oord__class_Oless(X4,X1,X0)
          | ~ c_Orderings_Oord__class_Oless(X4,X3,X2) ) )
      | c_Groups_Ominus__class_Ominus(X4,X3,X2) != c_Groups_Ominus__class_Ominus(X4,X1,X0)
      | ~ class_Groups_Oordered__ab__group__add(X4) ),
    inference(nnf_transformation,[],[f3360]) ).

fof(f3360,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ( c_Orderings_Oord__class_Oless(X4,X3,X2)
      <=> c_Orderings_Oord__class_Oless(X4,X1,X0) )
      | c_Groups_Ominus__class_Ominus(X4,X3,X2) != c_Groups_Ominus__class_Ominus(X4,X1,X0)
      | ~ class_Groups_Oordered__ab__group__add(X4) ),
    inference(flattening,[],[f3359]) ).

fof(f3359,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ( c_Orderings_Oord__class_Oless(X4,X3,X2)
      <=> c_Orderings_Oord__class_Oless(X4,X1,X0) )
      | c_Groups_Ominus__class_Ominus(X4,X3,X2) != c_Groups_Ominus__class_Ominus(X4,X1,X0)
      | ~ class_Groups_Oordered__ab__group__add(X4) ),
    inference(ennf_transformation,[],[f2238]) ).

fof(f2238,plain,
    ! [X0,X1,X2,X3,X4] :
      ( class_Groups_Oordered__ab__group__add(X4)
     => ( c_Groups_Ominus__class_Ominus(X4,X3,X2) = c_Groups_Ominus__class_Ominus(X4,X1,X0)
       => ( c_Orderings_Oord__class_Oless(X4,X3,X2)
        <=> c_Orderings_Oord__class_Oless(X4,X1,X0) ) ) ),
    inference(rectify,[],[f293]) ).

fof(f293,axiom,
    ! [X45,X25,X21,X24,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => ( c_Groups_Ominus__class_Ominus(X5,X24,X21) = c_Groups_Ominus__class_Ominus(X5,X25,X45)
       => ( c_Orderings_Oord__class_Oless(X5,X24,X21)
        <=> c_Orderings_Oord__class_Oless(X5,X25,X45) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__eq__diff__less) ).

fof(f22419,plain,
    spl50_1097,
    inference(avatar_split_clause,[],[f5480,f22417]) ).

fof(f22417,plain,
    ( spl50_1097
  <=> ! [X4,X0,X3,X2,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
        | ~ c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
        | c_Groups_Ominus__class_Ominus(X4,X3,X2) != c_Groups_Ominus__class_Ominus(X4,X1,X0)
        | ~ class_Groups_Oordered__ab__group__add(X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1097])]) ).

fof(f5480,plain,
    ! [X2,X3,X0,X1,X4] :
      ( c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
      | ~ c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
      | c_Groups_Ominus__class_Ominus(X4,X3,X2) != c_Groups_Ominus__class_Ominus(X4,X1,X0)
      | ~ class_Groups_Oordered__ab__group__add(X4) ),
    inference(cnf_transformation,[],[f3844]) ).

fof(f3844,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
          | ~ c_Orderings_Oord__class_Oless__eq(X4,X1,X0) )
        & ( c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
          | ~ c_Orderings_Oord__class_Oless__eq(X4,X3,X2) ) )
      | c_Groups_Ominus__class_Ominus(X4,X3,X2) != c_Groups_Ominus__class_Ominus(X4,X1,X0)
      | ~ class_Groups_Oordered__ab__group__add(X4) ),
    inference(nnf_transformation,[],[f3358]) ).

fof(f3358,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ( c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
      <=> c_Orderings_Oord__class_Oless__eq(X4,X1,X0) )
      | c_Groups_Ominus__class_Ominus(X4,X3,X2) != c_Groups_Ominus__class_Ominus(X4,X1,X0)
      | ~ class_Groups_Oordered__ab__group__add(X4) ),
    inference(flattening,[],[f3357]) ).

fof(f3357,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ( c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
      <=> c_Orderings_Oord__class_Oless__eq(X4,X1,X0) )
      | c_Groups_Ominus__class_Ominus(X4,X3,X2) != c_Groups_Ominus__class_Ominus(X4,X1,X0)
      | ~ class_Groups_Oordered__ab__group__add(X4) ),
    inference(ennf_transformation,[],[f2237]) ).

fof(f2237,plain,
    ! [X0,X1,X2,X3,X4] :
      ( class_Groups_Oordered__ab__group__add(X4)
     => ( c_Groups_Ominus__class_Ominus(X4,X3,X2) = c_Groups_Ominus__class_Ominus(X4,X1,X0)
       => ( c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
        <=> c_Orderings_Oord__class_Oless__eq(X4,X1,X0) ) ) ),
    inference(rectify,[],[f287]) ).

fof(f287,axiom,
    ! [X45,X25,X21,X24,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => ( c_Groups_Ominus__class_Ominus(X5,X24,X21) = c_Groups_Ominus__class_Ominus(X5,X25,X45)
       => ( c_Orderings_Oord__class_Oless__eq(X5,X24,X21)
        <=> c_Orderings_Oord__class_Oless__eq(X5,X25,X45) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__eq__diff__less__eq) ).

fof(f22415,plain,
    spl50_1096,
    inference(avatar_split_clause,[],[f5395,f22413]) ).

fof(f22413,plain,
    ( spl50_1096
  <=> ! [X0,X3,X2,X1] :
        ( c_Polynomial_Osmult(X3,X2,c_Polynomial_Osmult(X3,X1,X0)) = c_Polynomial_Osmult(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0)
        | ~ class_Rings_Ocomm__semiring__0(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1096])]) ).

fof(f5395,plain,
    ! [X2,X3,X0,X1] :
      ( c_Polynomial_Osmult(X3,X2,c_Polynomial_Osmult(X3,X1,X0)) = c_Polynomial_Osmult(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0)
      | ~ class_Rings_Ocomm__semiring__0(X3) ),
    inference(cnf_transformation,[],[f3240]) ).

fof(f3240,plain,
    ! [X0,X1,X2,X3] :
      ( c_Polynomial_Osmult(X3,X2,c_Polynomial_Osmult(X3,X1,X0)) = c_Polynomial_Osmult(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0)
      | ~ class_Rings_Ocomm__semiring__0(X3) ),
    inference(ennf_transformation,[],[f2159]) ).

fof(f2159,plain,
    ! [X0,X1,X2,X3] :
      ( class_Rings_Ocomm__semiring__0(X3)
     => c_Polynomial_Osmult(X3,X2,c_Polynomial_Osmult(X3,X1,X0)) = c_Polynomial_Osmult(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0) ),
    inference(rectify,[],[f649]) ).

fof(f649,axiom,
    ! [X54,X13,X4,X5] :
      ( class_Rings_Ocomm__semiring__0(X5)
     => c_Polynomial_Osmult(X5,X4,c_Polynomial_Osmult(X5,X13,X54)) = c_Polynomial_Osmult(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X13),X54) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__smult) ).

fof(f22411,plain,
    ( ~ spl50_160
    | spl50_1095
    | ~ spl50_376
    | ~ spl50_544 ),
    inference(avatar_split_clause,[],[f9648,f8980,f7844,f22409,f6846]) ).

fof(f6846,plain,
    ( spl50_160
  <=> class_Rings_Odvd(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_160])]) ).

fof(f22409,plain,
    ( spl50_1095
  <=> ! [X0] : c_Rings_Odvd__class_Odvd(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1095])]) ).

fof(f7844,plain,
    ( spl50_376
  <=> ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_376])]) ).

fof(f9648,plain,
    ( ! [X0] :
        ( c_Rings_Odvd__class_Odvd(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X0)
        | ~ class_Rings_Odvd(tc_RealDef_Oreal) )
    | ~ spl50_376
    | ~ spl50_544 ),
    inference(superposition,[],[f8981,f7845]) ).

fof(f7845,plain,
    ( ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X0) = X0
    | ~ spl50_376 ),
    inference(avatar_component_clause,[],[f7844]) ).

fof(f22407,plain,
    spl50_1094,
    inference(avatar_split_clause,[],[f5394,f22405]) ).

fof(f22405,plain,
    ( spl50_1094
  <=> ! [X0,X3,X2,X1] :
        ( c_Polynomial_Osmult(X3,X2,c_Polynomial_Omonom(X3,X1,X0)) = c_Polynomial_Omonom(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0)
        | ~ class_Rings_Ocomm__semiring__0(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1094])]) ).

fof(f5394,plain,
    ! [X2,X3,X0,X1] :
      ( c_Polynomial_Osmult(X3,X2,c_Polynomial_Omonom(X3,X1,X0)) = c_Polynomial_Omonom(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0)
      | ~ class_Rings_Ocomm__semiring__0(X3) ),
    inference(cnf_transformation,[],[f3239]) ).

fof(f3239,plain,
    ! [X0,X1,X2,X3] :
      ( c_Polynomial_Osmult(X3,X2,c_Polynomial_Omonom(X3,X1,X0)) = c_Polynomial_Omonom(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0)
      | ~ class_Rings_Ocomm__semiring__0(X3) ),
    inference(ennf_transformation,[],[f2158]) ).

fof(f2158,plain,
    ! [X0,X1,X2,X3] :
      ( class_Rings_Ocomm__semiring__0(X3)
     => c_Polynomial_Osmult(X3,X2,c_Polynomial_Omonom(X3,X1,X0)) = c_Polynomial_Omonom(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0) ),
    inference(rectify,[],[f676]) ).

fof(f676,axiom,
    ! [X3,X13,X4,X5] :
      ( class_Rings_Ocomm__semiring__0(X5)
     => c_Polynomial_Osmult(X5,X4,c_Polynomial_Omonom(X5,X13,X3)) = c_Polynomial_Omonom(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X13),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__monom) ).

fof(f22403,plain,
    spl50_1093,
    inference(avatar_split_clause,[],[f5264,f22401]) ).

fof(f22401,plain,
    ( spl50_1093
  <=> ! [X0,X3,X2,X1] :
        ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X0,X2),X1)
        | c_Groups_Ozero__class_Ozero(X3) = X0
        | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),X2,X1)
        | ~ class_Fields_Ofield(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1093])]) ).

fof(f5264,plain,
    ! [X2,X3,X0,X1] :
      ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X0,X2),X1)
      | c_Groups_Ozero__class_Ozero(X3) = X0
      | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),X2,X1)
      | ~ class_Fields_Ofield(X3) ),
    inference(cnf_transformation,[],[f3096]) ).

fof(f3096,plain,
    ! [X0,X1,X2,X3] :
      ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X0,X2),X1)
      | c_Groups_Ozero__class_Ozero(X3) = X0
      | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),X2,X1)
      | ~ class_Fields_Ofield(X3) ),
    inference(flattening,[],[f3095]) ).

fof(f3095,plain,
    ! [X0,X1,X2,X3] :
      ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X0,X2),X1)
      | c_Groups_Ozero__class_Ozero(X3) = X0
      | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),X2,X1)
      | ~ class_Fields_Ofield(X3) ),
    inference(ennf_transformation,[],[f2070]) ).

fof(f2070,plain,
    ! [X0,X1,X2,X3] :
      ( class_Fields_Ofield(X3)
     => ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),X2,X1)
       => ( c_Groups_Ozero__class_Ozero(X3) != X0
         => c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X0,X2),X1) ) ) ),
    inference(rectify,[],[f817]) ).

fof(f817,axiom,
    ! [X4,X53,X54,X5] :
      ( class_Fields_Ofield(X5)
     => ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5),X54,X53)
       => ( c_Groups_Ozero__class_Ozero(X5) != X4
         => c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5),c_Polynomial_Osmult(X5,X4,X54),X53) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__dvd) ).

fof(f22399,plain,
    spl50_1092,
    inference(avatar_split_clause,[],[f5263,f22397]) ).

fof(f22397,plain,
    ( spl50_1092
  <=> ! [X0,X3,X2,X1] :
        ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),X1,c_Polynomial_Osmult(X3,X2,X0))
        | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),X1,X0)
        | c_Groups_Ozero__class_Ozero(X3) = X2
        | ~ class_Fields_Ofield(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1092])]) ).

fof(f5263,plain,
    ! [X2,X3,X0,X1] :
      ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),X1,c_Polynomial_Osmult(X3,X2,X0))
      | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),X1,X0)
      | c_Groups_Ozero__class_Ozero(X3) = X2
      | ~ class_Fields_Ofield(X3) ),
    inference(cnf_transformation,[],[f3799]) ).

fof(f3799,plain,
    ! [X0,X1,X2,X3] :
      ( ( ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),X1,c_Polynomial_Osmult(X3,X2,X0))
          | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),X1,X0) )
        & ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),X1,X0)
          | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),X1,c_Polynomial_Osmult(X3,X2,X0)) ) )
      | c_Groups_Ozero__class_Ozero(X3) = X2
      | ~ class_Fields_Ofield(X3) ),
    inference(nnf_transformation,[],[f3094]) ).

fof(f3094,plain,
    ! [X0,X1,X2,X3] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),X1,c_Polynomial_Osmult(X3,X2,X0))
      <=> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),X1,X0) )
      | c_Groups_Ozero__class_Ozero(X3) = X2
      | ~ class_Fields_Ofield(X3) ),
    inference(flattening,[],[f3093]) ).

fof(f3093,plain,
    ! [X0,X1,X2,X3] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),X1,c_Polynomial_Osmult(X3,X2,X0))
      <=> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),X1,X0) )
      | c_Groups_Ozero__class_Ozero(X3) = X2
      | ~ class_Fields_Ofield(X3) ),
    inference(ennf_transformation,[],[f2069]) ).

fof(f2069,plain,
    ! [X0,X1,X2,X3] :
      ( class_Fields_Ofield(X3)
     => ( c_Groups_Ozero__class_Ozero(X3) != X2
       => ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),X1,c_Polynomial_Osmult(X3,X2,X0))
        <=> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),X1,X0) ) ) ),
    inference(rectify,[],[f816]) ).

fof(f816,axiom,
    ! [X66,X64,X24,X5] :
      ( class_Fields_Ofield(X5)
     => ( c_Groups_Ozero__class_Ozero(X5) != X24
       => ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5),X64,c_Polynomial_Osmult(X5,X24,X66))
        <=> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5),X64,X66) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__smult__iff) ).

fof(f22395,plain,
    spl50_1091,
    inference(avatar_split_clause,[],[f5262,f22393]) ).

fof(f22393,plain,
    ( spl50_1091
  <=> ! [X0,X3,X2,X1] :
        ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),X1,X0)
        | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),X1,c_Polynomial_Osmult(X3,X2,X0))
        | c_Groups_Ozero__class_Ozero(X3) = X2
        | ~ class_Fields_Ofield(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1091])]) ).

fof(f5262,plain,
    ! [X2,X3,X0,X1] :
      ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),X1,X0)
      | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),X1,c_Polynomial_Osmult(X3,X2,X0))
      | c_Groups_Ozero__class_Ozero(X3) = X2
      | ~ class_Fields_Ofield(X3) ),
    inference(cnf_transformation,[],[f3799]) ).

fof(f22391,plain,
    spl50_1090,
    inference(avatar_split_clause,[],[f5251,f22389]) ).

fof(f22389,plain,
    ( spl50_1090
  <=> ! [X2,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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1090])]) ).

fof(f5251,plain,
    ! [X2,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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)) ),
    inference(cnf_transformation,[],[f3795]) ).

fof(f3795,plain,
    ! [X0,X1,X2] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
        | ~ 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,X2,X0)
          & 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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)) ) ),
    inference(flattening,[],[f3794]) ).

fof(f3794,plain,
    ! [X0,X1,X2] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
        | ~ 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,X2,X0)
          & 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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)) ) ),
    inference(nnf_transformation,[],[f2063]) ).

fof(f2063,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
    <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
        & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ) ),
    inference(rectify,[],[f430]) ).

fof(f430,axiom,
    ! [X16,X36,X32] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X32),X36),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16),X36))
    <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X32,X16)
        & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X36) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel2) ).

fof(f22387,plain,
    spl50_1089,
    inference(avatar_split_clause,[],[f5248,f22385]) ).

fof(f22385,plain,
    ( spl50_1089
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1089])]) ).

fof(f5248,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)) ),
    inference(cnf_transformation,[],[f3793]) ).

fof(f3793,plain,
    ! [X0,X1,X2] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) )
      & ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) )
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)) ) ),
    inference(flattening,[],[f3792]) ).

fof(f3792,plain,
    ! [X0,X1,X2] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) )
      & ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) )
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)) ) ),
    inference(nnf_transformation,[],[f2062]) ).

fof(f2062,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0))
    <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
        & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ) ),
    inference(rectify,[],[f429]) ).

fof(f429,axiom,
    ! [X16,X32,X36] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X32),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X16))
    <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X32,X16)
        & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X36) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel1) ).

fof(f22383,plain,
    spl50_1088,
    inference(avatar_split_clause,[],[f5246,f22381]) ).

fof(f22381,plain,
    ( spl50_1088
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1088])]) ).

fof(f5246,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0))
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
    inference(cnf_transformation,[],[f3791]) ).

fof(f3791,plain,
    ! [X0,X1,X2] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0))
        | ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)) ) ),
    inference(flattening,[],[f3790]) ).

fof(f3790,plain,
    ! [X0,X1,X2] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0))
        | ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)) ) ),
    inference(nnf_transformation,[],[f3092]) ).

fof(f3092,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0))
    <=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ) ),
    inference(ennf_transformation,[],[f2061]) ).

fof(f2061,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0))
    <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
       => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
    inference(rectify,[],[f436]) ).

fof(f436,axiom,
    ! [X16,X32,X36] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X32),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X16))
    <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X36)
       => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X32,X16) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__cancel1) ).

fof(f22379,plain,
    spl50_1087,
    inference(avatar_split_clause,[],[f5243,f22377]) ).

fof(f22377,plain,
    ( spl50_1087
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1087])]) ).

fof(f5243,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(cnf_transformation,[],[f3789]) ).

fof(f3789,plain,
    ! [X0,X1,X2] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
        | ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)) ) ),
    inference(flattening,[],[f3788]) ).

fof(f3788,plain,
    ! [X0,X1,X2] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
        | ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)) ) ),
    inference(nnf_transformation,[],[f3091]) ).

fof(f3091,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
    <=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ) ),
    inference(ennf_transformation,[],[f2060]) ).

fof(f2060,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
    <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
       => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0) ) ),
    inference(rectify,[],[f269]) ).

fof(f269,axiom,
    ! [X16,X36,X32] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X32),X36),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16),X36))
    <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X36)
       => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X32,X16) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__cancel2) ).

fof(f22375,plain,
    spl50_1086,
    inference(avatar_split_clause,[],[f5167,f22373]) ).

fof(f22373,plain,
    ( spl50_1086
  <=> ! [X2,X0,X1] :
        ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X0)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1086])]) ).

fof(f5167,plain,
    ! [X2,X0,X1] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) ),
    inference(cnf_transformation,[],[f3060]) ).

fof(f3060,plain,
    ! [X0,X1,X2] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) ),
    inference(flattening,[],[f3059]) ).

fof(f3059,plain,
    ! [X0,X1,X2] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) ),
    inference(ennf_transformation,[],[f2029]) ).

fof(f2029,plain,
    ! [X0,X1,X2] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
       => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
         => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X0) ) ) ),
    inference(rectify,[],[f868]) ).

fof(f868,axiom,
    ! [X3,X17,X38] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X38,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X3))
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X38,X17)
       => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X17)
         => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X38,X3) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__diffD1) ).

fof(f22371,plain,
    spl50_1085,
    inference(avatar_split_clause,[],[f5166,f22369]) ).

fof(f22369,plain,
    ( spl50_1085
  <=> ! [X2,X0,X1] :
        ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X0)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1085])]) ).

fof(f5166,plain,
    ! [X2,X0,X1] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X0)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) ),
    inference(cnf_transformation,[],[f3058]) ).

fof(f3058,plain,
    ! [X0,X1,X2] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X0)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) ),
    inference(flattening,[],[f3057]) ).

fof(f3057,plain,
    ! [X0,X1,X2] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X0)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) ),
    inference(ennf_transformation,[],[f2028]) ).

fof(f2028,plain,
    ! [X0,X1,X2] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X0)
       => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
         => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ) ) ),
    inference(rectify,[],[f869]) ).

fof(f869,axiom,
    ! [X3,X17,X38] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X38,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X3))
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X38,X3)
       => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X17)
         => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X38,X17) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__diffD) ).

fof(f22367,plain,
    ( spl50_1084
    | ~ spl50_218
    | ~ spl50_525 ),
    inference(avatar_split_clause,[],[f9482,f8902,f7136,f22365]) ).

fof(f22365,plain,
    ( spl50_1084
  <=> ! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1084])]) ).

fof(f7136,plain,
    ( spl50_218
  <=> ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_218])]) ).

fof(f8902,plain,
    ( spl50_525
  <=> ! [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,[spl50_525])]) ).

fof(f9482,plain,
    ( ! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1))
    | ~ spl50_218
    | ~ spl50_525 ),
    inference(resolution,[],[f8903,f7137]) ).

fof(f7137,plain,
    ( ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X0)
    | ~ spl50_218 ),
    inference(avatar_component_clause,[],[f7136]) ).

fof(f8903,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) )
    | ~ spl50_525 ),
    inference(avatar_component_clause,[],[f8902]) ).

fof(f22363,plain,
    spl50_1083,
    inference(avatar_split_clause,[],[f5118,f22361]) ).

fof(f22361,plain,
    ( spl50_1083
  <=> ! [X2,X0,X1] :
        ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X0)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1083])]) ).

fof(f5118,plain,
    ! [X2,X0,X1] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    inference(cnf_transformation,[],[f3005]) ).

fof(f3005,plain,
    ! [X0,X1,X2] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    inference(ennf_transformation,[],[f1993]) ).

fof(f1993,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
     => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X0) ),
    inference(rectify,[],[f491]) ).

fof(f491,axiom,
    ! [X18,X39,X38] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X38,X39)
     => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X39,X38),X18) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X39,X18),X38) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__diff__assoc2) ).

fof(f22359,plain,
    spl50_1082,
    inference(avatar_split_clause,[],[f5116,f22357]) ).

fof(f22357,plain,
    ( spl50_1082
  <=> ! [X2,X0,X1] :
        ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1082])]) ).

fof(f5116,plain,
    ! [X2,X0,X1] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    inference(cnf_transformation,[],[f3003]) ).

fof(f3003,plain,
    ! [X0,X1,X2] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    inference(ennf_transformation,[],[f1991]) ).

fof(f1991,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
     => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2) ),
    inference(rectify,[],[f486]) ).

fof(f486,axiom,
    ! [X18,X39,X38] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X38,X39)
     => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X39,X38)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X39),X38) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__diff__assoc) ).

fof(f22355,plain,
    spl50_1081,
    inference(avatar_split_clause,[],[f5115,f22353]) ).

fof(f22353,plain,
    ( spl50_1081
  <=> ! [X2,X0,X1] :
        ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),X1)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1081])]) ).

fof(f5115,plain,
    ! [X2,X0,X1] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),X1)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    inference(cnf_transformation,[],[f3002]) ).

fof(f3002,plain,
    ! [X0,X1,X2] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),X1)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    inference(ennf_transformation,[],[f1990]) ).

fof(f1990,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
     => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),X1) ),
    inference(rectify,[],[f482]) ).

fof(f482,axiom,
    ! [X18,X39,X38] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X38,X39)
     => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X39,X38)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X38),X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__diff__right) ).

fof(f22351,plain,
    spl50_1080,
    inference(avatar_split_clause,[],[f5029,f22349]) ).

fof(f22349,plain,
    ( spl50_1080
  <=> ! [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
        | c_Groups_Ozero__class_Ozero(X2) = X1
        | ~ class_Rings_Ono__zero__divisors(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1080])]) ).

fof(f5029,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
      | c_Groups_Ozero__class_Ozero(X2) = X1
      | ~ class_Rings_Ono__zero__divisors(X2) ),
    inference(cnf_transformation,[],[f2907]) ).

fof(f2907,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_Ono__zero__divisors(X2) ),
    inference(flattening,[],[f2906]) ).

fof(f2906,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_Ono__zero__divisors(X2) ),
    inference(ennf_transformation,[],[f1924]) ).

fof(f1924,plain,
    ! [X0,X1,X2] :
      ( class_Rings_Ono__zero__divisors(X2)
     => ( c_Groups_Ozero__class_Ozero(X2) != X1
       => ( c_Groups_Ozero__class_Ozero(X2) != X0
         => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) != c_Groups_Ozero__class_Ozero(X2) ) ) ),
    inference(rectify,[],[f91]) ).

fof(f91,axiom,
    ! [X13,X4,X5] :
      ( class_Rings_Ono__zero__divisors(X5)
     => ( c_Groups_Ozero__class_Ozero(X5) != X4
       => ( c_Groups_Ozero__class_Ozero(X5) != X13
         => c_Groups_Ozero__class_Ozero(X5) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X13) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_no__zero__divisors) ).

fof(f22347,plain,
    spl50_1079,
    inference(avatar_split_clause,[],[f4996,f22345]) ).

fof(f22345,plain,
    ( spl50_1079
  <=> ! [X2,X0,X1] :
        ( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),c_Polynomial_OpCons(X2,X1,X0)) = c_Polynomial_OpCons(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),X0))
        | ~ class_Groups_Oab__group__add(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1079])]) ).

fof(f4996,plain,
    ! [X2,X0,X1] :
      ( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),c_Polynomial_OpCons(X2,X1,X0)) = c_Polynomial_OpCons(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),X0))
      | ~ class_Groups_Oab__group__add(X2) ),
    inference(cnf_transformation,[],[f2870]) ).

fof(f2870,plain,
    ! [X0,X1,X2] :
      ( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),c_Polynomial_OpCons(X2,X1,X0)) = c_Polynomial_OpCons(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),X0))
      | ~ class_Groups_Oab__group__add(X2) ),
    inference(ennf_transformation,[],[f1898]) ).

fof(f1898,plain,
    ! [X0,X1,X2] :
      ( class_Groups_Oab__group__add(X2)
     => c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),c_Polynomial_OpCons(X2,X1,X0)) = c_Polynomial_OpCons(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),X0)) ),
    inference(rectify,[],[f623]) ).

fof(f623,axiom,
    ! [X54,X4,X46] :
      ( class_Groups_Oab__group__add(X46)
     => c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X46),c_Polynomial_OpCons(X46,X4,X54)) = c_Polynomial_OpCons(X46,c_Groups_Ouminus__class_Ouminus(X46,X4),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X46),X54)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__poly__code_I2_J) ).

fof(f22343,plain,
    spl50_1078,
    inference(avatar_split_clause,[],[f4980,f22341]) ).

fof(f22341,plain,
    ( spl50_1078
  <=> ! [X2,X0,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) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1078])]) ).

fof(f4980,plain,
    ! [X2,X0,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(cnf_transformation,[],[f3704]) ).

fof(f3704,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,[],[f3703]) ).

fof(f3703,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,[],[f2861]) ).

fof(f2861,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,[],[f1889]) ).

fof(f1889,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,[],[f660]) ).

fof(f660,axiom,
    ! [X64,X24,X5] :
      ( class_Rings_Oidom(X5)
     => ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = c_Polynomial_Osmult(X5,X24,X64)
      <=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = X64
          | c_Groups_Ozero__class_Ozero(X5) = X24 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__eq__0__iff) ).

fof(f22339,plain,
    spl50_1077,
    inference(avatar_split_clause,[],[f4919,f22337]) ).

fof(f22337,plain,
    ( spl50_1077
  <=> ! [X2,X0,X1] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),c_Groups_Ouminus__class_Ouminus(X2,X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),X0)
        | ~ class_Rings_Oring(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1077])]) ).

fof(f4919,plain,
    ! [X2,X0,X1] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),c_Groups_Ouminus__class_Ouminus(X2,X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),X0)
      | ~ class_Rings_Oring(X2) ),
    inference(cnf_transformation,[],[f2788]) ).

fof(f2788,plain,
    ! [X0,X1,X2] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),c_Groups_Ouminus__class_Ouminus(X2,X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),X0)
      | ~ class_Rings_Oring(X2) ),
    inference(ennf_transformation,[],[f1845]) ).

fof(f1845,plain,
    ! [X0,X1,X2] :
      ( class_Rings_Oring(X2)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),c_Groups_Ouminus__class_Ouminus(X2,X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),X0) ),
    inference(rectify,[],[f309]) ).

fof(f309,axiom,
    ! [X13,X4,X5] :
      ( class_Rings_Oring(X5)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ouminus__class_Ouminus(X5,X4)),X13) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),c_Groups_Ouminus__class_Ouminus(X5,X13)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__mult__commute) ).

fof(f22335,plain,
    spl50_1076,
    inference(avatar_split_clause,[],[f4918,f22333]) ).

fof(f22333,plain,
    ( spl50_1076
  <=> ! [X2,X0,X1] :
        ( c_Groups_Ouminus__class_Ouminus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),X0)
        | ~ class_Rings_Oring(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1076])]) ).

fof(f4918,plain,
    ! [X2,X0,X1] :
      ( c_Groups_Ouminus__class_Ouminus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),X0)
      | ~ class_Rings_Oring(X2) ),
    inference(cnf_transformation,[],[f2787]) ).

fof(f2787,plain,
    ! [X0,X1,X2] :
      ( c_Groups_Ouminus__class_Ouminus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),X0)
      | ~ class_Rings_Oring(X2) ),
    inference(ennf_transformation,[],[f1844]) ).

fof(f1844,plain,
    ! [X0,X1,X2] :
      ( class_Rings_Oring(X2)
     => c_Groups_Ouminus__class_Ouminus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),X0) ),
    inference(rectify,[],[f314]) ).

fof(f314,axiom,
    ! [X13,X4,X5] :
      ( class_Rings_Oring(X5)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ouminus__class_Ouminus(X5,X4)),X13) = c_Groups_Ouminus__class_Ouminus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X13)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__mult__left) ).

fof(f22331,plain,
    spl50_1075,
    inference(avatar_split_clause,[],[f4917,f22329]) ).

fof(f22329,plain,
    ( spl50_1075
  <=> ! [X2,X0,X1] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),c_Groups_Ouminus__class_Ouminus(X2,X0)) = c_Groups_Ouminus__class_Ouminus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))
        | ~ class_Rings_Oring(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1075])]) ).

fof(f4917,plain,
    ! [X2,X0,X1] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),c_Groups_Ouminus__class_Ouminus(X2,X0)) = c_Groups_Ouminus__class_Ouminus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))
      | ~ class_Rings_Oring(X2) ),
    inference(cnf_transformation,[],[f2786]) ).

fof(f2786,plain,
    ! [X0,X1,X2] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),c_Groups_Ouminus__class_Ouminus(X2,X0)) = c_Groups_Ouminus__class_Ouminus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))
      | ~ class_Rings_Oring(X2) ),
    inference(ennf_transformation,[],[f1843]) ).

fof(f1843,plain,
    ! [X0,X1,X2] :
      ( class_Rings_Oring(X2)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),c_Groups_Ouminus__class_Ouminus(X2,X0)) = c_Groups_Ouminus__class_Ouminus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) ),
    inference(rectify,[],[f315]) ).

fof(f315,axiom,
    ! [X13,X4,X5] :
      ( class_Rings_Oring(X5)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),c_Groups_Ouminus__class_Ouminus(X5,X13)) = c_Groups_Ouminus__class_Ouminus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X13)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__mult__right) ).

fof(f22327,plain,
    spl50_1074,
    inference(avatar_split_clause,[],[f4916,f22325]) ).

fof(f22325,plain,
    ( spl50_1074
  <=> ! [X2,X0,X1] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),c_Groups_Ouminus__class_Ouminus(X2,X0))
        | ~ class_Rings_Oring(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1074])]) ).

fof(f4916,plain,
    ! [X2,X0,X1] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),c_Groups_Ouminus__class_Ouminus(X2,X0))
      | ~ class_Rings_Oring(X2) ),
    inference(cnf_transformation,[],[f2785]) ).

fof(f2785,plain,
    ! [X0,X1,X2] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),c_Groups_Ouminus__class_Ouminus(X2,X0))
      | ~ class_Rings_Oring(X2) ),
    inference(ennf_transformation,[],[f1842]) ).

fof(f1842,plain,
    ! [X0,X1,X2] :
      ( class_Rings_Oring(X2)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),c_Groups_Ouminus__class_Ouminus(X2,X0)) ),
    inference(rectify,[],[f308]) ).

fof(f308,axiom,
    ! [X13,X4,X5] :
      ( class_Rings_Oring(X5)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X13) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ouminus__class_Ouminus(X5,X4)),c_Groups_Ouminus__class_Ouminus(X5,X13)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__mult__minus) ).

fof(f22280,plain,
    spl50_1073,
    inference(avatar_split_clause,[],[f4905,f22278]) ).

fof(f22278,plain,
    ( spl50_1073
  <=> ! [X2,X0,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) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1073])]) ).

fof(f4905,plain,
    ! [X2,X0,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(cnf_transformation,[],[f3686]) ).

fof(f3686,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,[],[f3685]) ).

fof(f3685,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,[],[f2771]) ).

fof(f2771,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,[],[f1834]) ).

fof(f1834,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,[],[f92]) ).

fof(f92,axiom,
    ! [X21,X24,X5] :
      ( class_Rings_Oring__no__zero__divisors(X5)
     => ( c_Groups_Ozero__class_Ozero(X5) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X24),X21)
      <=> ( c_Groups_Ozero__class_Ozero(X5) = X21
          | c_Groups_Ozero__class_Ozero(X5) = X24 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__eq__0__iff) ).

fof(f22276,plain,
    spl50_1072,
    inference(avatar_split_clause,[],[f4837,f22274]) ).

fof(f22274,plain,
    ( spl50_1072
  <=> ! [X2,X0,X1] :
        ( c_Groups_Ouminus__class_Ouminus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),X0)
        | ~ class_RealVector_Oreal__normed__algebra(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1072])]) ).

fof(f4837,plain,
    ! [X2,X0,X1] :
      ( c_Groups_Ouminus__class_Ouminus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),X0)
      | ~ class_RealVector_Oreal__normed__algebra(X2) ),
    inference(cnf_transformation,[],[f2731]) ).

fof(f2731,plain,
    ! [X0,X1,X2] :
      ( c_Groups_Ouminus__class_Ouminus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),X0)
      | ~ class_RealVector_Oreal__normed__algebra(X2) ),
    inference(ennf_transformation,[],[f1803]) ).

fof(f1803,plain,
    ! [X0,X1,X2] :
      ( class_RealVector_Oreal__normed__algebra(X2)
     => c_Groups_Ouminus__class_Ouminus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),X0) ),
    inference(rectify,[],[f310]) ).

fof(f310,axiom,
    ! [X7,X9,X5] :
      ( class_RealVector_Oreal__normed__algebra(X5)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ouminus__class_Ouminus(X5,X9)),X7) = c_Groups_Ouminus__class_Ouminus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X9),X7)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left_Ominus) ).

fof(f22272,plain,
    spl50_1071,
    inference(avatar_split_clause,[],[f4835,f22270]) ).

fof(f22270,plain,
    ( spl50_1071
  <=> ! [X2,X0,X1] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),c_Groups_Ouminus__class_Ouminus(X2,X0)) = c_Groups_Ouminus__class_Ouminus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))
        | ~ class_RealVector_Oreal__normed__algebra(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1071])]) ).

fof(f4835,plain,
    ! [X2,X0,X1] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),c_Groups_Ouminus__class_Ouminus(X2,X0)) = c_Groups_Ouminus__class_Ouminus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))
      | ~ class_RealVector_Oreal__normed__algebra(X2) ),
    inference(cnf_transformation,[],[f2729]) ).

fof(f2729,plain,
    ! [X0,X1,X2] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),c_Groups_Ouminus__class_Ouminus(X2,X0)) = c_Groups_Ouminus__class_Ouminus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))
      | ~ class_RealVector_Oreal__normed__algebra(X2) ),
    inference(ennf_transformation,[],[f1801]) ).

fof(f1801,plain,
    ! [X0,X1,X2] :
      ( class_RealVector_Oreal__normed__algebra(X2)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),c_Groups_Ouminus__class_Ouminus(X2,X0)) = c_Groups_Ouminus__class_Ouminus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) ),
    inference(rectify,[],[f313]) ).

fof(f313,axiom,
    ! [X13,X4,X5] :
      ( class_RealVector_Oreal__normed__algebra(X5)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),c_Groups_Ouminus__class_Ouminus(X5,X13)) = c_Groups_Ouminus__class_Ouminus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X13)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Ominus__right) ).

fof(f22268,plain,
    spl50_1070,
    inference(avatar_split_clause,[],[f4819,f22266]) ).

fof(f22266,plain,
    ( spl50_1070
  <=> ! [X2,X0,X1] :
        ( c_Rings_Oinverse__class_Oinverse(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_Rings_Oinverse__class_Oinverse(X2,X1)),X0)
        | ~ class_Rings_Odivision__ring__inverse__zero(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1070])]) ).

fof(f4819,plain,
    ! [X2,X0,X1] :
      ( c_Rings_Oinverse__class_Oinverse(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_Rings_Oinverse__class_Oinverse(X2,X1)),X0)
      | ~ class_Rings_Odivision__ring__inverse__zero(X2) ),
    inference(cnf_transformation,[],[f2706]) ).

fof(f2706,plain,
    ! [X0,X1,X2] :
      ( c_Rings_Oinverse__class_Oinverse(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_Rings_Oinverse__class_Oinverse(X2,X1)),X0)
      | ~ class_Rings_Odivision__ring__inverse__zero(X2) ),
    inference(ennf_transformation,[],[f1786]) ).

fof(f1786,plain,
    ! [X0,X1,X2] :
      ( class_Rings_Odivision__ring__inverse__zero(X2)
     => c_Rings_Oinverse__class_Oinverse(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_Rings_Oinverse__class_Oinverse(X2,X1)),X0) ),
    inference(rectify,[],[f123]) ).

fof(f123,axiom,
    ! [X3,X4,X5] :
      ( class_Rings_Odivision__ring__inverse__zero(X5)
     => c_Rings_Oinverse__class_Oinverse(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),c_Rings_Oinverse__class_Oinverse(X5,X4)),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__inverse) ).

fof(f22264,plain,
    spl50_1069,
    inference(avatar_split_clause,[],[f4814,f22262]) ).

fof(f4814,plain,
    ! [X2,X0,X1] :
      ( c_RealVector_Onorm__class_Onorm(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2,X1)),X0)
      | ~ class_RealVector_Oreal__normed__div__algebra(X2) ),
    inference(cnf_transformation,[],[f2699]) ).

fof(f2699,plain,
    ! [X0,X1,X2] :
      ( c_RealVector_Onorm__class_Onorm(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2,X1)),X0)
      | ~ class_RealVector_Oreal__normed__div__algebra(X2) ),
    inference(ennf_transformation,[],[f1781]) ).

fof(f1781,plain,
    ! [X0,X1,X2] :
      ( class_RealVector_Oreal__normed__div__algebra(X2)
     => c_RealVector_Onorm__class_Onorm(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2,X1)),X0) ),
    inference(rectify,[],[f172]) ).

fof(f172,axiom,
    ! [X3,X9,X5] :
      ( class_RealVector_Oreal__normed__div__algebra(X5)
     => c_RealVector_Onorm__class_Onorm(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X9),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5,X9)),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__power) ).

fof(f22260,plain,
    spl50_1068,
    inference(avatar_split_clause,[],[f4806,f22258]) ).

fof(f22258,plain,
    ( spl50_1068
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless(X2,X0,X1)
        | ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
        | ~ c_Orderings_Oord__class_Oless(X2,c_Rings_Oinverse__class_Oinverse(X2,X1),c_Rings_Oinverse__class_Oinverse(X2,X0))
        | ~ class_Fields_Olinordered__field(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1068])]) ).

fof(f4806,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless(X2,X0,X1)
      | ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
      | ~ c_Orderings_Oord__class_Oless(X2,c_Rings_Oinverse__class_Oinverse(X2,X1),c_Rings_Oinverse__class_Oinverse(X2,X0))
      | ~ class_Fields_Olinordered__field(X2) ),
    inference(cnf_transformation,[],[f2692]) ).

fof(f2692,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(X2,X0,X1)
      | ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
      | ~ c_Orderings_Oord__class_Oless(X2,c_Rings_Oinverse__class_Oinverse(X2,X1),c_Rings_Oinverse__class_Oinverse(X2,X0))
      | ~ class_Fields_Olinordered__field(X2) ),
    inference(flattening,[],[f2691]) ).

fof(f2691,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(X2,X0,X1)
      | ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
      | ~ c_Orderings_Oord__class_Oless(X2,c_Rings_Oinverse__class_Oinverse(X2,X1),c_Rings_Oinverse__class_Oinverse(X2,X0))
      | ~ class_Fields_Olinordered__field(X2) ),
    inference(ennf_transformation,[],[f1775]) ).

fof(f1775,plain,
    ! [X0,X1,X2] :
      ( class_Fields_Olinordered__field(X2)
     => ( c_Orderings_Oord__class_Oless(X2,c_Rings_Oinverse__class_Oinverse(X2,X1),c_Rings_Oinverse__class_Oinverse(X2,X0))
       => ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
         => c_Orderings_Oord__class_Oless(X2,X0,X1) ) ) ),
    inference(rectify,[],[f154]) ).

fof(f154,axiom,
    ! [X13,X4,X5] :
      ( class_Fields_Olinordered__field(X5)
     => ( c_Orderings_Oord__class_Oless(X5,c_Rings_Oinverse__class_Oinverse(X5,X4),c_Rings_Oinverse__class_Oinverse(X5,X13))
       => ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X4)
         => c_Orderings_Oord__class_Oless(X5,X13,X4) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__less__imp__less) ).

fof(f22256,plain,
    spl50_1067,
    inference(avatar_split_clause,[],[f4805,f22254]) ).

fof(f22254,plain,
    ( spl50_1067
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless(X2,X0,X1)
        | ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
        | ~ c_Orderings_Oord__class_Oless(X2,c_Rings_Oinverse__class_Oinverse(X2,X1),c_Rings_Oinverse__class_Oinverse(X2,X0))
        | ~ class_Fields_Olinordered__field(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1067])]) ).

fof(f4805,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless(X2,X0,X1)
      | ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
      | ~ c_Orderings_Oord__class_Oless(X2,c_Rings_Oinverse__class_Oinverse(X2,X1),c_Rings_Oinverse__class_Oinverse(X2,X0))
      | ~ class_Fields_Olinordered__field(X2) ),
    inference(cnf_transformation,[],[f2690]) ).

fof(f2690,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(X2,X0,X1)
      | ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
      | ~ c_Orderings_Oord__class_Oless(X2,c_Rings_Oinverse__class_Oinverse(X2,X1),c_Rings_Oinverse__class_Oinverse(X2,X0))
      | ~ class_Fields_Olinordered__field(X2) ),
    inference(flattening,[],[f2689]) ).

fof(f2689,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(X2,X0,X1)
      | ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
      | ~ c_Orderings_Oord__class_Oless(X2,c_Rings_Oinverse__class_Oinverse(X2,X1),c_Rings_Oinverse__class_Oinverse(X2,X0))
      | ~ class_Fields_Olinordered__field(X2) ),
    inference(ennf_transformation,[],[f1774]) ).

fof(f1774,plain,
    ! [X0,X1,X2] :
      ( class_Fields_Olinordered__field(X2)
     => ( c_Orderings_Oord__class_Oless(X2,c_Rings_Oinverse__class_Oinverse(X2,X1),c_Rings_Oinverse__class_Oinverse(X2,X0))
       => ( c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
         => c_Orderings_Oord__class_Oless(X2,X0,X1) ) ) ),
    inference(rectify,[],[f153]) ).

fof(f153,axiom,
    ! [X13,X4,X5] :
      ( class_Fields_Olinordered__field(X5)
     => ( c_Orderings_Oord__class_Oless(X5,c_Rings_Oinverse__class_Oinverse(X5,X4),c_Rings_Oinverse__class_Oinverse(X5,X13))
       => ( c_Orderings_Oord__class_Oless(X5,X13,c_Groups_Ozero__class_Ozero(X5))
         => c_Orderings_Oord__class_Oless(X5,X13,X4) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__less__imp__less__neg) ).

fof(f22252,plain,
    spl50_1066,
    inference(avatar_split_clause,[],[f4804,f22250]) ).

fof(f22250,plain,
    ( spl50_1066
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
        | ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
        | ~ c_Orderings_Oord__class_Oless__eq(X2,c_Rings_Oinverse__class_Oinverse(X2,X1),c_Rings_Oinverse__class_Oinverse(X2,X0))
        | ~ class_Fields_Olinordered__field(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1066])]) ).

fof(f4804,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
      | ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
      | ~ c_Orderings_Oord__class_Oless__eq(X2,c_Rings_Oinverse__class_Oinverse(X2,X1),c_Rings_Oinverse__class_Oinverse(X2,X0))
      | ~ class_Fields_Olinordered__field(X2) ),
    inference(cnf_transformation,[],[f2688]) ).

fof(f2688,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
      | ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
      | ~ c_Orderings_Oord__class_Oless__eq(X2,c_Rings_Oinverse__class_Oinverse(X2,X1),c_Rings_Oinverse__class_Oinverse(X2,X0))
      | ~ class_Fields_Olinordered__field(X2) ),
    inference(flattening,[],[f2687]) ).

fof(f2687,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
      | ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
      | ~ c_Orderings_Oord__class_Oless__eq(X2,c_Rings_Oinverse__class_Oinverse(X2,X1),c_Rings_Oinverse__class_Oinverse(X2,X0))
      | ~ class_Fields_Olinordered__field(X2) ),
    inference(ennf_transformation,[],[f1773]) ).

fof(f1773,plain,
    ! [X0,X1,X2] :
      ( class_Fields_Olinordered__field(X2)
     => ( c_Orderings_Oord__class_Oless__eq(X2,c_Rings_Oinverse__class_Oinverse(X2,X1),c_Rings_Oinverse__class_Oinverse(X2,X0))
       => ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
         => c_Orderings_Oord__class_Oless__eq(X2,X0,X1) ) ) ),
    inference(rectify,[],[f73]) ).

fof(f73,axiom,
    ! [X13,X4,X5] :
      ( class_Fields_Olinordered__field(X5)
     => ( c_Orderings_Oord__class_Oless__eq(X5,c_Rings_Oinverse__class_Oinverse(X5,X4),c_Rings_Oinverse__class_Oinverse(X5,X13))
       => ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X4)
         => c_Orderings_Oord__class_Oless__eq(X5,X13,X4) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__le__imp__le) ).

fof(f22248,plain,
    spl50_1065,
    inference(avatar_split_clause,[],[f4803,f22246]) ).

fof(f22246,plain,
    ( spl50_1065
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
        | ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
        | ~ c_Orderings_Oord__class_Oless__eq(X2,c_Rings_Oinverse__class_Oinverse(X2,X1),c_Rings_Oinverse__class_Oinverse(X2,X0))
        | ~ class_Fields_Olinordered__field(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1065])]) ).

fof(f4803,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
      | ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
      | ~ c_Orderings_Oord__class_Oless__eq(X2,c_Rings_Oinverse__class_Oinverse(X2,X1),c_Rings_Oinverse__class_Oinverse(X2,X0))
      | ~ class_Fields_Olinordered__field(X2) ),
    inference(cnf_transformation,[],[f2686]) ).

fof(f2686,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
      | ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
      | ~ c_Orderings_Oord__class_Oless__eq(X2,c_Rings_Oinverse__class_Oinverse(X2,X1),c_Rings_Oinverse__class_Oinverse(X2,X0))
      | ~ class_Fields_Olinordered__field(X2) ),
    inference(flattening,[],[f2685]) ).

fof(f2685,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
      | ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
      | ~ c_Orderings_Oord__class_Oless__eq(X2,c_Rings_Oinverse__class_Oinverse(X2,X1),c_Rings_Oinverse__class_Oinverse(X2,X0))
      | ~ class_Fields_Olinordered__field(X2) ),
    inference(ennf_transformation,[],[f1772]) ).

fof(f1772,plain,
    ! [X0,X1,X2] :
      ( class_Fields_Olinordered__field(X2)
     => ( c_Orderings_Oord__class_Oless__eq(X2,c_Rings_Oinverse__class_Oinverse(X2,X1),c_Rings_Oinverse__class_Oinverse(X2,X0))
       => ( c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
         => c_Orderings_Oord__class_Oless__eq(X2,X0,X1) ) ) ),
    inference(rectify,[],[f72]) ).

fof(f72,axiom,
    ! [X13,X4,X5] :
      ( class_Fields_Olinordered__field(X5)
     => ( c_Orderings_Oord__class_Oless__eq(X5,c_Rings_Oinverse__class_Oinverse(X5,X4),c_Rings_Oinverse__class_Oinverse(X5,X13))
       => ( c_Orderings_Oord__class_Oless(X5,X13,c_Groups_Ozero__class_Ozero(X5))
         => c_Orderings_Oord__class_Oless__eq(X5,X13,X4) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__le__imp__le__neg) ).

fof(f22244,plain,
    spl50_1064,
    inference(avatar_split_clause,[],[f4802,f22242]) ).

fof(f22242,plain,
    ( spl50_1064
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless(X2,c_Rings_Oinverse__class_Oinverse(X2,X0),c_Rings_Oinverse__class_Oinverse(X2,X1))
        | ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
        | ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
        | ~ class_Fields_Olinordered__field(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1064])]) ).

fof(f4802,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless(X2,c_Rings_Oinverse__class_Oinverse(X2,X0),c_Rings_Oinverse__class_Oinverse(X2,X1))
      | ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
      | ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
      | ~ class_Fields_Olinordered__field(X2) ),
    inference(cnf_transformation,[],[f2684]) ).

fof(f2684,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(X2,c_Rings_Oinverse__class_Oinverse(X2,X0),c_Rings_Oinverse__class_Oinverse(X2,X1))
      | ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
      | ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
      | ~ class_Fields_Olinordered__field(X2) ),
    inference(flattening,[],[f2683]) ).

fof(f2683,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(X2,c_Rings_Oinverse__class_Oinverse(X2,X0),c_Rings_Oinverse__class_Oinverse(X2,X1))
      | ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
      | ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
      | ~ class_Fields_Olinordered__field(X2) ),
    inference(ennf_transformation,[],[f1771]) ).

fof(f1771,plain,
    ! [X0,X1,X2] :
      ( class_Fields_Olinordered__field(X2)
     => ( c_Orderings_Oord__class_Oless(X2,X1,X0)
       => ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
         => c_Orderings_Oord__class_Oless(X2,c_Rings_Oinverse__class_Oinverse(X2,X0),c_Rings_Oinverse__class_Oinverse(X2,X1)) ) ) ),
    inference(rectify,[],[f157]) ).

fof(f157,axiom,
    ! [X13,X4,X5] :
      ( class_Fields_Olinordered__field(X5)
     => ( c_Orderings_Oord__class_Oless(X5,X4,X13)
       => ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X4)
         => c_Orderings_Oord__class_Oless(X5,c_Rings_Oinverse__class_Oinverse(X5,X13),c_Rings_Oinverse__class_Oinverse(X5,X4)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__inverse__less) ).

fof(f22235,plain,
    spl50_1063,
    inference(avatar_split_clause,[],[f4801,f22233]) ).

fof(f22233,plain,
    ( spl50_1063
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless(X2,c_Rings_Oinverse__class_Oinverse(X2,X0),c_Rings_Oinverse__class_Oinverse(X2,X1))
        | ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
        | ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
        | ~ class_Fields_Olinordered__field(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1063])]) ).

fof(f4801,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless(X2,c_Rings_Oinverse__class_Oinverse(X2,X0),c_Rings_Oinverse__class_Oinverse(X2,X1))
      | ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
      | ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
      | ~ class_Fields_Olinordered__field(X2) ),
    inference(cnf_transformation,[],[f2682]) ).

fof(f2682,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(X2,c_Rings_Oinverse__class_Oinverse(X2,X0),c_Rings_Oinverse__class_Oinverse(X2,X1))
      | ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
      | ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
      | ~ class_Fields_Olinordered__field(X2) ),
    inference(flattening,[],[f2681]) ).

fof(f2681,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(X2,c_Rings_Oinverse__class_Oinverse(X2,X0),c_Rings_Oinverse__class_Oinverse(X2,X1))
      | ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
      | ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
      | ~ class_Fields_Olinordered__field(X2) ),
    inference(ennf_transformation,[],[f1770]) ).

fof(f1770,plain,
    ! [X0,X1,X2] :
      ( class_Fields_Olinordered__field(X2)
     => ( c_Orderings_Oord__class_Oless(X2,X1,X0)
       => ( c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
         => c_Orderings_Oord__class_Oless(X2,c_Rings_Oinverse__class_Oinverse(X2,X0),c_Rings_Oinverse__class_Oinverse(X2,X1)) ) ) ),
    inference(rectify,[],[f156]) ).

fof(f156,axiom,
    ! [X13,X4,X5] :
      ( class_Fields_Olinordered__field(X5)
     => ( c_Orderings_Oord__class_Oless(X5,X4,X13)
       => ( c_Orderings_Oord__class_Oless(X5,X13,c_Groups_Ozero__class_Ozero(X5))
         => c_Orderings_Oord__class_Oless(X5,c_Rings_Oinverse__class_Oinverse(X5,X13),c_Rings_Oinverse__class_Oinverse(X5,X4)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__inverse__less__neg) ).

fof(f22231,plain,
    spl50_1062,
    inference(avatar_split_clause,[],[f4800,f22229]) ).

fof(f22229,plain,
    ( spl50_1062
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X2,c_Rings_Oinverse__class_Oinverse(X2,X0),c_Rings_Oinverse__class_Oinverse(X2,X1))
        | ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
        | ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
        | ~ class_Fields_Olinordered__field(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1062])]) ).

fof(f4800,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X2,c_Rings_Oinverse__class_Oinverse(X2,X0),c_Rings_Oinverse__class_Oinverse(X2,X1))
      | ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
      | ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
      | ~ class_Fields_Olinordered__field(X2) ),
    inference(cnf_transformation,[],[f2680]) ).

fof(f2680,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(X2,c_Rings_Oinverse__class_Oinverse(X2,X0),c_Rings_Oinverse__class_Oinverse(X2,X1))
      | ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
      | ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
      | ~ class_Fields_Olinordered__field(X2) ),
    inference(flattening,[],[f2679]) ).

fof(f2679,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(X2,c_Rings_Oinverse__class_Oinverse(X2,X0),c_Rings_Oinverse__class_Oinverse(X2,X1))
      | ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
      | ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
      | ~ class_Fields_Olinordered__field(X2) ),
    inference(ennf_transformation,[],[f1769]) ).

fof(f1769,plain,
    ! [X0,X1,X2] :
      ( class_Fields_Olinordered__field(X2)
     => ( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
       => ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
         => c_Orderings_Oord__class_Oless__eq(X2,c_Rings_Oinverse__class_Oinverse(X2,X0),c_Rings_Oinverse__class_Oinverse(X2,X1)) ) ) ),
    inference(rectify,[],[f75]) ).

fof(f75,axiom,
    ! [X13,X4,X5] :
      ( class_Fields_Olinordered__field(X5)
     => ( c_Orderings_Oord__class_Oless__eq(X5,X4,X13)
       => ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X4)
         => c_Orderings_Oord__class_Oless__eq(X5,c_Rings_Oinverse__class_Oinverse(X5,X13),c_Rings_Oinverse__class_Oinverse(X5,X4)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__inverse__le) ).

fof(f22227,plain,
    spl50_1061,
    inference(avatar_split_clause,[],[f4799,f22225]) ).

fof(f22225,plain,
    ( spl50_1061
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X2,c_Rings_Oinverse__class_Oinverse(X2,X0),c_Rings_Oinverse__class_Oinverse(X2,X1))
        | ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
        | ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
        | ~ class_Fields_Olinordered__field(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1061])]) ).

fof(f4799,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X2,c_Rings_Oinverse__class_Oinverse(X2,X0),c_Rings_Oinverse__class_Oinverse(X2,X1))
      | ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
      | ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
      | ~ class_Fields_Olinordered__field(X2) ),
    inference(cnf_transformation,[],[f2678]) ).

fof(f2678,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(X2,c_Rings_Oinverse__class_Oinverse(X2,X0),c_Rings_Oinverse__class_Oinverse(X2,X1))
      | ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
      | ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
      | ~ class_Fields_Olinordered__field(X2) ),
    inference(flattening,[],[f2677]) ).

fof(f2677,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(X2,c_Rings_Oinverse__class_Oinverse(X2,X0),c_Rings_Oinverse__class_Oinverse(X2,X1))
      | ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
      | ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
      | ~ class_Fields_Olinordered__field(X2) ),
    inference(ennf_transformation,[],[f1768]) ).

fof(f1768,plain,
    ! [X0,X1,X2] :
      ( class_Fields_Olinordered__field(X2)
     => ( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
       => ( c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
         => c_Orderings_Oord__class_Oless__eq(X2,c_Rings_Oinverse__class_Oinverse(X2,X0),c_Rings_Oinverse__class_Oinverse(X2,X1)) ) ) ),
    inference(rectify,[],[f74]) ).

fof(f74,axiom,
    ! [X13,X4,X5] :
      ( class_Fields_Olinordered__field(X5)
     => ( c_Orderings_Oord__class_Oless__eq(X5,X4,X13)
       => ( c_Orderings_Oord__class_Oless(X5,X13,c_Groups_Ozero__class_Ozero(X5))
         => c_Orderings_Oord__class_Oless__eq(X5,c_Rings_Oinverse__class_Oinverse(X5,X13),c_Rings_Oinverse__class_Oinverse(X5,X4)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__inverse__le__neg) ).

fof(f22223,plain,
    spl50_1060,
    inference(avatar_split_clause,[],[f4760,f22221]) ).

fof(f22221,plain,
    ( spl50_1060
  <=> ! [X0,X1] :
        ( 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)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1060])]) ).

fof(f4760,plain,
    ! [X0,X1] :
      ( 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(cnf_transformation,[],[f3644]) ).

fof(f3644,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,[],[f3643]) ).

fof(f3643,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,[],[f1739]) ).

fof(f1739,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,[],[f440]) ).

fof(f440,axiom,
    ! [X16,X12] :
      ( 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),X12),X16))
    <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X12)
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X16 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__power__nat__eq) ).

fof(f22219,plain,
    spl50_1059,
    inference(avatar_split_clause,[],[f4413,f22217]) ).

fof(f22217,plain,
    ( spl50_1059
  <=> ! [X0,X1] :
        ( c_Groups_Osgn__class_Osgn(X1,X0) = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))
        | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
        | c_Groups_Ozero__class_Ozero(X1) = X0
        | ~ class_Groups_Osgn__if(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1059])]) ).

fof(f4413,plain,
    ! [X0,X1] :
      ( c_Groups_Osgn__class_Osgn(X1,X0) = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))
      | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
      | c_Groups_Ozero__class_Ozero(X1) = X0
      | ~ class_Groups_Osgn__if(X1) ),
    inference(cnf_transformation,[],[f2459]) ).

fof(f2459,plain,
    ! [X0,X1] :
      ( ( ( ( ( c_Groups_Osgn__class_Osgn(X1,X0) = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))
              | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
            & ( c_Groups_Oone__class_Oone(X1) = c_Groups_Osgn__class_Osgn(X1,X0)
              | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) ) )
          | c_Groups_Ozero__class_Ozero(X1) = X0 )
        & ( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Osgn__class_Osgn(X1,X0)
          | c_Groups_Ozero__class_Ozero(X1) != X0 ) )
      | ~ class_Groups_Osgn__if(X1) ),
    inference(ennf_transformation,[],[f1520]) ).

fof(f1520,plain,
    ! [X0,X1] :
      ( class_Groups_Osgn__if(X1)
     => ( ( c_Groups_Ozero__class_Ozero(X1) != X0
         => ( ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
             => c_Groups_Osgn__class_Osgn(X1,X0) = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1)) )
            & ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
             => c_Groups_Oone__class_Oone(X1) = c_Groups_Osgn__class_Osgn(X1,X0) ) ) )
        & ( c_Groups_Ozero__class_Ozero(X1) = X0
         => c_Groups_Ozero__class_Ozero(X1) = c_Groups_Osgn__class_Osgn(X1,X0) ) ) ),
    inference(rectify,[],[f848]) ).

fof(f848,axiom,
    ! [X9,X5] :
      ( class_Groups_Osgn__if(X5)
     => ( ( c_Groups_Ozero__class_Ozero(X5) != X9
         => ( ( ~ c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X9)
             => c_Groups_Ouminus__class_Ouminus(X5,c_Groups_Oone__class_Oone(X5)) = c_Groups_Osgn__class_Osgn(X5,X9) )
            & ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X9)
             => c_Groups_Oone__class_Oone(X5) = c_Groups_Osgn__class_Osgn(X5,X9) ) ) )
        & ( c_Groups_Ozero__class_Ozero(X5) = X9
         => c_Groups_Ozero__class_Ozero(X5) = c_Groups_Osgn__class_Osgn(X5,X9) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__if) ).

fof(f22215,plain,
    spl50_1058,
    inference(avatar_split_clause,[],[f4370,f22213]) ).

fof(f22213,plain,
    ( spl50_1058
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
        | ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Oone__class_Oone(X1))
        | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
        | ~ class_Fields_Olinordered__field(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1058])]) ).

fof(f4370,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
      | ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Oone__class_Oone(X1))
      | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
      | ~ class_Fields_Olinordered__field(X1) ),
    inference(cnf_transformation,[],[f2417]) ).

fof(f2417,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
      | ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Oone__class_Oone(X1))
      | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
      | ~ class_Fields_Olinordered__field(X1) ),
    inference(flattening,[],[f2416]) ).

fof(f2416,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
      | ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Oone__class_Oone(X1))
      | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
      | ~ class_Fields_Olinordered__field(X1) ),
    inference(ennf_transformation,[],[f1488]) ).

fof(f1488,plain,
    ! [X0,X1] :
      ( class_Fields_Olinordered__field(X1)
     => ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
       => ( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Oone__class_Oone(X1))
         => c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X0)) ) ) ),
    inference(rectify,[],[f16]) ).

fof(f16,axiom,
    ! [X4,X5] :
      ( class_Fields_Olinordered__field(X5)
     => ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X4)
       => ( c_Orderings_Oord__class_Oless(X5,X4,c_Groups_Oone__class_Oone(X5))
         => c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5),c_Rings_Oinverse__class_Oinverse(X5,X4)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__less__inverse) ).

fof(f22211,plain,
    spl50_1057,
    inference(avatar_split_clause,[],[f4369,f22209]) ).

fof(f22209,plain,
    ( spl50_1057
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
        | ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Oone__class_Oone(X1))
        | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
        | ~ class_Fields_Olinordered__field(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1057])]) ).

fof(f4369,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
      | ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Oone__class_Oone(X1))
      | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
      | ~ class_Fields_Olinordered__field(X1) ),
    inference(cnf_transformation,[],[f2415]) ).

fof(f2415,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
      | ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Oone__class_Oone(X1))
      | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
      | ~ class_Fields_Olinordered__field(X1) ),
    inference(flattening,[],[f2414]) ).

fof(f2414,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
      | ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Oone__class_Oone(X1))
      | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
      | ~ class_Fields_Olinordered__field(X1) ),
    inference(ennf_transformation,[],[f1487]) ).

fof(f1487,plain,
    ! [X0,X1] :
      ( class_Fields_Olinordered__field(X1)
     => ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
       => ( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Oone__class_Oone(X1))
         => c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X0)) ) ) ),
    inference(rectify,[],[f82]) ).

fof(f82,axiom,
    ! [X4,X5] :
      ( class_Fields_Olinordered__field(X5)
     => ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X4)
       => ( c_Orderings_Oord__class_Oless__eq(X5,X4,c_Groups_Oone__class_Oone(X5))
         => c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oone__class_Oone(X5),c_Rings_Oinverse__class_Oinverse(X5,X4)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__le__inverse) ).

fof(f22207,plain,
    spl50_1056,
    inference(avatar_split_clause,[],[f4362,f22205]) ).

fof(f22205,plain,
    ( spl50_1056
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X0)
        | c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
        | ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Oone__class_Oone(X1))
        | ~ class_Fields_Olinordered__field__inverse__zero(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1056])]) ).

fof(f4362,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X0)
      | c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
      | ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Oone__class_Oone(X1))
      | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(cnf_transformation,[],[f3503]) ).

fof(f3503,plain,
    ! [X0,X1] :
      ( ( ( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Oone__class_Oone(X1))
          | ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X0)
            & ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ) )
        & ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X0)
          | c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
          | ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Oone__class_Oone(X1)) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(flattening,[],[f3502]) ).

fof(f3502,plain,
    ! [X0,X1] :
      ( ( ( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Oone__class_Oone(X1))
          | ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X0)
            & ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ) )
        & ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X0)
          | c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
          | ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Oone__class_Oone(X1)) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(nnf_transformation,[],[f2408]) ).

fof(f2408,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Oone__class_Oone(X1))
      <=> ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X0)
          | c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(ennf_transformation,[],[f1483]) ).

fof(f1483,plain,
    ! [X0,X1] :
      ( class_Fields_Olinordered__field__inverse__zero(X1)
     => ( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Oone__class_Oone(X1))
      <=> ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X0)
          | c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ) ) ),
    inference(rectify,[],[f83]) ).

fof(f83,axiom,
    ! [X12,X5] :
      ( class_Fields_Olinordered__field__inverse__zero(X5)
     => ( c_Orderings_Oord__class_Oless(X5,c_Rings_Oinverse__class_Oinverse(X5,X12),c_Groups_Oone__class_Oone(X5))
      <=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5),X12)
          | c_Orderings_Oord__class_Oless__eq(X5,X12,c_Groups_Ozero__class_Ozero(X5)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__less__1__iff) ).

fof(f22203,plain,
    spl50_1055,
    inference(avatar_split_clause,[],[f4359,f22201]) ).

fof(f22201,plain,
    ( spl50_1055
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
        | ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Oone__class_Oone(X1))
        | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
        | ~ class_Fields_Olinordered__field__inverse__zero(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1055])]) ).

fof(f4359,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
      | ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Oone__class_Oone(X1))
      | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
      | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(cnf_transformation,[],[f3500]) ).

fof(f3500,plain,
    ! [X0,X1] :
      ( ( ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
          | ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Oone__class_Oone(X1))
          | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
        & ( ( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Oone__class_Oone(X1))
            & c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
          | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X0)) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(flattening,[],[f3499]) ).

fof(f3499,plain,
    ! [X0,X1] :
      ( ( ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
          | ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Oone__class_Oone(X1))
          | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
        & ( ( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Oone__class_Oone(X1))
            & c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
          | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X0)) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(nnf_transformation,[],[f2406]) ).

fof(f2406,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
      <=> ( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Oone__class_Oone(X1))
          & c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(ennf_transformation,[],[f1481]) ).

fof(f1481,plain,
    ! [X0,X1] :
      ( class_Fields_Olinordered__field__inverse__zero(X1)
     => ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
      <=> ( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Oone__class_Oone(X1))
          & c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) ) ) ),
    inference(rectify,[],[f15]) ).

fof(f15,axiom,
    ! [X12,X5] :
      ( class_Fields_Olinordered__field__inverse__zero(X5)
     => ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5),c_Rings_Oinverse__class_Oinverse(X5,X12))
      <=> ( c_Orderings_Oord__class_Oless(X5,X12,c_Groups_Oone__class_Oone(X5))
          & c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X12) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__less__inverse__iff) ).

fof(f22199,plain,
    spl50_1054,
    inference(avatar_split_clause,[],[f4352,f22197]) ).

fof(f22197,plain,
    ( spl50_1054
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),X0)
        | c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
        | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Oone__class_Oone(X1))
        | ~ class_Fields_Olinordered__field__inverse__zero(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1054])]) ).

fof(f4352,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),X0)
      | c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
      | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Oone__class_Oone(X1))
      | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(cnf_transformation,[],[f3497]) ).

fof(f3497,plain,
    ! [X0,X1] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Oone__class_Oone(X1))
          | ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),X0)
            & ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ) )
        & ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),X0)
          | c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
          | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Oone__class_Oone(X1)) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(flattening,[],[f3496]) ).

fof(f3496,plain,
    ! [X0,X1] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Oone__class_Oone(X1))
          | ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),X0)
            & ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ) )
        & ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),X0)
          | c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
          | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Oone__class_Oone(X1)) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(nnf_transformation,[],[f2404]) ).

fof(f2404,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Oone__class_Oone(X1))
      <=> ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),X0)
          | c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(ennf_transformation,[],[f1479]) ).

fof(f1479,plain,
    ! [X0,X1] :
      ( class_Fields_Olinordered__field__inverse__zero(X1)
     => ( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Oone__class_Oone(X1))
      <=> ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),X0)
          | c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ) ) ),
    inference(rectify,[],[f76]) ).

fof(f76,axiom,
    ! [X12,X5] :
      ( class_Fields_Olinordered__field__inverse__zero(X5)
     => ( c_Orderings_Oord__class_Oless__eq(X5,c_Rings_Oinverse__class_Oinverse(X5,X12),c_Groups_Oone__class_Oone(X5))
      <=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oone__class_Oone(X5),X12)
          | c_Orderings_Oord__class_Oless__eq(X5,X12,c_Groups_Ozero__class_Ozero(X5)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__le__1__iff) ).

fof(f22151,plain,
    spl50_1053,
    inference(avatar_split_clause,[],[f4349,f22149]) ).

fof(f22149,plain,
    ( spl50_1053
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
        | ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Oone__class_Oone(X1))
        | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
        | ~ class_Fields_Olinordered__field__inverse__zero(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1053])]) ).

fof(f4349,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
      | ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Oone__class_Oone(X1))
      | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
      | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(cnf_transformation,[],[f3494]) ).

fof(f3494,plain,
    ! [X0,X1] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
          | ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Oone__class_Oone(X1))
          | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
        & ( ( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Oone__class_Oone(X1))
            & c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
          | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X0)) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(flattening,[],[f3493]) ).

fof(f3493,plain,
    ! [X0,X1] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
          | ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Oone__class_Oone(X1))
          | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
        & ( ( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Oone__class_Oone(X1))
            & c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
          | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X0)) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(nnf_transformation,[],[f2402]) ).

fof(f2402,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
      <=> ( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Oone__class_Oone(X1))
          & c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(ennf_transformation,[],[f1477]) ).

fof(f1477,plain,
    ! [X0,X1] :
      ( class_Fields_Olinordered__field__inverse__zero(X1)
     => ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
      <=> ( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Oone__class_Oone(X1))
          & c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) ) ) ),
    inference(rectify,[],[f84]) ).

fof(f84,axiom,
    ! [X12,X5] :
      ( class_Fields_Olinordered__field__inverse__zero(X5)
     => ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oone__class_Oone(X5),c_Rings_Oinverse__class_Oinverse(X5,X12))
      <=> ( c_Orderings_Oord__class_Oless__eq(X5,X12,c_Groups_Oone__class_Oone(X5))
          & c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X12) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__le__inverse__iff) ).

fof(f20350,plain,
    ( spl50_1052
    | ~ spl50_188
    | ~ spl50_890
    | ~ spl50_1001 ),
    inference(avatar_split_clause,[],[f20132,f20128,f15443,f6986,f20347]) ).

fof(f20347,plain,
    ( spl50_1052
  <=> c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_a____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),sK17),v_k____))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1052])]) ).

fof(f6986,plain,
    ( spl50_188
  <=> class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_188])]) ).

fof(f15443,plain,
    ( spl50_890
  <=> ! [X2,X0,X1] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1)
        | ~ class_Rings_Ocomm__semiring__1(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_890])]) ).

fof(f20128,plain,
    ( spl50_1001
  <=> c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),sK17),v_k____)),v_a____)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1001])]) ).

fof(f20132,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_a____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),sK17),v_k____)))
    | ~ spl50_188
    | ~ spl50_890
    | ~ spl50_1001 ),
    inference(forward_demodulation,[],[f20130,f16790]) ).

fof(f16790,plain,
    ( ! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X0)
    | ~ spl50_188
    | ~ spl50_890 ),
    inference(resolution,[],[f15444,f6988]) ).

fof(f6988,plain,
    ( class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)
    | ~ spl50_188 ),
    inference(avatar_component_clause,[],[f6986]) ).

fof(f15444,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Rings_Ocomm__semiring__1(X2)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1) )
    | ~ spl50_890 ),
    inference(avatar_component_clause,[],[f15443]) ).

fof(f20130,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),sK17),v_k____)),v_a____))
    | ~ spl50_1001 ),
    inference(avatar_component_clause,[],[f20128]) ).

fof(f20345,plain,
    spl50_1051,
    inference(avatar_split_clause,[],[f5909,f20342]) ).

fof(f20342,plain,
    ( spl50_1051
  <=> c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1051])]) ).

fof(f5909,plain,
    c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),
    inference(forward_demodulation,[],[f4120,f4114]) ).

fof(f4114,plain,
    hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),
    inference(cnf_transformation,[],[f559]) ).

fof(f559,axiom,
    hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pqc0) ).

fof(f4120,plain,
    c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),
    inference(cnf_transformation,[],[f571]) ).

fof(f571,axiom,
    c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_r01) ).

fof(f20340,plain,
    spl50_1050,
    inference(avatar_split_clause,[],[f5875,f20338]) ).

fof(f20338,plain,
    ( spl50_1050
  <=> ! [X0,X1,X3] :
        ( c_Rings_Odvd__class_Odvd(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),c_Groups_Ozero__class_Ozero(X3)),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),c_Groups_Ozero__class_Ozero(X3)),X0))
        | ~ class_Rings_Oidom(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1050])]) ).

fof(f5875,plain,
    ! [X3,X0,X1] :
      ( c_Rings_Odvd__class_Odvd(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),c_Groups_Ozero__class_Ozero(X3)),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),c_Groups_Ozero__class_Ozero(X3)),X0))
      | ~ class_Rings_Oidom(X3) ),
    inference(equality_resolution,[],[f5355]) ).

fof(f5355,plain,
    ! [X2,X3,X0,X1] :
      ( c_Rings_Odvd__class_Odvd(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
      | c_Groups_Ozero__class_Ozero(X3) != X2
      | ~ class_Rings_Oidom(X3) ),
    inference(cnf_transformation,[],[f3826]) ).

fof(f20336,plain,
    spl50_1049,
    inference(avatar_split_clause,[],[f5874,f20334]) ).

fof(f20334,plain,
    ( spl50_1049
  <=> ! [X2,X0,X3] :
        ( c_Rings_Odvd__class_Odvd(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),c_Groups_Ozero__class_Ozero(X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),c_Groups_Ozero__class_Ozero(X3)))
        | ~ class_Rings_Oidom(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1049])]) ).

fof(f5874,plain,
    ! [X2,X3,X0] :
      ( c_Rings_Odvd__class_Odvd(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),c_Groups_Ozero__class_Ozero(X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),c_Groups_Ozero__class_Ozero(X3)))
      | ~ class_Rings_Oidom(X3) ),
    inference(equality_resolution,[],[f5352]) ).

fof(f5352,plain,
    ! [X2,X3,X0,X1] :
      ( c_Rings_Odvd__class_Odvd(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
      | c_Groups_Ozero__class_Ozero(X3) != X1
      | ~ class_Rings_Oidom(X3) ),
    inference(cnf_transformation,[],[f3824]) ).

fof(f20332,plain,
    spl50_1048,
    inference(avatar_split_clause,[],[f5854,f20330]) ).

fof(f20330,plain,
    ( spl50_1048
  <=> ! [X2,X1] :
        ( c_Groups_Ozero__class_Ozero(X2) != hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ class_Rings_Ozero__neq__one(X2)
        | ~ class_Rings_Ono__zero__divisors(X2)
        | ~ class_Rings_Omult__zero(X2)
        | ~ class_Power_Opower(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1048])]) ).

fof(f5854,plain,
    ! [X2,X1] :
      ( c_Groups_Ozero__class_Ozero(X2) != hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      | ~ class_Rings_Ozero__neq__one(X2)
      | ~ class_Rings_Ono__zero__divisors(X2)
      | ~ class_Rings_Omult__zero(X2)
      | ~ class_Power_Opower(X2) ),
    inference(equality_resolution,[],[f5184]) ).

fof(f5184,plain,
    ! [X2,X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
      | c_Groups_Ozero__class_Ozero(X2) != hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)
      | ~ class_Rings_Ozero__neq__one(X2)
      | ~ class_Rings_Ono__zero__divisors(X2)
      | ~ class_Rings_Omult__zero(X2)
      | ~ class_Power_Opower(X2) ),
    inference(cnf_transformation,[],[f3754]) ).

fof(f20328,plain,
    spl50_1047,
    inference(avatar_split_clause,[],[f5641,f20326]) ).

fof(f20326,plain,
    ( spl50_1047
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK34(X0,X1),X0)
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = 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))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1047])]) ).

fof(f5641,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK34(X0,X1),X0)
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = 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))) ),
    inference(definition_unfolding,[],[f4686,f4164]) ).

fof(f4686,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK34(X0,X1),X0)
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) ),
    inference(cnf_transformation,[],[f3604]) ).

fof(f3604,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
        | ( ! [X2] :
              ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
              | c_Nat_OSuc(X2) != X1 )
          & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ) )
      & ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK34(X0,X1),X0)
          & c_Nat_OSuc(sK34(X0,X1)) = X1 )
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK34])],[f3602,f3603]) ).

fof(f3603,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X0)
          & c_Nat_OSuc(X3) = X1 )
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK34(X0,X1),X0)
        & c_Nat_OSuc(sK34(X0,X1)) = X1 ) ),
    introduced(choice_axiom,[]) ).

fof(f3602,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
        | ( ! [X2] :
              ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
              | c_Nat_OSuc(X2) != X1 )
          & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ) )
      & ( ? [X3] :
            ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X0)
            & c_Nat_OSuc(X3) = X1 )
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) ) ),
    inference(rectify,[],[f3601]) ).

fof(f3601,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
        | ( ! [X2] :
              ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
              | c_Nat_OSuc(X2) != X1 )
          & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ) )
      & ( ? [X2] :
            ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
            & c_Nat_OSuc(X2) = X1 )
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) ) ),
    inference(flattening,[],[f3600]) ).

fof(f3600,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
        | ( ! [X2] :
              ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
              | c_Nat_OSuc(X2) != X1 )
          & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ) )
      & ( ? [X2] :
            ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
            & c_Nat_OSuc(X2) = X1 )
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) ) ),
    inference(nnf_transformation,[],[f1713]) ).

fof(f1713,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
    <=> ( ? [X2] :
            ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
            & c_Nat_OSuc(X2) = X1 )
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 ) ),
    inference(rectify,[],[f959]) ).

fof(f959,axiom,
    ! [X16,X32] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X32,c_Nat_OSuc(X16))
    <=> ( ? [X86] :
            ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X86,X16)
            & c_Nat_OSuc(X86) = X32 )
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X32 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq__0__disj) ).

fof(f20324,plain,
    spl50_1046,
    inference(avatar_split_clause,[],[f5621,f20322]) ).

fof(f20322,plain,
    ( spl50_1046
  <=> ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
        | ~ class_Rings_Osemiring__0(X1)
        | ~ class_Power_Opower(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1046])]) ).

fof(f5621,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
      | ~ class_Rings_Osemiring__0(X1)
      | ~ class_Power_Opower(X1) ),
    inference(definition_unfolding,[],[f4617,f4164]) ).

fof(f4617,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),c_Nat_OSuc(X0))
      | ~ class_Rings_Osemiring__0(X1)
      | ~ class_Power_Opower(X1) ),
    inference(cnf_transformation,[],[f2656]) ).

fof(f2656,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),c_Nat_OSuc(X0))
      | ~ class_Rings_Osemiring__0(X1)
      | ~ class_Power_Opower(X1) ),
    inference(flattening,[],[f2655]) ).

fof(f2655,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),c_Nat_OSuc(X0))
      | ~ class_Rings_Osemiring__0(X1)
      | ~ class_Power_Opower(X1) ),
    inference(ennf_transformation,[],[f1680]) ).

fof(f1680,plain,
    ! [X0,X1] :
      ( ( class_Rings_Osemiring__0(X1)
        & class_Power_Opower(X1) )
     => c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),c_Nat_OSuc(X0)) ),
    inference(rectify,[],[f919]) ).

fof(f919,axiom,
    ! [X3,X5] :
      ( ( class_Rings_Osemiring__0(X5)
        & class_Power_Opower(X5) )
     => c_Groups_Ozero__class_Ozero(X5) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),c_Groups_Ozero__class_Ozero(X5)),c_Nat_OSuc(X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__0__Suc) ).

fof(f20320,plain,
    spl50_1045,
    inference(avatar_split_clause,[],[f5559,f20318]) ).

fof(f20318,plain,
    ( spl50_1045
  <=> ! [X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),X1)),sK45)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1045])]) ).

fof(f5559,plain,
    ! [X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),X1)),sK45)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ),
    inference(cnf_transformation,[],[f3869]) ).

fof(f3869,plain,
    ( ! [X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),X1)),sK45)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) )
    & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK45) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK45])],[f3438,f3868]) ).

fof(f3868,plain,
    ( ? [X0] :
        ( ! [X1] :
            ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),X1)),X0)
            | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) )
        & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) )
   => ( ! [X1] :
          ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),X1)),sK45)
          | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) )
      & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK45) ) ),
    introduced(choice_axiom,[]) ).

fof(f3438,plain,
    ? [X0] :
      ( ! [X1] :
          ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),X1)),X0)
          | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) )
      & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ),
    inference(ennf_transformation,[],[f2293]) ).

fof(f2293,plain,
    ? [X0] :
      ( ! [X1] :
          ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
         => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),X1)),X0) )
      & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ),
    inference(rectify,[],[f263]) ).

fof(f263,axiom,
    ? [X44] :
      ( ! [X34] :
          ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X34),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
         => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),X34)),X44) )
      & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X44) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096EX_Am_0620_O_AALL_Az_O_Acmod_Az_A_060_061_Acmod_Aw_A_N_N_062_Acmod_A_Ipoly_As_Az_J_A_060_061_Am_096) ).

fof(f20316,plain,
    spl50_1044,
    inference(avatar_split_clause,[],[f5464,f20314]) ).

fof(f20314,plain,
    ( spl50_1044
  <=> ! [X0,X3,X2,X1] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,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,X3,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1044])]) ).

fof(f5464,plain,
    ! [X2,X3,X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,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,X3,X2) ),
    inference(cnf_transformation,[],[f3338]) ).

fof(f3338,plain,
    ! [X0,X1,X2,X3] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,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,X3,X2) ),
    inference(flattening,[],[f3337]) ).

fof(f3337,plain,
    ! [X0,X1,X2,X3] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,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,X3,X2) ),
    inference(ennf_transformation,[],[f2225]) ).

fof(f2225,plain,
    ! [X0,X1,X2,X3] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
     => ( 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,X3,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)) ) ),
    inference(rectify,[],[f392]) ).

fof(f392,axiom,
    ! [X51,X38,X39,X18] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X39)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X38,X51)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X38),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X39,X51)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__mono) ).

fof(f20312,plain,
    spl50_1043,
    inference(avatar_split_clause,[],[f5463,f20310]) ).

fof(f20310,plain,
    ( spl50_1043
  <=> ! [X0,X3,X2,X1] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X0))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1043])]) ).

fof(f5463,plain,
    ! [X2,X3,X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X0))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X2) ),
    inference(cnf_transformation,[],[f3336]) ).

fof(f3336,plain,
    ! [X0,X1,X2,X3] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X0))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X2) ),
    inference(flattening,[],[f3335]) ).

fof(f3335,plain,
    ! [X0,X1,X2,X3] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X0))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X2) ),
    inference(ennf_transformation,[],[f2224]) ).

fof(f2224,plain,
    ! [X0,X1,X2,X3] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X2)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
       => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X0)) ) ),
    inference(rectify,[],[f610]) ).

fof(f610,axiom,
    ! [X14,X67,X15,X68] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X68,X15)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X67,X14)
       => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X68,X67),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X15,X14)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__zless__mono) ).

fof(f20308,plain,
    ( ~ spl50_201
    | ~ spl50_1042
    | ~ spl50_291
    | ~ spl50_446 ),
    inference(avatar_split_clause,[],[f8522,f8310,f7434,f20305,f7051]) ).

fof(f7051,plain,
    ( spl50_201
  <=> class_Orderings_Opreorder(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_201])]) ).

fof(f20305,plain,
    ( spl50_1042
  <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK45,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1042])]) ).

fof(f7434,plain,
    ( spl50_291
  <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK45) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_291])]) ).

fof(f8310,plain,
    ( spl50_446
  <=> ! [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,[spl50_446])]) ).

fof(f8522,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK45,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    | ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
    | ~ spl50_291
    | ~ spl50_446 ),
    inference(resolution,[],[f8311,f7436]) ).

fof(f7436,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK45)
    | ~ spl50_291 ),
    inference(avatar_component_clause,[],[f7434]) ).

fof(f8311,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
        | ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
        | ~ class_Orderings_Opreorder(X2) )
    | ~ spl50_446 ),
    inference(avatar_component_clause,[],[f8310]) ).

fof(f20303,plain,
    spl50_1041,
    inference(avatar_split_clause,[],[f5461,f20301]) ).

fof(f20301,plain,
    ( spl50_1041
  <=> ! [X0,X3,X2,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,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,X3,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1041])]) ).

fof(f5461,plain,
    ! [X2,X3,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,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,X3,X2) ),
    inference(cnf_transformation,[],[f3332]) ).

fof(f3332,plain,
    ! [X0,X1,X2,X3] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,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,X3,X2) ),
    inference(flattening,[],[f3331]) ).

fof(f3331,plain,
    ! [X0,X1,X2,X3] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,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,X3,X2) ),
    inference(ennf_transformation,[],[f2222]) ).

fof(f2222,plain,
    ! [X0,X1,X2,X3] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,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,X3,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)) ) ),
    inference(rectify,[],[f407]) ).

fof(f407,axiom,
    ! [X51,X38,X39,X18] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X39)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X38,X51)
       => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X38),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X39,X51)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__mono) ).

fof(f20299,plain,
    spl50_1040,
    inference(avatar_split_clause,[],[f5372,f20297]) ).

fof(f20297,plain,
    ( spl50_1040
  <=> ! [X0,X3,X2,X1] :
        ( c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0))
        | ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
        | ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
        | ~ class_Rings_Olinordered__semidom(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1040])]) ).

fof(f5372,plain,
    ! [X2,X3,X0,X1] :
      ( c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0))
      | ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
      | ~ class_Rings_Olinordered__semidom(X3) ),
    inference(cnf_transformation,[],[f3212]) ).

fof(f3212,plain,
    ! [X0,X1,X2,X3] :
      ( c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0))
      | ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
      | ~ class_Rings_Olinordered__semidom(X3) ),
    inference(flattening,[],[f3211]) ).

fof(f3211,plain,
    ! [X0,X1,X2,X3] :
      ( c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0))
      | ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
      | ~ class_Rings_Olinordered__semidom(X3) ),
    inference(ennf_transformation,[],[f2139]) ).

fof(f2139,plain,
    ! [X0,X1,X2,X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
       => ( c_Orderings_Oord__class_Oless(X3,X1,X0)
         => c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0)) ) ) ),
    inference(rectify,[],[f142]) ).

fof(f142,axiom,
    ! [X23,X13,X4,X5] :
      ( class_Rings_Olinordered__semidom(X5)
     => ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X4)
       => ( c_Orderings_Oord__class_Oless(X5,X13,X23)
         => c_Orderings_Oord__class_Oless(X5,X13,c_Groups_Oplus__class_Oplus(X5,X4,X23)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__add__strict) ).

fof(f20295,plain,
    spl50_1039,
    inference(avatar_split_clause,[],[f5344,f20293]) ).

fof(f20293,plain,
    ( spl50_1039
  <=> ! [X0,X3,X2,X1] :
        ( c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0))
        | ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
        | ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
        | ~ class_Groups_Oordered__comm__monoid__add(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1039])]) ).

fof(f5344,plain,
    ! [X2,X3,X0,X1] :
      ( c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0))
      | ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
      | ~ class_Groups_Oordered__comm__monoid__add(X3) ),
    inference(cnf_transformation,[],[f3173]) ).

fof(f3173,plain,
    ! [X0,X1,X2,X3] :
      ( c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0))
      | ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
      | ~ class_Groups_Oordered__comm__monoid__add(X3) ),
    inference(flattening,[],[f3172]) ).

fof(f3172,plain,
    ! [X0,X1,X2,X3] :
      ( c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0))
      | ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
      | ~ class_Groups_Oordered__comm__monoid__add(X3) ),
    inference(ennf_transformation,[],[f2118]) ).

fof(f2118,plain,
    ! [X0,X1,X2,X3] :
      ( class_Groups_Oordered__comm__monoid__add(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
       => ( c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
         => c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0)) ) ) ),
    inference(rectify,[],[f261]) ).

fof(f261,axiom,
    ! [X23,X13,X4,X5] :
      ( class_Groups_Oordered__comm__monoid__add(X5)
     => ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X4)
       => ( c_Orderings_Oord__class_Oless__eq(X5,X13,X23)
         => c_Orderings_Oord__class_Oless(X5,X13,c_Groups_Oplus__class_Oplus(X5,X4,X23)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__increasing) ).

fof(f20291,plain,
    spl50_1038,
    inference(avatar_split_clause,[],[f5343,f20289]) ).

fof(f20289,plain,
    ( spl50_1038
  <=> ! [X0,X3,X2,X1] :
        ( c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0))
        | ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
        | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
        | ~ class_Groups_Oordered__comm__monoid__add(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1038])]) ).

fof(f5343,plain,
    ! [X2,X3,X0,X1] :
      ( c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0))
      | ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
      | ~ class_Groups_Oordered__comm__monoid__add(X3) ),
    inference(cnf_transformation,[],[f3171]) ).

fof(f3171,plain,
    ! [X0,X1,X2,X3] :
      ( c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0))
      | ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
      | ~ class_Groups_Oordered__comm__monoid__add(X3) ),
    inference(flattening,[],[f3170]) ).

fof(f3170,plain,
    ! [X0,X1,X2,X3] :
      ( c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0))
      | ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
      | ~ class_Groups_Oordered__comm__monoid__add(X3) ),
    inference(ennf_transformation,[],[f2117]) ).

fof(f2117,plain,
    ! [X0,X1,X2,X3] :
      ( class_Groups_Oordered__comm__monoid__add(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
       => ( c_Orderings_Oord__class_Oless(X3,X1,X0)
         => c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0)) ) ) ),
    inference(rectify,[],[f190]) ).

fof(f190,axiom,
    ! [X23,X13,X4,X5] :
      ( class_Groups_Oordered__comm__monoid__add(X5)
     => ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X4)
       => ( c_Orderings_Oord__class_Oless(X5,X13,X23)
         => c_Orderings_Oord__class_Oless(X5,X13,c_Groups_Oplus__class_Oplus(X5,X4,X23)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__increasing2) ).

fof(f20287,plain,
    spl50_1037,
    inference(avatar_split_clause,[],[f5342,f20285]) ).

fof(f20285,plain,
    ( spl50_1037
  <=> ! [X0,X3,X2,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X3,X1,c_Groups_Oplus__class_Oplus(X3,X0,X2))
        | ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
        | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
        | ~ class_Groups_Oordered__comm__monoid__add(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1037])]) ).

fof(f5342,plain,
    ! [X2,X3,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X3,X1,c_Groups_Oplus__class_Oplus(X3,X0,X2))
      | ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
      | ~ class_Groups_Oordered__comm__monoid__add(X3) ),
    inference(cnf_transformation,[],[f3169]) ).

fof(f3169,plain,
    ! [X0,X1,X2,X3] :
      ( c_Orderings_Oord__class_Oless__eq(X3,X1,c_Groups_Oplus__class_Oplus(X3,X0,X2))
      | ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
      | ~ class_Groups_Oordered__comm__monoid__add(X3) ),
    inference(flattening,[],[f3168]) ).

fof(f3168,plain,
    ! [X0,X1,X2,X3] :
      ( c_Orderings_Oord__class_Oless__eq(X3,X1,c_Groups_Oplus__class_Oplus(X3,X0,X2))
      | ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
      | ~ class_Groups_Oordered__comm__monoid__add(X3) ),
    inference(ennf_transformation,[],[f2116]) ).

fof(f2116,plain,
    ! [X0,X1,X2,X3] :
      ( class_Groups_Oordered__comm__monoid__add(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
       => ( c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
         => c_Orderings_Oord__class_Oless__eq(X3,X1,c_Groups_Oplus__class_Oplus(X3,X0,X2)) ) ) ),
    inference(rectify,[],[f246]) ).

fof(f246,axiom,
    ! [X4,X13,X23,X5] :
      ( class_Groups_Oordered__comm__monoid__add(X5)
     => ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X23)
       => ( c_Orderings_Oord__class_Oless__eq(X5,X13,X4)
         => c_Orderings_Oord__class_Oless__eq(X5,X13,c_Groups_Oplus__class_Oplus(X5,X4,X23)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__increasing2) ).

fof(f20283,plain,
    spl50_1036,
    inference(avatar_split_clause,[],[f5341,f20281]) ).

fof(f20281,plain,
    ( spl50_1036
  <=> ! [X0,X3,X2,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0))
        | ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
        | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
        | ~ class_Groups_Oordered__comm__monoid__add(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1036])]) ).

fof(f5341,plain,
    ! [X2,X3,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0))
      | ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
      | ~ class_Groups_Oordered__comm__monoid__add(X3) ),
    inference(cnf_transformation,[],[f3167]) ).

fof(f3167,plain,
    ! [X0,X1,X2,X3] :
      ( c_Orderings_Oord__class_Oless__eq(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0))
      | ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
      | ~ class_Groups_Oordered__comm__monoid__add(X3) ),
    inference(flattening,[],[f3166]) ).

fof(f3166,plain,
    ! [X0,X1,X2,X3] :
      ( c_Orderings_Oord__class_Oless__eq(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0))
      | ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
      | ~ class_Groups_Oordered__comm__monoid__add(X3) ),
    inference(ennf_transformation,[],[f2115]) ).

fof(f2115,plain,
    ! [X0,X1,X2,X3] :
      ( class_Groups_Oordered__comm__monoid__add(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
       => ( c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
         => c_Orderings_Oord__class_Oless__eq(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0)) ) ) ),
    inference(rectify,[],[f245]) ).

fof(f245,axiom,
    ! [X23,X13,X4,X5] :
      ( class_Groups_Oordered__comm__monoid__add(X5)
     => ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X4)
       => ( c_Orderings_Oord__class_Oless__eq(X5,X13,X23)
         => c_Orderings_Oord__class_Oless__eq(X5,X13,c_Groups_Oplus__class_Oplus(X5,X4,X23)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__increasing) ).

fof(f20279,plain,
    spl50_1035,
    inference(avatar_split_clause,[],[f5267,f20277]) ).

fof(f20277,plain,
    ( spl50_1035
  <=> ! [X0,X3,X2,X1] :
        ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X0,X2),X3)
        | ~ sP9(X3,X2,X1,X0)
        | ~ sP10(X0,X1,X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1035])]) ).

fof(f5267,plain,
    ! [X2,X3,X0,X1] :
      ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X0,X2),X3)
      | ~ sP9(X3,X2,X1,X0)
      | ~ sP10(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f3801]) ).

fof(f3801,plain,
    ! [X0,X1,X2,X3] :
      ( ( ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X0,X2),X3)
          | ~ sP9(X3,X2,X1,X0) )
        & ( sP9(X3,X2,X1,X0)
          | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X0,X2),X3) ) )
      | ~ sP10(X0,X1,X2,X3) ),
    inference(rectify,[],[f3800]) ).

fof(f3800,plain,
    ! [X2,X3,X1,X0] :
      ( ( ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X1),X0)
          | ~ sP9(X0,X1,X3,X2) )
        & ( sP9(X0,X1,X3,X2)
          | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X1),X0) ) )
      | ~ sP10(X2,X3,X1,X0) ),
    inference(nnf_transformation,[],[f3456]) ).

fof(f3456,plain,
    ! [X2,X3,X1,X0] :
      ( ( 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(f20275,plain,
    spl50_1034,
    inference(avatar_split_clause,[],[f5266,f20273]) ).

fof(f20273,plain,
    ( spl50_1034
  <=> ! [X0,X3,X2,X1] :
        ( sP9(X3,X2,X1,X0)
        | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X0,X2),X3)
        | ~ sP10(X0,X1,X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1034])]) ).

fof(f5266,plain,
    ! [X2,X3,X0,X1] :
      ( sP9(X3,X2,X1,X0)
      | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X0,X2),X3)
      | ~ sP10(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f3801]) ).

fof(f20271,plain,
    spl50_1033,
    inference(avatar_split_clause,[],[f5252,f20269]) ).

fof(f20269,plain,
    ( spl50_1033
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1033])]) ).

fof(f5252,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)) ),
    inference(cnf_transformation,[],[f3795]) ).

fof(f20267,plain,
    spl50_1032,
    inference(avatar_split_clause,[],[f5249,f20265]) ).

fof(f20265,plain,
    ( spl50_1032
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1032])]) ).

fof(f5249,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)) ),
    inference(cnf_transformation,[],[f3793]) ).

fof(f20258,plain,
    spl50_1031,
    inference(avatar_split_clause,[],[f5241,f20256]) ).

fof(f20256,plain,
    ( spl50_1031
  <=> ! [X2,X0,X1] :
        ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0))
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1031])]) ).

fof(f5241,plain,
    ! [X2,X0,X1] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0))
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0) ),
    inference(cnf_transformation,[],[f3787]) ).

fof(f3787,plain,
    ! [X0,X1,X2] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0))
        | ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0)
          & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2 ) )
      & ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0)
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)) ) ),
    inference(flattening,[],[f3786]) ).

fof(f3786,plain,
    ! [X0,X1,X2] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0))
        | ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0)
          & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2 ) )
      & ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0)
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)) ) ),
    inference(nnf_transformation,[],[f2059]) ).

fof(f2059,plain,
    ! [X0,X1,X2] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0))
    <=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0)
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2 ) ),
    inference(rectify,[],[f859]) ).

fof(f859,axiom,
    ! [X16,X32,X36] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X32),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X16))
    <=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X32,X16)
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X36 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__dvd__cancel__disj) ).

fof(f20254,plain,
    spl50_1030,
    inference(avatar_split_clause,[],[f5211,f20252]) ).

fof(f20252,plain,
    ( spl50_1030
  <=> ! [X2,X0,X1] :
        ( sP8(X0,X1,X2)
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,sK41(X0,X1,X2)) = X1
        | ~ hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1030])]) ).

fof(f5211,plain,
    ! [X2,X0,X1] :
      ( sP8(X0,X1,X2)
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,sK41(X0,X1,X2)) = X1
      | ~ hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(cnf_transformation,[],[f3771]) ).

fof(f3771,plain,
    ! [X0,X1,X2] :
      ( ( sP8(X0,X1,X2)
        | ( ~ hBOOL(hAPP(X0,sK41(X0,X1,X2)))
          & c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,sK41(X0,X1,X2)) = X1 )
        | ( ~ hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ) )
      & ( ( ! [X4] :
              ( hBOOL(hAPP(X0,X4))
              | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X4) != X1 )
          & ( hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ) )
        | ~ sP8(X0,X1,X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK41])],[f3769,f3770]) ).

fof(f3770,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ~ hBOOL(hAPP(X0,X3))
          & c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3) = X1 )
     => ( ~ hBOOL(hAPP(X0,sK41(X0,X1,X2)))
        & c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,sK41(X0,X1,X2)) = X1 ) ),
    introduced(choice_axiom,[]) ).

fof(f3769,plain,
    ! [X0,X1,X2] :
      ( ( sP8(X0,X1,X2)
        | ? [X3] :
            ( ~ hBOOL(hAPP(X0,X3))
            & c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3) = X1 )
        | ( ~ hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ) )
      & ( ( ! [X4] :
              ( hBOOL(hAPP(X0,X4))
              | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X4) != X1 )
          & ( hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ) )
        | ~ sP8(X0,X1,X2) ) ),
    inference(rectify,[],[f3768]) ).

fof(f3768,plain,
    ! [X2,X1,X0] :
      ( ( sP8(X2,X1,X0)
        | ? [X3] :
            ( ~ hBOOL(hAPP(X2,X3))
            & c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3) = X1 )
        | ( ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) )
      & ( ( ! [X3] :
              ( hBOOL(hAPP(X2,X3))
              | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3) != X1 )
          & ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) )
        | ~ sP8(X2,X1,X0) ) ),
    inference(flattening,[],[f3767]) ).

fof(f3767,plain,
    ! [X2,X1,X0] :
      ( ( sP8(X2,X1,X0)
        | ? [X3] :
            ( ~ hBOOL(hAPP(X2,X3))
            & c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3) = X1 )
        | ( ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) )
      & ( ( ! [X3] :
              ( hBOOL(hAPP(X2,X3))
              | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3) != X1 )
          & ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) )
        | ~ sP8(X2,X1,X0) ) ),
    inference(nnf_transformation,[],[f3453]) ).

fof(f3453,plain,
    ! [X2,X1,X0] :
      ( sP8(X2,X1,X0)
    <=> ( ! [X3] :
            ( hBOOL(hAPP(X2,X3))
            | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3) != X1 )
        & ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).

fof(f20250,plain,
    spl50_1029,
    inference(avatar_split_clause,[],[f5203,f20248]) ).

fof(f20248,plain,
    ( spl50_1029
  <=> ! [X2,X0,X1] :
        ( sP7(X0,X1,X2)
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,sK40(X0,X1,X2)) = X1
        | ~ hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1029])]) ).

fof(f5203,plain,
    ! [X2,X0,X1] :
      ( sP7(X0,X1,X2)
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,sK40(X0,X1,X2)) = X1
      | ~ hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(cnf_transformation,[],[f3765]) ).

fof(f3765,plain,
    ! [X0,X1,X2] :
      ( ( sP7(X0,X1,X2)
        | ( ~ hBOOL(hAPP(X0,sK40(X0,X1,X2)))
          & c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,sK40(X0,X1,X2)) = X1 )
        | ( ~ hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ) )
      & ( ( ! [X4] :
              ( hBOOL(hAPP(X0,X4))
              | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X4) != X1 )
          & ( hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ) )
        | ~ sP7(X0,X1,X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK40])],[f3763,f3764]) ).

fof(f3764,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ~ hBOOL(hAPP(X0,X3))
          & c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3) = X1 )
     => ( ~ hBOOL(hAPP(X0,sK40(X0,X1,X2)))
        & c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,sK40(X0,X1,X2)) = X1 ) ),
    introduced(choice_axiom,[]) ).

fof(f3763,plain,
    ! [X0,X1,X2] :
      ( ( sP7(X0,X1,X2)
        | ? [X3] :
            ( ~ hBOOL(hAPP(X0,X3))
            & c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3) = X1 )
        | ( ~ hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ) )
      & ( ( ! [X4] :
              ( hBOOL(hAPP(X0,X4))
              | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X4) != X1 )
          & ( hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ) )
        | ~ sP7(X0,X1,X2) ) ),
    inference(rectify,[],[f3762]) ).

fof(f3762,plain,
    ! [X2,X1,X0] :
      ( ( sP7(X2,X1,X0)
        | ? [X3] :
            ( ~ hBOOL(hAPP(X2,X3))
            & c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3) = X1 )
        | ( ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) )
      & ( ( ! [X3] :
              ( hBOOL(hAPP(X2,X3))
              | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3) != X1 )
          & ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) )
        | ~ sP7(X2,X1,X0) ) ),
    inference(flattening,[],[f3761]) ).

fof(f3761,plain,
    ! [X2,X1,X0] :
      ( ( sP7(X2,X1,X0)
        | ? [X3] :
            ( ~ hBOOL(hAPP(X2,X3))
            & c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3) = X1 )
        | ( ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) )
      & ( ( ! [X3] :
              ( hBOOL(hAPP(X2,X3))
              | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3) != X1 )
          & ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) )
        | ~ sP7(X2,X1,X0) ) ),
    inference(nnf_transformation,[],[f3451]) ).

fof(f3451,plain,
    ! [X2,X1,X0] :
      ( sP7(X2,X1,X0)
    <=> ( ! [X3] :
            ( hBOOL(hAPP(X2,X3))
            | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3) != X1 )
        & ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).

fof(f20246,plain,
    spl50_1028,
    inference(avatar_split_clause,[],[f5142,f20244]) ).

fof(f20244,plain,
    ( spl50_1028
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless(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(tc_Nat_Onat,X2,X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1028])]) ).

fof(f5142,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless(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(tc_Nat_Onat,X2,X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
    inference(cnf_transformation,[],[f3033]) ).

fof(f3033,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(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(tc_Nat_Onat,X2,X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
    inference(flattening,[],[f3032]) ).

fof(f3032,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(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(tc_Nat_Onat,X2,X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
    inference(ennf_transformation,[],[f2012]) ).

fof(f2012,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
       => c_Orderings_Oord__class_Oless(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,[],[f452]) ).

fof(f452,axiom,
    ! [X51,X3,X17] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X3)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X51)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X51,X3),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X51,X17)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__less__mono2) ).

fof(f20242,plain,
    spl50_1027,
    inference(avatar_split_clause,[],[f5140,f20240]) ).

fof(f20240,plain,
    ( spl50_1027
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless(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,X0,X2)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1027])]) ).

fof(f5140,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless(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,X0,X2)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
    inference(cnf_transformation,[],[f3029]) ).

fof(f3029,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(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,X0,X2)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
    inference(flattening,[],[f3028]) ).

fof(f3028,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(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,X0,X2)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
    inference(ennf_transformation,[],[f2010]) ).

fof(f2010,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X2)
       => c_Orderings_Oord__class_Oless(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,[],[f478]) ).

fof(f478,axiom,
    ! [X23,X13,X4] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X13)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X23,X4)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4,X23),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X13,X23)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__less__mono) ).

fof(f20238,plain,
    spl50_1026,
    inference(avatar_split_clause,[],[f5130,f20236]) ).

fof(f20236,plain,
    ( spl50_1026
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),X1)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1026])]) ).

fof(f5130,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),X1)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    inference(cnf_transformation,[],[f3737]) ).

fof(f3737,plain,
    ! [X0,X1,X2] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),X1) )
        & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),X1)
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) ) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    inference(nnf_transformation,[],[f3018]) ).

fof(f3018,plain,
    ! [X0,X1,X2] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
      <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),X1) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    inference(ennf_transformation,[],[f2001]) ).

fof(f2001,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,X1,X2))
      <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),X1) ) ),
    inference(rectify,[],[f487]) ).

fof(f487,axiom,
    ! [X56,X55,X36] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,X55)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X56,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X55,X36))
      <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X56,X36),X55) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__diff__conv2) ).

fof(f20234,plain,
    spl50_1025,
    inference(avatar_split_clause,[],[f5114,f20232]) ).

fof(f20232,plain,
    ( spl50_1025
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1025])]) ).

fof(f5114,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    inference(cnf_transformation,[],[f3001]) ).

fof(f3001,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    inference(ennf_transformation,[],[f1989]) ).

fof(f1989,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)) ),
    inference(rectify,[],[f419]) ).

fof(f419,axiom,
    ! [X38,X39,X18] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X39)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X38),X18),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X38),X39)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__mono2) ).

fof(f20230,plain,
    spl50_1024,
    inference(avatar_split_clause,[],[f5113,f20228]) ).

fof(f20228,plain,
    ( spl50_1024
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1024])]) ).

fof(f5113,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    inference(cnf_transformation,[],[f3000]) ).

fof(f3000,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    inference(ennf_transformation,[],[f1988]) ).

fof(f1988,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ),
    inference(rectify,[],[f420]) ).

fof(f420,axiom,
    ! [X38,X39,X18] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X39)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18),X38),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X38)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__mono1) ).

fof(f20226,plain,
    spl50_1023,
    inference(avatar_split_clause,[],[f4928,f20224]) ).

fof(f20224,plain,
    ( spl50_1023
  <=> ! [X2,X0,X1] :
        ( hAPP(c_Polynomial_Opoly(X2,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),X1)),X0) = c_Groups_Ouminus__class_Ouminus(X2,hAPP(c_Polynomial_Opoly(X2,X1),X0))
        | ~ class_Rings_Ocomm__ring(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1023])]) ).

fof(f4928,plain,
    ! [X2,X0,X1] :
      ( hAPP(c_Polynomial_Opoly(X2,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),X1)),X0) = c_Groups_Ouminus__class_Ouminus(X2,hAPP(c_Polynomial_Opoly(X2,X1),X0))
      | ~ class_Rings_Ocomm__ring(X2) ),
    inference(cnf_transformation,[],[f2795]) ).

fof(f2795,plain,
    ! [X0,X1,X2] :
      ( hAPP(c_Polynomial_Opoly(X2,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),X1)),X0) = c_Groups_Ouminus__class_Ouminus(X2,hAPP(c_Polynomial_Opoly(X2,X1),X0))
      | ~ class_Rings_Ocomm__ring(X2) ),
    inference(ennf_transformation,[],[f1852]) ).

fof(f1852,plain,
    ! [X0,X1,X2] :
      ( class_Rings_Ocomm__ring(X2)
     => hAPP(c_Polynomial_Opoly(X2,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),X1)),X0) = c_Groups_Ouminus__class_Ouminus(X2,hAPP(c_Polynomial_Opoly(X2,X1),X0)) ),
    inference(rectify,[],[f650]) ).

fof(f650,axiom,
    ! [X9,X54,X5] :
      ( class_Rings_Ocomm__ring(X5)
     => hAPP(c_Polynomial_Opoly(X5,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X5),X54)),X9) = c_Groups_Ouminus__class_Ouminus(X5,hAPP(c_Polynomial_Opoly(X5,X54),X9)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__minus) ).

fof(f20222,plain,
    spl50_1022,
    inference(avatar_split_clause,[],[f4856,f20220]) ).

fof(f20220,plain,
    ( spl50_1022
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X2),c_Groups_Ozero__class_Ozero(X1))
        | ~ sP4(X2,X1,X0)
        | ~ sP5(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1022])]) ).

fof(f4856,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X2),c_Groups_Ozero__class_Ozero(X1))
      | ~ sP4(X2,X1,X0)
      | ~ sP5(X0,X1,X2) ),
    inference(cnf_transformation,[],[f3662]) ).

fof(f3662,plain,
    ! [X0,X1,X2] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X2),c_Groups_Ozero__class_Ozero(X1))
          | ~ sP4(X2,X1,X0) )
        & ( sP4(X2,X1,X0)
          | ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X2),c_Groups_Ozero__class_Ozero(X1)) ) )
      | ~ sP5(X0,X1,X2) ),
    inference(rectify,[],[f3661]) ).

fof(f3661,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) )
        & ( sP4(X0,X2,X1)
          | ~ c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),c_Groups_Ozero__class_Ozero(X2)) ) )
      | ~ sP5(X1,X2,X0) ),
    inference(nnf_transformation,[],[f3447]) ).

fof(f3447,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(f20218,plain,
    ( ~ spl50_201
    | ~ spl50_1021
    | ~ spl50_230
    | ~ spl50_446 ),
    inference(avatar_split_clause,[],[f8518,f8310,f7189,f20215,f7051]) ).

fof(f20215,plain,
    ( spl50_1021
  <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK18,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1021])]) ).

fof(f7189,plain,
    ( spl50_230
  <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK18) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_230])]) ).

fof(f8518,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK18,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    | ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
    | ~ spl50_230
    | ~ spl50_446 ),
    inference(resolution,[],[f8311,f7191]) ).

fof(f7191,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK18)
    | ~ spl50_230 ),
    inference(avatar_component_clause,[],[f7189]) ).

fof(f20213,plain,
    spl50_1020,
    inference(avatar_split_clause,[],[f4855,f20211]) ).

fof(f20211,plain,
    ( spl50_1020
  <=> ! [X2,X0,X1] :
        ( sP4(X2,X1,X0)
        | ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X2),c_Groups_Ozero__class_Ozero(X1))
        | ~ sP5(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1020])]) ).

fof(f4855,plain,
    ! [X2,X0,X1] :
      ( sP4(X2,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X2),c_Groups_Ozero__class_Ozero(X1))
      | ~ sP5(X0,X1,X2) ),
    inference(cnf_transformation,[],[f3662]) ).

fof(f20209,plain,
    spl50_1019,
    inference(avatar_split_clause,[],[f4847,f20207]) ).

fof(f20207,plain,
    ( spl50_1019
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1))
        | ~ sP2(X2,X1,X0)
        | ~ sP3(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1019])]) ).

fof(f4847,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1))
      | ~ sP2(X2,X1,X0)
      | ~ sP3(X0,X1,X2) ),
    inference(cnf_transformation,[],[f3657]) ).

fof(f3657,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),X0),X1))
          | ~ sP2(X2,X1,X0) )
        & ( sP2(X2,X1,X0)
          | ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1)) ) )
      | ~ sP3(X0,X1,X2) ),
    inference(rectify,[],[f3656]) ).

fof(f3656,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) )
        & ( sP2(X2,X0,X1)
          | ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) ) )
      | ~ sP3(X1,X0,X2) ),
    inference(nnf_transformation,[],[f3444]) ).

fof(f3444,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(f20205,plain,
    spl50_1018,
    inference(avatar_split_clause,[],[f4846,f20203]) ).

fof(f20203,plain,
    ( spl50_1018
  <=> ! [X2,X0,X1] :
        ( sP2(X2,X1,X0)
        | ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1))
        | ~ sP3(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1018])]) ).

fof(f4846,plain,
    ! [X2,X0,X1] :
      ( sP2(X2,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1))
      | ~ sP3(X0,X1,X2) ),
    inference(cnf_transformation,[],[f3657]) ).

fof(f20201,plain,
    spl50_1017,
    inference(avatar_split_clause,[],[f4834,f20199]) ).

fof(f20199,plain,
    ( spl50_1017
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,X1),c_RealVector_Onorm__class_Onorm(X2,X0)),c_RealVector_Onorm__class_Onorm(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0)))
        | ~ class_RealVector_Oreal__normed__vector(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1017])]) ).

fof(f4834,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,X1),c_RealVector_Onorm__class_Onorm(X2,X0)),c_RealVector_Onorm__class_Onorm(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0)))
      | ~ class_RealVector_Oreal__normed__vector(X2) ),
    inference(cnf_transformation,[],[f2728]) ).

fof(f2728,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,X1),c_RealVector_Onorm__class_Onorm(X2,X0)),c_RealVector_Onorm__class_Onorm(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0)))
      | ~ class_RealVector_Oreal__normed__vector(X2) ),
    inference(ennf_transformation,[],[f1800]) ).

fof(f1800,plain,
    ! [X0,X1,X2] :
      ( class_RealVector_Oreal__normed__vector(X2)
     => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,X1),c_RealVector_Onorm__class_Onorm(X2,X0)),c_RealVector_Onorm__class_Onorm(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0))) ),
    inference(rectify,[],[f494]) ).

fof(f494,axiom,
    ! [X13,X4,X5] :
      ( class_RealVector_Oreal__normed__vector(X5)
     => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,X4),c_RealVector_Onorm__class_Onorm(X5,X13)),c_RealVector_Onorm__class_Onorm(X5,c_Groups_Oplus__class_Oplus(X5,X4,X13))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__diff__ineq) ).

fof(f20197,plain,
    spl50_1016,
    inference(avatar_split_clause,[],[f4833,f20195]) ).

fof(f20195,plain,
    ( spl50_1016
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,X1),c_RealVector_Onorm__class_Onorm(X2,X0)),c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0)))
        | ~ class_RealVector_Oreal__normed__vector(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1016])]) ).

fof(f4833,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,X1),c_RealVector_Onorm__class_Onorm(X2,X0)),c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0)))
      | ~ class_RealVector_Oreal__normed__vector(X2) ),
    inference(cnf_transformation,[],[f2727]) ).

fof(f2727,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,X1),c_RealVector_Onorm__class_Onorm(X2,X0)),c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0)))
      | ~ class_RealVector_Oreal__normed__vector(X2) ),
    inference(ennf_transformation,[],[f1799]) ).

fof(f1799,plain,
    ! [X0,X1,X2] :
      ( class_RealVector_Oreal__normed__vector(X2)
     => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,X1),c_RealVector_Onorm__class_Onorm(X2,X0)),c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0))) ),
    inference(rectify,[],[f282]) ).

fof(f282,axiom,
    ! [X13,X4,X5] :
      ( class_RealVector_Oreal__normed__vector(X5)
     => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,X4),c_RealVector_Onorm__class_Onorm(X5,X13)),c_RealVector_Onorm__class_Onorm(X5,c_Groups_Ominus__class_Ominus(X5,X4,X13))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__triangle__ineq2) ).

fof(f20193,plain,
    spl50_1015,
    inference(avatar_split_clause,[],[f4832,f20191]) ).

fof(f20191,plain,
    ( spl50_1015
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,X1),c_RealVector_Onorm__class_Onorm(X2,X0)))
        | ~ class_RealVector_Oreal__normed__vector(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1015])]) ).

fof(f4832,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,X1),c_RealVector_Onorm__class_Onorm(X2,X0)))
      | ~ class_RealVector_Oreal__normed__vector(X2) ),
    inference(cnf_transformation,[],[f2726]) ).

fof(f2726,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,X1),c_RealVector_Onorm__class_Onorm(X2,X0)))
      | ~ class_RealVector_Oreal__normed__vector(X2) ),
    inference(ennf_transformation,[],[f1798]) ).

fof(f1798,plain,
    ! [X0,X1,X2] :
      ( class_RealVector_Oreal__normed__vector(X2)
     => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,X1),c_RealVector_Onorm__class_Onorm(X2,X0))) ),
    inference(rectify,[],[f53]) ).

fof(f53,axiom,
    ! [X7,X9,X5] :
      ( class_RealVector_Oreal__normed__vector(X5)
     => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,c_Groups_Oplus__class_Oplus(X5,X9,X7)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,X9),c_RealVector_Onorm__class_Onorm(X5,X7))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__triangle__ineq) ).

fof(f20189,plain,
    spl50_1014,
    inference(avatar_split_clause,[],[f4831,f20187]) ).

fof(f20187,plain,
    ( spl50_1014
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,X1),c_RealVector_Onorm__class_Onorm(X2,X0)))
        | ~ class_RealVector_Oreal__normed__vector(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1014])]) ).

fof(f4831,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,X1),c_RealVector_Onorm__class_Onorm(X2,X0)))
      | ~ class_RealVector_Oreal__normed__vector(X2) ),
    inference(cnf_transformation,[],[f2725]) ).

fof(f2725,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,X1),c_RealVector_Onorm__class_Onorm(X2,X0)))
      | ~ class_RealVector_Oreal__normed__vector(X2) ),
    inference(ennf_transformation,[],[f1797]) ).

fof(f1797,plain,
    ! [X0,X1,X2] :
      ( class_RealVector_Oreal__normed__vector(X2)
     => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,X1),c_RealVector_Onorm__class_Onorm(X2,X0))) ),
    inference(rectify,[],[f352]) ).

fof(f352,axiom,
    ! [X13,X4,X5] :
      ( class_RealVector_Oreal__normed__vector(X5)
     => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,c_Groups_Ominus__class_Ominus(X5,X4,X13)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,X4),c_RealVector_Onorm__class_Onorm(X5,X13))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__triangle__ineq4) ).

fof(f20185,plain,
    spl50_1013,
    inference(avatar_split_clause,[],[f4740,f20183]) ).

fof(f20183,plain,
    ( spl50_1013
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,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_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1013])]) ).

fof(f4740,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,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_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) ),
    inference(cnf_transformation,[],[f3631]) ).

fof(f3631,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
        | ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,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_Orderings_Oord__class_Oless(tc_Nat_Onat,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_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) ) ),
    inference(flattening,[],[f3630]) ).

fof(f3630,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
        | ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,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_Orderings_Oord__class_Oless(tc_Nat_Onat,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_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) ) ),
    inference(nnf_transformation,[],[f1732]) ).

fof(f1732,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
    <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,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) ) ),
    inference(rectify,[],[f427]) ).

fof(f427,axiom,
    ! [X16,X32] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X32,X16))
    <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X16)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X32) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__gr__0) ).

fof(f20181,plain,
    spl50_1012,
    inference(avatar_split_clause,[],[f4619,f20179]) ).

fof(f20179,plain,
    ( spl50_1012
  <=> ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),X0)
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
        | ~ class_Rings_Osemiring__0(X1)
        | ~ class_Power_Opower(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1012])]) ).

fof(f4619,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),X0)
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
      | ~ class_Rings_Osemiring__0(X1)
      | ~ class_Power_Opower(X1) ),
    inference(cnf_transformation,[],[f2658]) ).

fof(f2658,plain,
    ! [X0,X1] :
      ( ( ( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),X0)
          | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
        & ( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),X0)
          | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) )
      | ~ class_Rings_Osemiring__0(X1)
      | ~ class_Power_Opower(X1) ),
    inference(flattening,[],[f2657]) ).

fof(f2657,plain,
    ! [X0,X1] :
      ( ( ( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),X0)
          | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
        & ( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),X0)
          | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) )
      | ~ class_Rings_Osemiring__0(X1)
      | ~ class_Power_Opower(X1) ),
    inference(ennf_transformation,[],[f1681]) ).

fof(f1681,plain,
    ! [X0,X1] :
      ( ( class_Rings_Osemiring__0(X1)
        & class_Power_Opower(X1) )
     => ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
         => c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),X0) )
        & ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
         => c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),X0) ) ) ),
    inference(rectify,[],[f148]) ).

fof(f148,axiom,
    ! [X3,X5] :
      ( ( class_Rings_Osemiring__0(X5)
        & class_Power_Opower(X5) )
     => ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X3
         => c_Groups_Ozero__class_Ozero(X5) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),c_Groups_Ozero__class_Ozero(X5)),X3) )
        & ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X3
         => c_Groups_Oone__class_Oone(X5) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),c_Groups_Ozero__class_Ozero(X5)),X3) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__0__left) ).

fof(f20177,plain,
    spl50_1011,
    inference(avatar_split_clause,[],[f4601,f20175]) ).

fof(f20175,plain,
    ( spl50_1011
  <=> ! [X0,X1] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(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,[spl50_1011])]) ).

fof(f4601,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(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,[],[f3556]) ).

fof(f3556,plain,
    ! [X0,X1] :
      ( ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1),X1)
          | c_Groups_Oone__class_Oone(tc_Nat_Onat) != X0 )
        & ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
          | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1),X1) ) )
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(nnf_transformation,[],[f2633]) ).

fof(f2633,plain,
    ! [X0,X1] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1),X1)
      <=> 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),X1) ),
    inference(ennf_transformation,[],[f1666]) ).

fof(f1666,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1),X1)
      <=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0 ) ),
    inference(rectify,[],[f878]) ).

fof(f878,axiom,
    ! [X16,X32] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X32)
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16),X32),X32)
      <=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = X16 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult__cancel2) ).

fof(f20168,plain,
    spl50_1010,
    inference(avatar_split_clause,[],[f4599,f20166]) ).

fof(f20166,plain,
    ( spl50_1010
  <=> ! [X0,X1] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0),X1)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1010])]) ).

fof(f4599,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0),X1)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(cnf_transformation,[],[f3555]) ).

fof(f3555,plain,
    ! [X0,X1] :
      ( ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0),X1)
          | c_Groups_Oone__class_Oone(tc_Nat_Onat) != X0 )
        & ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
          | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0),X1) ) )
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(nnf_transformation,[],[f2632]) ).

fof(f2632,plain,
    ! [X0,X1] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0),X1)
      <=> 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),X1) ),
    inference(ennf_transformation,[],[f1665]) ).

fof(f1665,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0),X1)
      <=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0 ) ),
    inference(rectify,[],[f877]) ).

fof(f877,axiom,
    ! [X16,X32] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X32)
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X32),X16),X32)
      <=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = X16 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult__cancel1) ).

fof(f20164,plain,
    spl50_1009,
    inference(avatar_split_clause,[],[f4594,f20162]) ).

fof(f20162,plain,
    ( spl50_1009
  <=> ! [X0,X1] :
        ( c_Groups_Oone__class_Oone(tc_Int_Oint) = X0
        | c_Groups_Oone__class_Oone(tc_Int_Oint) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1009])]) ).

fof(f4594,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(tc_Int_Oint) = X0
      | c_Groups_Oone__class_Oone(tc_Int_Oint) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(cnf_transformation,[],[f3554]) ).

fof(f3554,plain,
    ! [X0,X1] :
      ( ( ( c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0)
          | c_Groups_Oone__class_Oone(tc_Int_Oint) != X0
          | c_Groups_Oone__class_Oone(tc_Int_Oint) != X1 )
        & ( ( c_Groups_Oone__class_Oone(tc_Int_Oint) = X0
            & c_Groups_Oone__class_Oone(tc_Int_Oint) = X1 )
          | c_Groups_Oone__class_Oone(tc_Int_Oint) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0) ) )
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(flattening,[],[f3553]) ).

fof(f3553,plain,
    ! [X0,X1] :
      ( ( ( c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0)
          | c_Groups_Oone__class_Oone(tc_Int_Oint) != X0
          | c_Groups_Oone__class_Oone(tc_Int_Oint) != X1 )
        & ( ( c_Groups_Oone__class_Oone(tc_Int_Oint) = X0
            & c_Groups_Oone__class_Oone(tc_Int_Oint) = X1 )
          | c_Groups_Oone__class_Oone(tc_Int_Oint) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0) ) )
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(nnf_transformation,[],[f2625]) ).

fof(f2625,plain,
    ! [X0,X1] :
      ( ( c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0)
      <=> ( c_Groups_Oone__class_Oone(tc_Int_Oint) = X0
          & c_Groups_Oone__class_Oone(tc_Int_Oint) = X1 ) )
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(ennf_transformation,[],[f1661]) ).

fof(f1661,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
     => ( c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0)
      <=> ( c_Groups_Oone__class_Oone(tc_Int_Oint) = X0
          & c_Groups_Oone__class_Oone(tc_Int_Oint) = X1 ) ) ),
    inference(rectify,[],[f585]) ).

fof(f585,axiom,
    ! [X16,X32] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X32)
     => ( c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X32),X16)
      <=> ( c_Groups_Oone__class_Oone(tc_Int_Oint) = X16
          & c_Groups_Oone__class_Oone(tc_Int_Oint) = X32 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__zmult__eq__1__iff) ).

fof(f20160,plain,
    spl50_1008,
    inference(avatar_split_clause,[],[f4593,f20158]) ).

fof(f20158,plain,
    ( spl50_1008
  <=> ! [X0,X1] :
        ( c_Groups_Oone__class_Oone(tc_Int_Oint) = X1
        | c_Groups_Oone__class_Oone(tc_Int_Oint) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1008])]) ).

fof(f4593,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(tc_Int_Oint) = X1
      | c_Groups_Oone__class_Oone(tc_Int_Oint) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(cnf_transformation,[],[f3554]) ).

fof(f20156,plain,
    spl50_1007,
    inference(avatar_split_clause,[],[f4588,f20154]) ).

fof(f20154,plain,
    ( spl50_1007
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1007])]) ).

fof(f4588,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(cnf_transformation,[],[f2616]) ).

fof(f2616,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(flattening,[],[f2615]) ).

fof(f2615,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(ennf_transformation,[],[f1656]) ).

fof(f1656,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_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
       => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) ) ),
    inference(rectify,[],[f696]) ).

fof(f696,axiom,
    ! [X7,X9] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X9)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X7)
       => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X9,X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).

fof(f20152,plain,
    spl50_1006,
    inference(avatar_split_clause,[],[f4529,f20150]) ).

fof(f20150,plain,
    ( spl50_1006
  <=> ! [X0,X1] :
        ( c_Groups_Oplus__class_Oplus(X1,X0,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1))),X0)
        | ~ class_Rings_Ocomm__semiring__1(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1006])]) ).

fof(f4529,plain,
    ! [X0,X1] :
      ( c_Groups_Oplus__class_Oplus(X1,X0,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1))),X0)
      | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(cnf_transformation,[],[f2547]) ).

fof(f2547,plain,
    ! [X0,X1] :
      ( c_Groups_Oplus__class_Oplus(X1,X0,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1))),X0)
      | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(ennf_transformation,[],[f1605]) ).

fof(f1605,plain,
    ! [X0,X1] :
      ( class_Rings_Ocomm__semiring__1(X1)
     => c_Groups_Oplus__class_Oplus(X1,X0,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1))),X0) ),
    inference(rectify,[],[f544]) ).

fof(f544,axiom,
    ! [X17,X5] :
      ( class_Rings_Ocomm__semiring__1(X5)
     => c_Groups_Oplus__class_Oplus(X5,X17,X17) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Oplus__class_Oplus(X5,c_Groups_Oone__class_Oone(X5),c_Groups_Oone__class_Oone(X5))),X17) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).

fof(f20148,plain,
    spl50_1005,
    inference(avatar_split_clause,[],[f4372,f20146]) ).

fof(f20146,plain,
    ( spl50_1005
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
        | c_Groups_Ozero__class_Ozero(X1) = X0
        | ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Ozero__class_Ozero(X1))
        | ~ class_Fields_Olinordered__field(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1005])]) ).

fof(f4372,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
      | c_Groups_Ozero__class_Ozero(X1) = X0
      | ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Ozero__class_Ozero(X1))
      | ~ class_Fields_Olinordered__field(X1) ),
    inference(cnf_transformation,[],[f2421]) ).

fof(f2421,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
      | c_Groups_Ozero__class_Ozero(X1) = X0
      | ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Ozero__class_Ozero(X1))
      | ~ class_Fields_Olinordered__field(X1) ),
    inference(flattening,[],[f2420]) ).

fof(f2420,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
      | c_Groups_Ozero__class_Ozero(X1) = X0
      | ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Ozero__class_Ozero(X1))
      | ~ class_Fields_Olinordered__field(X1) ),
    inference(ennf_transformation,[],[f1490]) ).

fof(f1490,plain,
    ! [X0,X1] :
      ( class_Fields_Olinordered__field(X1)
     => ( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Ozero__class_Ozero(X1))
       => ( c_Groups_Ozero__class_Ozero(X1) != X0
         => c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ) ) ),
    inference(rectify,[],[f155]) ).

fof(f155,axiom,
    ! [X4,X5] :
      ( class_Fields_Olinordered__field(X5)
     => ( c_Orderings_Oord__class_Oless(X5,c_Rings_Oinverse__class_Oinverse(X5,X4),c_Groups_Ozero__class_Ozero(X5))
       => ( c_Groups_Ozero__class_Ozero(X5) != X4
         => c_Orderings_Oord__class_Oless(X5,X4,c_Groups_Ozero__class_Ozero(X5)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__negative__imp__negative) ).

fof(f20144,plain,
    spl50_1004,
    inference(avatar_split_clause,[],[f4371,f20142]) ).

fof(f20142,plain,
    ( spl50_1004
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
        | c_Groups_Ozero__class_Ozero(X1) = X0
        | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
        | ~ class_Fields_Olinordered__field(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1004])]) ).

fof(f4371,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
      | c_Groups_Ozero__class_Ozero(X1) = X0
      | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
      | ~ class_Fields_Olinordered__field(X1) ),
    inference(cnf_transformation,[],[f2419]) ).

fof(f2419,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
      | c_Groups_Ozero__class_Ozero(X1) = X0
      | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
      | ~ class_Fields_Olinordered__field(X1) ),
    inference(flattening,[],[f2418]) ).

fof(f2418,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
      | c_Groups_Ozero__class_Ozero(X1) = X0
      | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
      | ~ class_Fields_Olinordered__field(X1) ),
    inference(ennf_transformation,[],[f1489]) ).

fof(f1489,plain,
    ! [X0,X1] :
      ( class_Fields_Olinordered__field(X1)
     => ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
       => ( c_Groups_Ozero__class_Ozero(X1) != X0
         => c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) ) ) ),
    inference(rectify,[],[f159]) ).

fof(f159,axiom,
    ! [X4,X5] :
      ( class_Fields_Olinordered__field(X5)
     => ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),c_Rings_Oinverse__class_Oinverse(X5,X4))
       => ( c_Groups_Ozero__class_Ozero(X5) != X4
         => c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X4) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__positive__imp__positive) ).

fof(f20140,plain,
    spl50_1003,
    inference(avatar_split_clause,[],[f4282,f20138]) ).

fof(f20138,plain,
    ( spl50_1003
  <=> ! [X0] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),X0)),v_m____)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1003])]) ).

fof(f4282,plain,
    ! [X0] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),X0)),v_m____)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ),
    inference(cnf_transformation,[],[f2396]) ).

fof(f2396,plain,
    ! [X0] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),X0)),v_m____)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ),
    inference(ennf_transformation,[],[f1423]) ).

fof(f1423,plain,
    ! [X0] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
     => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),X0)),v_m____) ),
    inference(rectify,[],[f183]) ).

fof(f183,axiom,
    ! [X34] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X34),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
     => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),X34)),v_m____) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_m_I2_J) ).

fof(f20136,plain,
    spl50_1002,
    inference(avatar_split_clause,[],[f4129,f20134]) ).

fof(f20134,plain,
    ( spl50_1002
  <=> ! [X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),X1)),sK18)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1002])]) ).

fof(f4129,plain,
    ! [X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),X1)),sK18)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ),
    inference(cnf_transformation,[],[f3471]) ).

fof(f3471,plain,
    ( ! [X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),X1)),sK18)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) )
    & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK18) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f2302,f3470]) ).

fof(f3470,plain,
    ( ? [X0] :
        ( ! [X1] :
            ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),X1)),X0)
            | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) )
        & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) )
   => ( ! [X1] :
          ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),X1)),sK18)
          | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) )
      & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK18) ) ),
    introduced(choice_axiom,[]) ).

fof(f2302,plain,
    ? [X0] :
      ( ! [X1] :
          ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),X1)),X0)
          | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) )
      & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ),
    inference(ennf_transformation,[],[f1278]) ).

fof(f1278,plain,
    ~ ! [X0] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
       => ~ ! [X1] :
              ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
             => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),X1)),X0) ) ),
    inference(rectify,[],[f552]) ).

fof(f552,axiom,
    ~ ! [X44] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X44)
       => ~ ! [X34] :
              ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X34),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
             => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),X34)),X44) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_Bm_O_A_091_124_A0_A_060_Am_059_AALL_Az_O_Acmod_Az_A_060_061_Acmod_Aw_A_N_N_062_Acmod_A_Ipoly_As_Az_J_A_060_061_Am_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).

fof(f20131,plain,
    spl50_1001,
    inference(avatar_split_clause,[],[f4127,f20128]) ).

fof(f4127,plain,
    c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),sK17),v_k____)),v_a____)),
    inference(cnf_transformation,[],[f3469]) ).

fof(f3469,plain,
    c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),sK17),v_k____)),v_a____)),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f2301,f3468]) ).

fof(f3468,plain,
    ( ? [X0] : c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),v_k____)),v_a____))
   => c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),sK17),v_k____)),v_a____)) ),
    introduced(choice_axiom,[]) ).

fof(f2301,plain,
    ? [X0] : c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),v_k____)),v_a____)),
    inference(ennf_transformation,[],[f1277]) ).

fof(f1277,plain,
    ~ ! [X0] : c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),v_k____)),v_a____)),
    inference(rectify,[],[f262]) ).

fof(f262,axiom,
    ~ ! [X43] : c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X43),v_k____)),v_a____)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_Bw_O_A1_A_L_Aw_A_094_Ak_A_K_Aa_A_061_A0_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).

fof(f20126,plain,
    ( ~ spl50_201
    | ~ spl50_1000
    | ~ spl50_229
    | ~ spl50_446 ),
    inference(avatar_split_clause,[],[f8517,f8310,f7184,f20123,f7051]) ).

fof(f20123,plain,
    ( spl50_1000
  <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_m____,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1000])]) ).

fof(f8517,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_m____,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    | ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
    | ~ spl50_229
    | ~ spl50_446 ),
    inference(resolution,[],[f8311,f7186]) ).

fof(f7186,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____)
    | ~ spl50_229 ),
    inference(avatar_component_clause,[],[f7184]) ).

fof(f19159,plain,
    ( spl50_999
    | ~ spl50_393
    | ~ spl50_957 ),
    inference(avatar_split_clause,[],[f18894,f18891,f7913,f19157]) ).

fof(f19157,plain,
    ( spl50_999
  <=> ! [X0] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_999])]) ).

fof(f7913,plain,
    ( spl50_393
  <=> ! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_393])]) ).

fof(f18891,plain,
    ( spl50_957
  <=> ! [X0] :
        ( c_Orderings_Oord__class_Oless(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),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_957])]) ).

fof(f18894,plain,
    ( ! [X0] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
    | ~ spl50_393
    | ~ spl50_957 ),
    inference(forward_demodulation,[],[f18892,f7914]) ).

fof(f7914,plain,
    ( ! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)
    | ~ spl50_393 ),
    inference(avatar_component_clause,[],[f7913]) ).

fof(f18892,plain,
    ( ! [X0] :
        ( c_Orderings_Oord__class_Oless(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),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
    | ~ spl50_957 ),
    inference(avatar_component_clause,[],[f18891]) ).

fof(f19155,plain,
    ( ~ spl50_86
    | spl50_998
    | ~ spl50_444
    | ~ spl50_950 ),
    inference(avatar_split_clause,[],[f17433,f17338,f8302,f19153,f6476]) ).

fof(f6476,plain,
    ( spl50_86
  <=> class_Orderings_Olinorder(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_86])]) ).

fof(f19153,plain,
    ( spl50_998
  <=> ! [X0] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_998])]) ).

fof(f8302,plain,
    ( spl50_444
  <=> ! [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,[spl50_444])]) ).

fof(f17338,plain,
    ( spl50_950
  <=> ! [X0] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_950])]) ).

fof(f17433,plain,
    ( ! [X0] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))
        | ~ class_Orderings_Olinorder(tc_RealDef_Oreal) )
    | ~ spl50_444
    | ~ spl50_950 ),
    inference(resolution,[],[f17339,f8303]) ).

fof(f8303,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
        | ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
        | ~ class_Orderings_Olinorder(X2) )
    | ~ spl50_444 ),
    inference(avatar_component_clause,[],[f8302]) ).

fof(f17339,plain,
    ( ! [X0] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X0)
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
    | ~ spl50_950 ),
    inference(avatar_component_clause,[],[f17338]) ).

fof(f19151,plain,
    ( spl50_997
    | ~ spl50_393
    | ~ spl50_956 ),
    inference(avatar_split_clause,[],[f18889,f18886,f7913,f19149]) ).

fof(f19149,plain,
    ( spl50_997
  <=> ! [X0] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_997])]) ).

fof(f18886,plain,
    ( spl50_956
  <=> ! [X0] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless(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),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_956])]) ).

fof(f18889,plain,
    ( ! [X0] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
    | ~ spl50_393
    | ~ spl50_956 ),
    inference(forward_demodulation,[],[f18887,f7914]) ).

fof(f18887,plain,
    ( ! [X0] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless(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),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
    | ~ spl50_956 ),
    inference(avatar_component_clause,[],[f18886]) ).

fof(f19077,plain,
    spl50_996,
    inference(avatar_split_clause,[],[f6006,f19075]) ).

fof(f19075,plain,
    ( spl50_996
  <=> ! [X0,X1] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0)
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_996])]) ).

fof(f6006,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0)
      | c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
    inference(forward_demodulation,[],[f6005,f4161]) ).

fof(f6005,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_Oone__class_Oone(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) = X0 ),
    inference(forward_demodulation,[],[f6004,f4313]) ).

fof(f6004,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
      | 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)) ),
    inference(forward_demodulation,[],[f6003,f4161]) ).

fof(f6003,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) = X0
      | 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)) ),
    inference(forward_demodulation,[],[f5666,f4313]) ).

fof(f5666,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)) = X1
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
      | 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)) ),
    inference(definition_unfolding,[],[f4754,f4164,f4164]) ).

fof(f4754,plain,
    ! [X0,X1] :
      ( 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(cnf_transformation,[],[f3640]) ).

fof(f3640,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,[],[f3639]) ).

fof(f3639,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,[],[f1737]) ).

fof(f1737,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,[],[f948]) ).

fof(f948,axiom,
    ! [X32,X12] :
      ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X12),X32)
    <=> ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X12
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X32 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__power__eq__Suc__0__iff) ).

fof(f19073,plain,
    spl50_995,
    inference(avatar_split_clause,[],[f5929,f19071]) ).

fof(f19071,plain,
    ( spl50_995
  <=> ! [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_Oone__class_Oone(tc_Nat_Onat)))
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_995])]) ).

fof(f5929,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_Oone__class_Oone(tc_Nat_Onat)))
      | c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
    inference(forward_demodulation,[],[f5928,f4161]) ).

fof(f5928,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_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(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 ),
    inference(forward_demodulation,[],[f5927,f5579]) ).

fof(f5579,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,[],[f4165,f4164]) ).

fof(f4165,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,[],[f1313]) ).

fof(f1313,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,[],[f943]) ).

fof(f943,axiom,
    ! [X3] : c_Nat_OSuc(X3) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).

fof(f5927,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_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
      | c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
    inference(forward_demodulation,[],[f5926,f5579]) ).

fof(f5926,plain,
    ! [X0] :
      ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = 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_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(forward_demodulation,[],[f5925,f4161]) ).

fof(f5925,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)) = 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_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(forward_demodulation,[],[f5582,f5579]) ).

fof(f5582,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)) = 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_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(definition_unfolding,[],[f4281,f4164,f4164,f4164]) ).

fof(f4281,plain,
    ! [X0] :
      ( c_Nat_OSuc(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_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
    inference(cnf_transformation,[],[f2395]) ).

fof(f2395,plain,
    ! [X0] :
      ( c_Nat_OSuc(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_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
    inference(flattening,[],[f2394]) ).

fof(f2394,plain,
    ! [X0] :
      ( c_Nat_OSuc(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_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
    inference(ennf_transformation,[],[f1422]) ).

fof(f1422,plain,
    ! [X0] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
     => ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) ),
    inference(rectify,[],[f960]) ).

fof(f960,axiom,
    ! [X9] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X9,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
     => ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X9
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X9 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__lt__two__imp__zero__or__one) ).

fof(f19069,plain,
    spl50_994,
    inference(avatar_split_clause,[],[f5904,f19067]) ).

fof(f19067,plain,
    ( spl50_994
  <=> ! [X2] :
        ( c_Groups_Ozero__class_Ozero(X2) = c_Groups_Oplus__class_Oplus(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Ozero__class_Ozero(X2))
        | ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Ozero__class_Ozero(X2))
        | ~ class_Groups_Oordered__comm__monoid__add(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_994])]) ).

fof(f5904,plain,
    ! [X2] :
      ( c_Groups_Ozero__class_Ozero(X2) = c_Groups_Oplus__class_Oplus(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Ozero__class_Ozero(X2))
      | ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Ozero__class_Ozero(X2))
      | ~ class_Groups_Oordered__comm__monoid__add(X2) ),
    inference(duplicate_literal_removal,[],[f5804]) ).

fof(f5804,plain,
    ! [X2] :
      ( c_Groups_Ozero__class_Ozero(X2) = c_Groups_Oplus__class_Oplus(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Ozero__class_Ozero(X2))
      | ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Ozero__class_Ozero(X2))
      | ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Ozero__class_Ozero(X2))
      | ~ class_Groups_Oordered__comm__monoid__add(X2) ),
    inference(equality_resolution,[],[f5803]) ).

fof(f5803,plain,
    ! [X2,X1] :
      ( c_Groups_Ozero__class_Ozero(X2) = c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Ozero__class_Ozero(X2))
      | c_Groups_Ozero__class_Ozero(X2) != X1
      | ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Ozero__class_Ozero(X2))
      | ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
      | ~ class_Groups_Oordered__comm__monoid__add(X2) ),
    inference(equality_resolution,[],[f4934]) ).

fof(f4934,plain,
    ! [X2,X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X2) = c_Groups_Oplus__class_Oplus(X2,X1,X0)
      | c_Groups_Ozero__class_Ozero(X2) != X0
      | 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,c_Groups_Ozero__class_Ozero(X2),X1)
      | ~ class_Groups_Oordered__comm__monoid__add(X2) ),
    inference(cnf_transformation,[],[f3690]) ).

fof(f3690,plain,
    ! [X0,X1,X2] :
      ( ( ( c_Groups_Ozero__class_Ozero(X2) = c_Groups_Oplus__class_Oplus(X2,X1,X0)
          | 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 )
          | c_Groups_Ozero__class_Ozero(X2) != c_Groups_Oplus__class_Oplus(X2,X1,X0) ) )
      | ~ 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_Groups_Oordered__comm__monoid__add(X2) ),
    inference(flattening,[],[f3689]) ).

fof(f3689,plain,
    ! [X0,X1,X2] :
      ( ( ( c_Groups_Ozero__class_Ozero(X2) = c_Groups_Oplus__class_Oplus(X2,X1,X0)
          | 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 )
          | c_Groups_Ozero__class_Ozero(X2) != c_Groups_Oplus__class_Oplus(X2,X1,X0) ) )
      | ~ 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_Groups_Oordered__comm__monoid__add(X2) ),
    inference(nnf_transformation,[],[f2803]) ).

fof(f2803,plain,
    ! [X0,X1,X2] :
      ( ( c_Groups_Ozero__class_Ozero(X2) = c_Groups_Oplus__class_Oplus(X2,X1,X0)
      <=> ( c_Groups_Ozero__class_Ozero(X2) = X0
          & 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,c_Groups_Ozero__class_Ozero(X2),X1)
      | ~ class_Groups_Oordered__comm__monoid__add(X2) ),
    inference(flattening,[],[f2802]) ).

fof(f2802,plain,
    ! [X0,X1,X2] :
      ( ( c_Groups_Ozero__class_Ozero(X2) = c_Groups_Oplus__class_Oplus(X2,X1,X0)
      <=> ( c_Groups_Ozero__class_Ozero(X2) = X0
          & 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,c_Groups_Ozero__class_Ozero(X2),X1)
      | ~ class_Groups_Oordered__comm__monoid__add(X2) ),
    inference(ennf_transformation,[],[f1856]) ).

fof(f1856,plain,
    ! [X0,X1,X2] :
      ( class_Groups_Oordered__comm__monoid__add(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_Groups_Ozero__class_Ozero(X2) = c_Groups_Oplus__class_Oplus(X2,X1,X0)
          <=> ( c_Groups_Ozero__class_Ozero(X2) = X0
              & c_Groups_Ozero__class_Ozero(X2) = X1 ) ) ) ) ),
    inference(rectify,[],[f244]) ).

fof(f244,axiom,
    ! [X20,X12,X5] :
      ( class_Groups_Oordered__comm__monoid__add(X5)
     => ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X12)
       => ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X20)
         => ( c_Groups_Ozero__class_Ozero(X5) = c_Groups_Oplus__class_Oplus(X5,X12,X20)
          <=> ( c_Groups_Ozero__class_Ozero(X5) = X20
              & c_Groups_Ozero__class_Ozero(X5) = X12 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonneg__eq__0__iff) ).

fof(f19065,plain,
    spl50_993,
    inference(avatar_split_clause,[],[f5718,f19063]) ).

fof(f19063,plain,
    ( spl50_993
  <=> ! [X1] :
        ( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))),c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1)))
        | ~ class_Rings_Oring__1__no__zero__divisors(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_993])]) ).

fof(f5718,plain,
    ! [X1] :
      ( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))),c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1)))
      | ~ class_Rings_Oring__1__no__zero__divisors(X1) ),
    inference(equality_resolution,[],[f4470]) ).

fof(f4470,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
      | ~ class_Rings_Oring__1__no__zero__divisors(X1) ),
    inference(cnf_transformation,[],[f3538]) ).

fof(f19061,plain,
    spl50_992,
    inference(avatar_split_clause,[],[f5465,f19059]) ).

fof(f19059,plain,
    ( spl50_992
  <=> ! [X0,X3,X2,X1] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_992])]) ).

fof(f5465,plain,
    ! [X2,X3,X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2) ),
    inference(cnf_transformation,[],[f3340]) ).

fof(f3340,plain,
    ! [X0,X1,X2,X3] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2) ),
    inference(flattening,[],[f3339]) ).

fof(f3339,plain,
    ! [X0,X1,X2,X3] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2) ),
    inference(ennf_transformation,[],[f2226]) ).

fof(f2226,plain,
    ! [X0,X1,X2,X3] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
     => ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X0)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
    inference(rectify,[],[f391]) ).

fof(f391,axiom,
    ! [X3,X17,X51,X38] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X38,X51)
     => ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X51) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X38,X3)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X3) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__eq__less) ).

fof(f19057,plain,
    spl50_991,
    inference(avatar_split_clause,[],[f5434,f19055]) ).

fof(f19055,plain,
    ( spl50_991
  <=> ! [X0,X3,X2,X1] :
        ( c_Rings_Odvd__class_Odvd(X3,X2,c_Groups_Oplus__class_Oplus(X3,X1,X0))
        | ~ c_Rings_Odvd__class_Odvd(X3,X2,X0)
        | ~ c_Rings_Odvd__class_Odvd(X3,X2,X1)
        | ~ class_Rings_Ocomm__semiring__1(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_991])]) ).

fof(f5434,plain,
    ! [X2,X3,X0,X1] :
      ( c_Rings_Odvd__class_Odvd(X3,X2,c_Groups_Oplus__class_Oplus(X3,X1,X0))
      | ~ c_Rings_Odvd__class_Odvd(X3,X2,X0)
      | ~ c_Rings_Odvd__class_Odvd(X3,X2,X1)
      | ~ class_Rings_Ocomm__semiring__1(X3) ),
    inference(cnf_transformation,[],[f3287]) ).

fof(f3287,plain,
    ! [X0,X1,X2,X3] :
      ( c_Rings_Odvd__class_Odvd(X3,X2,c_Groups_Oplus__class_Oplus(X3,X1,X0))
      | ~ c_Rings_Odvd__class_Odvd(X3,X2,X0)
      | ~ c_Rings_Odvd__class_Odvd(X3,X2,X1)
      | ~ class_Rings_Ocomm__semiring__1(X3) ),
    inference(flattening,[],[f3286]) ).

fof(f3286,plain,
    ! [X0,X1,X2,X3] :
      ( c_Rings_Odvd__class_Odvd(X3,X2,c_Groups_Oplus__class_Oplus(X3,X1,X0))
      | ~ c_Rings_Odvd__class_Odvd(X3,X2,X0)
      | ~ c_Rings_Odvd__class_Odvd(X3,X2,X1)
      | ~ class_Rings_Ocomm__semiring__1(X3) ),
    inference(ennf_transformation,[],[f2198]) ).

fof(f2198,plain,
    ! [X0,X1,X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => ( c_Rings_Odvd__class_Odvd(X3,X2,X1)
       => ( c_Rings_Odvd__class_Odvd(X3,X2,X0)
         => c_Rings_Odvd__class_Odvd(X3,X2,c_Groups_Oplus__class_Oplus(X3,X1,X0)) ) ) ),
    inference(rectify,[],[f838]) ).

fof(f838,axiom,
    ! [X23,X13,X4,X5] :
      ( class_Rings_Ocomm__semiring__1(X5)
     => ( c_Rings_Odvd__class_Odvd(X5,X4,X13)
       => ( c_Rings_Odvd__class_Odvd(X5,X4,X23)
         => c_Rings_Odvd__class_Odvd(X5,X4,c_Groups_Oplus__class_Oplus(X5,X13,X23)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__add) ).

fof(f19034,plain,
    spl50_990,
    inference(avatar_split_clause,[],[f5416,f19032]) ).

fof(f19032,plain,
    ( spl50_990
  <=> ! [X0,X3,X2,X1] :
        ( c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X0),X1)
        | ~ class_Rings_Ocomm__semiring__1(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_990])]) ).

fof(f5416,plain,
    ! [X2,X3,X0,X1] :
      ( c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X0),X1)
      | ~ class_Rings_Ocomm__semiring__1(X3) ),
    inference(cnf_transformation,[],[f3263]) ).

fof(f3263,plain,
    ! [X0,X1,X2,X3] :
      ( c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X0),X1)
      | ~ class_Rings_Ocomm__semiring__1(X3) ),
    inference(ennf_transformation,[],[f2180]) ).

fof(f2180,plain,
    ! [X0,X1,X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X0),X1) ),
    inference(rectify,[],[f519]) ).

fof(f519,axiom,
    ! [X23,X13,X4,X5] :
      ( class_Rings_Ocomm__semiring__1(X5)
     => c_Groups_Oplus__class_Oplus(X5,c_Groups_Oplus__class_Oplus(X5,X4,X13),X23) = c_Groups_Oplus__class_Oplus(X5,c_Groups_Oplus__class_Oplus(X5,X4,X23),X13) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).

fof(f19030,plain,
    spl50_989,
    inference(avatar_split_clause,[],[f5414,f19028]) ).

fof(f19028,plain,
    ( spl50_989
  <=> ! [X0,X3,X2,X1] :
        ( c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oplus__class_Oplus(X3,X1,X0))
        | ~ class_Rings_Ocomm__semiring__1(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_989])]) ).

fof(f5414,plain,
    ! [X2,X3,X0,X1] :
      ( c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oplus__class_Oplus(X3,X1,X0))
      | ~ class_Rings_Ocomm__semiring__1(X3) ),
    inference(cnf_transformation,[],[f3261]) ).

fof(f3261,plain,
    ! [X0,X1,X2,X3] :
      ( c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oplus__class_Oplus(X3,X1,X0))
      | ~ class_Rings_Ocomm__semiring__1(X3) ),
    inference(ennf_transformation,[],[f2178]) ).

fof(f2178,plain,
    ! [X0,X1,X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oplus__class_Oplus(X3,X1,X0)) ),
    inference(rectify,[],[f517]) ).

fof(f517,axiom,
    ! [X22,X23,X4,X5] :
      ( class_Rings_Ocomm__semiring__1(X5)
     => c_Groups_Oplus__class_Oplus(X5,X4,c_Groups_Oplus__class_Oplus(X5,X23,X22)) = c_Groups_Oplus__class_Oplus(X5,c_Groups_Oplus__class_Oplus(X5,X4,X23),X22) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).

fof(f19026,plain,
    spl50_988,
    inference(avatar_split_clause,[],[f5413,f19024]) ).

fof(f19024,plain,
    ( spl50_988
  <=> ! [X0,X3,X2,X1] :
        ( c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oplus__class_Oplus(X3,X1,X0)) = c_Groups_Oplus__class_Oplus(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0))
        | ~ class_Rings_Ocomm__semiring__1(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_988])]) ).

fof(f5413,plain,
    ! [X2,X3,X0,X1] :
      ( c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oplus__class_Oplus(X3,X1,X0)) = c_Groups_Oplus__class_Oplus(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0))
      | ~ class_Rings_Ocomm__semiring__1(X3) ),
    inference(cnf_transformation,[],[f3260]) ).

fof(f3260,plain,
    ! [X0,X1,X2,X3] :
      ( c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oplus__class_Oplus(X3,X1,X0)) = c_Groups_Oplus__class_Oplus(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0))
      | ~ class_Rings_Ocomm__semiring__1(X3) ),
    inference(ennf_transformation,[],[f2177]) ).

fof(f2177,plain,
    ! [X0,X1,X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oplus__class_Oplus(X3,X1,X0)) = c_Groups_Oplus__class_Oplus(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0)) ),
    inference(rectify,[],[f516]) ).

fof(f516,axiom,
    ! [X22,X23,X4,X5] :
      ( class_Rings_Ocomm__semiring__1(X5)
     => c_Groups_Oplus__class_Oplus(X5,X4,c_Groups_Oplus__class_Oplus(X5,X23,X22)) = c_Groups_Oplus__class_Oplus(X5,X23,c_Groups_Oplus__class_Oplus(X5,X4,X22)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).

fof(f19022,plain,
    spl50_987,
    inference(avatar_split_clause,[],[f5377,f19020]) ).

fof(f19020,plain,
    ( spl50_987
  <=> ! [X0,X3,X2,X1] :
        ( c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oplus__class_Oplus(X3,X1,X0))
        | ~ class_Groups_Oab__semigroup__add(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_987])]) ).

fof(f5377,plain,
    ! [X2,X3,X0,X1] :
      ( c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oplus__class_Oplus(X3,X1,X0))
      | ~ class_Groups_Oab__semigroup__add(X3) ),
    inference(cnf_transformation,[],[f3221]) ).

fof(f3221,plain,
    ! [X0,X1,X2,X3] :
      ( c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oplus__class_Oplus(X3,X1,X0))
      | ~ class_Groups_Oab__semigroup__add(X3) ),
    inference(ennf_transformation,[],[f2144]) ).

fof(f2144,plain,
    ! [X0,X1,X2,X3] :
      ( class_Groups_Oab__semigroup__add(X3)
     => c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oplus__class_Oplus(X3,X1,X0)) ),
    inference(rectify,[],[f195]) ).

fof(f195,axiom,
    ! [X23,X13,X4,X5] :
      ( class_Groups_Oab__semigroup__add(X5)
     => c_Groups_Oplus__class_Oplus(X5,c_Groups_Oplus__class_Oplus(X5,X4,X13),X23) = c_Groups_Oplus__class_Oplus(X5,X4,c_Groups_Oplus__class_Oplus(X5,X13,X23)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ab__semigroup__add__class_Oadd__ac_I1_J) ).

fof(f19018,plain,
    spl50_986,
    inference(avatar_split_clause,[],[f5337,f19016]) ).

fof(f19016,plain,
    ( spl50_986
  <=> ! [X0,X3,X2,X1] :
        ( c_Rings_Odvd__class_Odvd(X3,X2,c_Groups_Ominus__class_Ominus(X3,X1,X0))
        | ~ c_Rings_Odvd__class_Odvd(X3,X2,X0)
        | ~ c_Rings_Odvd__class_Odvd(X3,X2,X1)
        | ~ class_Rings_Ocomm__ring__1(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_986])]) ).

fof(f5337,plain,
    ! [X2,X3,X0,X1] :
      ( c_Rings_Odvd__class_Odvd(X3,X2,c_Groups_Ominus__class_Ominus(X3,X1,X0))
      | ~ c_Rings_Odvd__class_Odvd(X3,X2,X0)
      | ~ c_Rings_Odvd__class_Odvd(X3,X2,X1)
      | ~ class_Rings_Ocomm__ring__1(X3) ),
    inference(cnf_transformation,[],[f3162]) ).

fof(f3162,plain,
    ! [X0,X1,X2,X3] :
      ( c_Rings_Odvd__class_Odvd(X3,X2,c_Groups_Ominus__class_Ominus(X3,X1,X0))
      | ~ c_Rings_Odvd__class_Odvd(X3,X2,X0)
      | ~ c_Rings_Odvd__class_Odvd(X3,X2,X1)
      | ~ class_Rings_Ocomm__ring__1(X3) ),
    inference(flattening,[],[f3161]) ).

fof(f3161,plain,
    ! [X0,X1,X2,X3] :
      ( c_Rings_Odvd__class_Odvd(X3,X2,c_Groups_Ominus__class_Ominus(X3,X1,X0))
      | ~ c_Rings_Odvd__class_Odvd(X3,X2,X0)
      | ~ c_Rings_Odvd__class_Odvd(X3,X2,X1)
      | ~ class_Rings_Ocomm__ring__1(X3) ),
    inference(ennf_transformation,[],[f2111]) ).

fof(f2111,plain,
    ! [X0,X1,X2,X3] :
      ( class_Rings_Ocomm__ring__1(X3)
     => ( c_Rings_Odvd__class_Odvd(X3,X2,X1)
       => ( c_Rings_Odvd__class_Odvd(X3,X2,X0)
         => c_Rings_Odvd__class_Odvd(X3,X2,c_Groups_Ominus__class_Ominus(X3,X1,X0)) ) ) ),
    inference(rectify,[],[f832]) ).

fof(f832,axiom,
    ! [X14,X7,X9,X5] :
      ( class_Rings_Ocomm__ring__1(X5)
     => ( c_Rings_Odvd__class_Odvd(X5,X9,X7)
       => ( c_Rings_Odvd__class_Odvd(X5,X9,X14)
         => c_Rings_Odvd__class_Odvd(X5,X9,c_Groups_Ominus__class_Ominus(X5,X7,X14)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__diff) ).

fof(f19014,plain,
    spl50_985,
    inference(avatar_split_clause,[],[f5210,f19012]) ).

fof(f19012,plain,
    ( spl50_985
  <=> ! [X2,X0,X1] :
        ( sP8(X0,X1,X2)
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,sK41(X0,X1,X2)) = X1
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_985])]) ).

fof(f5210,plain,
    ! [X2,X0,X1] :
      ( sP8(X0,X1,X2)
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,sK41(X0,X1,X2)) = X1
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(cnf_transformation,[],[f3771]) ).

fof(f19010,plain,
    spl50_984,
    inference(avatar_split_clause,[],[f5202,f19008]) ).

fof(f19008,plain,
    ( spl50_984
  <=> ! [X2,X0,X1] :
        ( sP7(X0,X1,X2)
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,sK40(X0,X1,X2)) = X1
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_984])]) ).

fof(f5202,plain,
    ! [X2,X0,X1] :
      ( sP7(X0,X1,X2)
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,sK40(X0,X1,X2)) = X1
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(cnf_transformation,[],[f3765]) ).

fof(f19006,plain,
    spl50_983,
    inference(avatar_split_clause,[],[f5194,f19004]) ).

fof(f19004,plain,
    ( spl50_983
  <=> ! [X2,X0,X1] :
        ( hBOOL(hAPP(hAPP(X0,X1),X2))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
        | X1 = X2
        | sP6(X2,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_983])]) ).

fof(f5194,plain,
    ! [X2,X0,X1] :
      ( hBOOL(hAPP(hAPP(X0,X1),X2))
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
      | X1 = X2
      | sP6(X2,X1,X0) ),
    inference(cnf_transformation,[],[f3450]) ).

fof(f3450,plain,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP(hAPP(X0,X1),X2))
      | ( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
        & c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) )
      | ( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
        & X1 = X2 )
      | sP6(X2,X1,X0) ),
    inference(definition_folding,[],[f3088,f3449]) ).

fof(f3449,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(f3088,plain,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP(hAPP(X0,X1),X2))
      | ( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
        & c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) )
      | ( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
        & X1 = X2 )
      | ( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
        & c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ) ),
    inference(flattening,[],[f3087]) ).

fof(f3087,plain,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP(hAPP(X0,X1),X2))
      | ( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
        & c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) )
      | ( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
        & X1 = X2 )
      | ( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
        & c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ) ),
    inference(ennf_transformation,[],[f2045]) ).

fof(f2045,plain,
    ! [X0,X1,X2] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
       => hBOOL(hAPP(hAPP(X0,X1),X2)) )
     => ( ( X1 = X2
         => hBOOL(hAPP(hAPP(X0,X1),X2)) )
       => ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
           => hBOOL(hAPP(hAPP(X0,X1),X2)) )
         => hBOOL(hAPP(hAPP(X0,X1),X2)) ) ) ),
    inference(rectify,[],[f353]) ).

fof(f353,axiom,
    ! [X49,X16,X32] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X32,X16)
       => hBOOL(hAPP(hAPP(X49,X16),X32)) )
     => ( ( X16 = X32
         => hBOOL(hAPP(hAPP(X49,X16),X32)) )
       => ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X16,X32)
           => hBOOL(hAPP(hAPP(X49,X16),X32)) )
         => hBOOL(hAPP(hAPP(X49,X16),X32)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__cases) ).

fof(f19002,plain,
    spl50_982,
    inference(avatar_split_clause,[],[f5027,f19000]) ).

fof(f19000,plain,
    ( spl50_982
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0))
        | ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
        | ~ class_Rings_Olinordered__semidom(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_982])]) ).

fof(f5027,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0))
      | ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
      | ~ class_Rings_Olinordered__semidom(X2) ),
    inference(cnf_transformation,[],[f2903]) ).

fof(f2903,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0))
      | ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
      | ~ class_Rings_Olinordered__semidom(X2) ),
    inference(flattening,[],[f2902]) ).

fof(f2902,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0))
      | ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
      | ~ class_Rings_Olinordered__semidom(X2) ),
    inference(ennf_transformation,[],[f1922]) ).

fof(f1922,plain,
    ! [X0,X1,X2] :
      ( class_Rings_Olinordered__semidom(X2)
     => ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
       => c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) ) ),
    inference(rectify,[],[f146]) ).

fof(f146,axiom,
    ! [X3,X4,X5] :
      ( class_Rings_Olinordered__semidom(X5)
     => ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X4)
       => c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X3)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__power) ).

fof(f18998,plain,
    spl50_981,
    inference(avatar_split_clause,[],[f5021,f18996]) ).

fof(f18996,plain,
    ( spl50_981
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0))
        | ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
        | ~ class_Rings_Olinordered__semidom(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_981])]) ).

fof(f5021,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0))
      | ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
      | ~ class_Rings_Olinordered__semidom(X2) ),
    inference(cnf_transformation,[],[f2891]) ).

fof(f2891,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0))
      | ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
      | ~ class_Rings_Olinordered__semidom(X2) ),
    inference(flattening,[],[f2890]) ).

fof(f2890,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0))
      | ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
      | ~ class_Rings_Olinordered__semidom(X2) ),
    inference(ennf_transformation,[],[f1916]) ).

fof(f1916,plain,
    ! [X0,X1,X2] :
      ( class_Rings_Olinordered__semidom(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),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) ) ),
    inference(rectify,[],[f49]) ).

fof(f49,axiom,
    ! [X3,X4,X5] :
      ( class_Rings_Olinordered__semidom(X5)
     => ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X4)
       => c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X3)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__power) ).

fof(f18994,plain,
    ( ~ spl50_86
    | spl50_980
    | ~ spl50_443
    | ~ spl50_911 ),
    inference(avatar_split_clause,[],[f17164,f17115,f8298,f18992,f6476]) ).

fof(f18992,plain,
    ( spl50_980
  <=> ! [X0] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_980])]) ).

fof(f8298,plain,
    ( spl50_443
  <=> ! [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,[spl50_443])]) ).

fof(f17115,plain,
    ( spl50_911
  <=> ! [X0] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_911])]) ).

fof(f17164,plain,
    ( ! [X0] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X0)
        | ~ class_Orderings_Olinorder(tc_RealDef_Oreal) )
    | ~ spl50_443
    | ~ spl50_911 ),
    inference(resolution,[],[f17116,f8299]) ).

fof(f8299,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) )
    | ~ spl50_443 ),
    inference(avatar_component_clause,[],[f8298]) ).

fof(f17116,plain,
    ( ! [X0] :
        ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
    | ~ spl50_911 ),
    inference(avatar_component_clause,[],[f17115]) ).

fof(f18990,plain,
    spl50_979,
    inference(avatar_split_clause,[],[f5020,f18988]) ).

fof(f18988,plain,
    ( spl50_979
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oone__class_Oone(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0))
        | ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oone__class_Oone(X2),X1)
        | ~ class_Rings_Olinordered__semidom(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_979])]) ).

fof(f5020,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oone__class_Oone(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0))
      | ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oone__class_Oone(X2),X1)
      | ~ class_Rings_Olinordered__semidom(X2) ),
    inference(cnf_transformation,[],[f2889]) ).

fof(f2889,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oone__class_Oone(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0))
      | ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oone__class_Oone(X2),X1)
      | ~ class_Rings_Olinordered__semidom(X2) ),
    inference(flattening,[],[f2888]) ).

fof(f2888,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oone__class_Oone(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0))
      | ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oone__class_Oone(X2),X1)
      | ~ class_Rings_Olinordered__semidom(X2) ),
    inference(ennf_transformation,[],[f1915]) ).

fof(f1915,plain,
    ! [X0,X1,X2] :
      ( class_Rings_Olinordered__semidom(X2)
     => ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oone__class_Oone(X2),X1)
       => c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oone__class_Oone(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) ) ),
    inference(rectify,[],[f50]) ).

fof(f50,axiom,
    ! [X3,X4,X5] :
      ( class_Rings_Olinordered__semidom(X5)
     => ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oone__class_Oone(X5),X4)
       => c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oone__class_Oone(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X3)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__le__power) ).

fof(f18986,plain,
    spl50_978,
    inference(avatar_split_clause,[],[f5006,f18984]) ).

fof(f18984,plain,
    ( spl50_978
  <=> ! [X2,X0,X1] :
        ( c_Groups_Ouminus__class_Ouminus(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0)) = c_Groups_Oplus__class_Oplus(X2,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,[spl50_978])]) ).

fof(f5006,plain,
    ! [X2,X0,X1] :
      ( c_Groups_Ouminus__class_Ouminus(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0)) = c_Groups_Oplus__class_Oplus(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Groups_Ouminus__class_Ouminus(X2,X1))
      | ~ class_Groups_Ogroup__add(X2) ),
    inference(cnf_transformation,[],[f2879]) ).

fof(f2879,plain,
    ! [X0,X1,X2] :
      ( c_Groups_Ouminus__class_Ouminus(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0)) = c_Groups_Oplus__class_Oplus(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Groups_Ouminus__class_Ouminus(X2,X1))
      | ~ class_Groups_Ogroup__add(X2) ),
    inference(ennf_transformation,[],[f1907]) ).

fof(f1907,plain,
    ! [X0,X1,X2] :
      ( class_Groups_Ogroup__add(X2)
     => c_Groups_Ouminus__class_Ouminus(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0)) = c_Groups_Oplus__class_Oplus(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Groups_Ouminus__class_Ouminus(X2,X1)) ),
    inference(rectify,[],[f318]) ).

fof(f318,axiom,
    ! [X13,X4,X5] :
      ( class_Groups_Ogroup__add(X5)
     => c_Groups_Ouminus__class_Ouminus(X5,c_Groups_Oplus__class_Oplus(X5,X4,X13)) = c_Groups_Oplus__class_Oplus(X5,c_Groups_Ouminus__class_Ouminus(X5,X13),c_Groups_Ouminus__class_Ouminus(X5,X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__add) ).

fof(f18982,plain,
    spl50_977,
    inference(avatar_split_clause,[],[f4995,f18980]) ).

fof(f18980,plain,
    ( spl50_977
  <=> ! [X2,X0,X1] :
        ( c_Groups_Ouminus__class_Ouminus(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0)) = c_Groups_Oplus__class_Oplus(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
        | ~ class_Groups_Oab__group__add(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_977])]) ).

fof(f4995,plain,
    ! [X2,X0,X1] :
      ( c_Groups_Ouminus__class_Ouminus(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0)) = c_Groups_Oplus__class_Oplus(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
      | ~ class_Groups_Oab__group__add(X2) ),
    inference(cnf_transformation,[],[f2869]) ).

fof(f2869,plain,
    ! [X0,X1,X2] :
      ( c_Groups_Ouminus__class_Ouminus(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0)) = c_Groups_Oplus__class_Oplus(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
      | ~ class_Groups_Oab__group__add(X2) ),
    inference(ennf_transformation,[],[f1897]) ).

fof(f1897,plain,
    ! [X0,X1,X2] :
      ( class_Groups_Oab__group__add(X2)
     => c_Groups_Ouminus__class_Ouminus(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0)) = c_Groups_Oplus__class_Oplus(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0)) ),
    inference(rectify,[],[f319]) ).

fof(f319,axiom,
    ! [X13,X4,X5] :
      ( class_Groups_Oab__group__add(X5)
     => c_Groups_Ouminus__class_Ouminus(X5,c_Groups_Oplus__class_Oplus(X5,X4,X13)) = c_Groups_Oplus__class_Oplus(X5,c_Groups_Ouminus__class_Ouminus(X5,X4),c_Groups_Ouminus__class_Ouminus(X5,X13)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__add__distrib) ).

fof(f18978,plain,
    spl50_976,
    inference(avatar_split_clause,[],[f4994,f18976]) ).

fof(f18976,plain,
    ( spl50_976
  <=> ! [X2,X0,X1] :
        ( c_Groups_Ouminus__class_Ouminus(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0)) = c_Groups_Ominus__class_Ominus(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
        | ~ class_Groups_Oab__group__add(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_976])]) ).

fof(f4994,plain,
    ! [X2,X0,X1] :
      ( c_Groups_Ouminus__class_Ouminus(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0)) = c_Groups_Ominus__class_Ominus(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
      | ~ class_Groups_Oab__group__add(X2) ),
    inference(cnf_transformation,[],[f2868]) ).

fof(f2868,plain,
    ! [X0,X1,X2] :
      ( c_Groups_Ouminus__class_Ouminus(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0)) = c_Groups_Ominus__class_Ominus(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
      | ~ class_Groups_Oab__group__add(X2) ),
    inference(ennf_transformation,[],[f1896]) ).

fof(f1896,plain,
    ! [X0,X1,X2] :
      ( class_Groups_Oab__group__add(X2)
     => c_Groups_Ouminus__class_Ouminus(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0)) = c_Groups_Ominus__class_Ominus(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0)) ),
    inference(rectify,[],[f785]) ).

fof(f785,axiom,
    ! [X13,X4,X5] :
      ( class_Groups_Oab__group__add(X5)
     => c_Groups_Ouminus__class_Ouminus(X5,c_Groups_Ominus__class_Ominus(X5,X4,X13)) = c_Groups_Ominus__class_Ominus(X5,c_Groups_Ouminus__class_Ouminus(X5,X4),c_Groups_Ouminus__class_Ouminus(X5,X13)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Limits_Ominus__diff__minus) ).

fof(f18974,plain,
    spl50_975,
    inference(avatar_split_clause,[],[f4979,f18972]) ).

fof(f18972,plain,
    ( spl50_975
  <=> ! [X2,X0,X1] :
        ( 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)
        | ~ class_Rings_Oidom(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_975])]) ).

fof(f4979,plain,
    ! [X2,X0,X1] :
      ( 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)
      | ~ class_Rings_Oidom(X2) ),
    inference(cnf_transformation,[],[f3702]) ).

fof(f3702,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,[],[f3701]) ).

fof(f3701,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,[],[f2860]) ).

fof(f2860,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,[],[f1888]) ).

fof(f1888,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,[],[f700]) ).

fof(f700,axiom,
    ! [X24,X64,X5] :
      ( class_Rings_Oidom(X5)
     => ( c_Groups_Ozero__class_Ozero(X5) = hAPP(c_Polynomial_Opoly(X5,X64),X24)
      <=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Polynomial_Oorder(X5,X24,X64)
          | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = X64 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__root) ).

fof(f18970,plain,
    spl50_974,
    inference(avatar_split_clause,[],[f4927,f18968]) ).

fof(f18968,plain,
    ( spl50_974
  <=> ! [X2,X0,X1] :
        ( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),c_Polynomial_Osmult(X2,X1,X0)) = c_Polynomial_Osmult(X2,X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),X0))
        | ~ class_Rings_Ocomm__ring(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_974])]) ).

fof(f4927,plain,
    ! [X2,X0,X1] :
      ( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),c_Polynomial_Osmult(X2,X1,X0)) = c_Polynomial_Osmult(X2,X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),X0))
      | ~ class_Rings_Ocomm__ring(X2) ),
    inference(cnf_transformation,[],[f2794]) ).

fof(f2794,plain,
    ! [X0,X1,X2] :
      ( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),c_Polynomial_Osmult(X2,X1,X0)) = c_Polynomial_Osmult(X2,X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),X0))
      | ~ class_Rings_Ocomm__ring(X2) ),
    inference(ennf_transformation,[],[f1851]) ).

fof(f1851,plain,
    ! [X0,X1,X2] :
      ( class_Rings_Ocomm__ring(X2)
     => c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),c_Polynomial_Osmult(X2,X1,X0)) = c_Polynomial_Osmult(X2,X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),X0)) ),
    inference(rectify,[],[f644]) ).

fof(f644,axiom,
    ! [X54,X4,X5] :
      ( class_Rings_Ocomm__ring(X5)
     => c_Polynomial_Osmult(X5,X4,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X5),X54)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X5),c_Polynomial_Osmult(X5,X4,X54)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__minus__right) ).

fof(f18966,plain,
    spl50_973,
    inference(avatar_split_clause,[],[f4896,f18964]) ).

fof(f18964,plain,
    ( spl50_973
  <=> ! [X2,X0,X1] :
        ( c_Polynomial_Opos__poly(X2,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X2),X0,X1))
        | X0 = X1
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X2),X1,X0)
        | ~ class_Rings_Olinordered__idom(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_973])]) ).

fof(f4896,plain,
    ! [X2,X0,X1] :
      ( c_Polynomial_Opos__poly(X2,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X2),X0,X1))
      | X0 = X1
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X2),X1,X0)
      | ~ class_Rings_Olinordered__idom(X2) ),
    inference(cnf_transformation,[],[f3681]) ).

fof(f3681,plain,
    ! [X0,X1,X2] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X2),X1,X0)
          | ( ~ c_Polynomial_Opos__poly(X2,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X2),X0,X1))
            & X0 != X1 ) )
        & ( c_Polynomial_Opos__poly(X2,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X2),X0,X1))
          | X0 = X1
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X2),X1,X0) ) )
      | ~ class_Rings_Olinordered__idom(X2) ),
    inference(flattening,[],[f3680]) ).

fof(f3680,plain,
    ! [X0,X1,X2] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X2),X1,X0)
          | ( ~ c_Polynomial_Opos__poly(X2,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X2),X0,X1))
            & X0 != X1 ) )
        & ( c_Polynomial_Opos__poly(X2,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X2),X0,X1))
          | X0 = X1
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X2),X1,X0) ) )
      | ~ class_Rings_Olinordered__idom(X2) ),
    inference(nnf_transformation,[],[f2768]) ).

fof(f2768,plain,
    ! [X0,X1,X2] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X2),X1,X0)
      <=> ( c_Polynomial_Opos__poly(X2,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X2),X0,X1))
          | X0 = X1 ) )
      | ~ class_Rings_Olinordered__idom(X2) ),
    inference(ennf_transformation,[],[f1831]) ).

fof(f1831,plain,
    ! [X0,X1,X2] :
      ( class_Rings_Olinordered__idom(X2)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X2),X1,X0)
      <=> ( c_Polynomial_Opos__poly(X2,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X2),X0,X1))
          | X0 = X1 ) ) ),
    inference(rectify,[],[f788]) ).

fof(f788,axiom,
    ! [X20,X12,X5] :
      ( class_Rings_Olinordered__idom(X5)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X5),X12,X20)
      <=> ( c_Polynomial_Opos__poly(X5,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X5),X20,X12))
          | X12 = X20 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__poly__def) ).

fof(f18962,plain,
    spl50_972,
    inference(avatar_split_clause,[],[f4893,f18960]) ).

fof(f18960,plain,
    ( spl50_972
  <=> ! [X2,X0,X1] :
        ( c_Polynomial_Opos__poly(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X2)),X1),X0))
        | ~ c_Polynomial_Opos__poly(X2,X0)
        | ~ c_Polynomial_Opos__poly(X2,X1)
        | ~ class_Rings_Olinordered__idom(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_972])]) ).

fof(f4893,plain,
    ! [X2,X0,X1] :
      ( c_Polynomial_Opos__poly(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X2)),X1),X0))
      | ~ c_Polynomial_Opos__poly(X2,X0)
      | ~ c_Polynomial_Opos__poly(X2,X1)
      | ~ class_Rings_Olinordered__idom(X2) ),
    inference(cnf_transformation,[],[f2763]) ).

fof(f2763,plain,
    ! [X0,X1,X2] :
      ( c_Polynomial_Opos__poly(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X2)),X1),X0))
      | ~ c_Polynomial_Opos__poly(X2,X0)
      | ~ c_Polynomial_Opos__poly(X2,X1)
      | ~ class_Rings_Olinordered__idom(X2) ),
    inference(flattening,[],[f2762]) ).

fof(f2762,plain,
    ! [X0,X1,X2] :
      ( c_Polynomial_Opos__poly(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X2)),X1),X0))
      | ~ c_Polynomial_Opos__poly(X2,X0)
      | ~ c_Polynomial_Opos__poly(X2,X1)
      | ~ class_Rings_Olinordered__idom(X2) ),
    inference(ennf_transformation,[],[f1828]) ).

fof(f1828,plain,
    ! [X0,X1,X2] :
      ( class_Rings_Olinordered__idom(X2)
     => ( c_Polynomial_Opos__poly(X2,X1)
       => ( c_Polynomial_Opos__poly(X2,X0)
         => c_Polynomial_Opos__poly(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X2)),X1),X0)) ) ) ),
    inference(rectify,[],[f787]) ).

fof(f787,axiom,
    ! [X53,X54,X5] :
      ( class_Rings_Olinordered__idom(X5)
     => ( c_Polynomial_Opos__poly(X5,X54)
       => ( c_Polynomial_Opos__poly(X5,X53)
         => c_Polynomial_Opos__poly(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X5)),X54),X53)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__poly__mult) ).

fof(f18958,plain,
    spl50_971,
    inference(avatar_split_clause,[],[f4751,f18956]) ).

fof(f18956,plain,
    ( spl50_971
  <=> ! [X0,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) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_971])]) ).

fof(f4751,plain,
    ! [X0,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) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) ),
    inference(cnf_transformation,[],[f3638]) ).

fof(f3638,plain,
    ! [X0,X1] :
      ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(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) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) ) ),
    inference(flattening,[],[f3637]) ).

fof(f3637,plain,
    ! [X0,X1] :
      ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(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) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) ) ),
    inference(nnf_transformation,[],[f1736]) ).

fof(f1736,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(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,[],[f386]) ).

fof(f386,axiom,
    ! [X16,X32] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X32),X16)
    <=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X16
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X32 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__is__0) ).

fof(f18954,plain,
    spl50_970,
    inference(avatar_split_clause,[],[f4612,f18952]) ).

fof(f18952,plain,
    ( spl50_970
  <=> ! [X0,X1] :
        ( X0 = X1
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_970])]) ).

fof(f4612,plain,
    ! [X0,X1] :
      ( X0 = X1
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0) ),
    inference(cnf_transformation,[],[f2648]) ).

fof(f2648,plain,
    ! [X0,X1] :
      ( X0 = X1
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0) ),
    inference(flattening,[],[f2647]) ).

fof(f2647,plain,
    ! [X0,X1] :
      ( X0 = X1
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0) ),
    inference(ennf_transformation,[],[f1676]) ).

fof(f1676,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)
     => ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)
       => X0 = X1 ) ),
    inference(rectify,[],[f451]) ).

fof(f451,axiom,
    ! [X3,X17] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X3)
     => ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X17)
       => X3 = X17 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diffs0__imp__equal) ).

fof(f18942,plain,
    spl50_969,
    inference(avatar_split_clause,[],[f4598,f18940]) ).

fof(f18940,plain,
    ( spl50_969
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,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) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_969])]) ).

fof(f4598,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,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) ),
    inference(cnf_transformation,[],[f2631]) ).

fof(f2631,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,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) ),
    inference(flattening,[],[f2630]) ).

fof(f2630,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,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) ),
    inference(ennf_transformation,[],[f1664]) ).

fof(f1664,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_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),X0) ) ),
    inference(rectify,[],[f470]) ).

fof(f470,axiom,
    ! [X17,X3] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X17)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X3),X17) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__less) ).

fof(f18938,plain,
    spl50_968,
    inference(avatar_split_clause,[],[f4587,f18936]) ).

fof(f18936,plain,
    ( spl50_968
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(X1,X0))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_968])]) ).

fof(f4587,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(X1,X0))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(cnf_transformation,[],[f2614]) ).

fof(f2614,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(X1,X0))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(flattening,[],[f2613]) ).

fof(f2613,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(X1,X0))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(ennf_transformation,[],[f1655]) ).

fof(f1655,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_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
       => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(X1,X0)) ) ),
    inference(rectify,[],[f778]) ).

fof(f778,axiom,
    ! [X7,X9] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X9)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X7)
       => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(X9,X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J) ).

fof(f18934,plain,
    spl50_967,
    inference(avatar_split_clause,[],[f4539,f18932]) ).

fof(f18932,plain,
    ( spl50_967
  <=> ! [X0,X1] :
        ( c_SEQ_Odecseq(X1,X0)
        | ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,sK28(X0,X1)),hAPP(X0,sK27(X0,X1)))
        | ~ class_Orderings_Oorder(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_967])]) ).

fof(f4539,plain,
    ! [X0,X1] :
      ( c_SEQ_Odecseq(X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,sK28(X0,X1)),hAPP(X0,sK27(X0,X1)))
      | ~ class_Orderings_Oorder(X1) ),
    inference(cnf_transformation,[],[f3547]) ).

fof(f3547,plain,
    ! [X0,X1] :
      ( ( ( c_SEQ_Odecseq(X1,X0)
          | ( ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,sK28(X0,X1)),hAPP(X0,sK27(X0,X1)))
            & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK27(X0,X1),sK28(X0,X1)) ) )
        & ( ! [X4,X5] :
              ( c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X5),hAPP(X0,X4))
              | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X5) )
          | ~ c_SEQ_Odecseq(X1,X0) ) )
      | ~ class_Orderings_Oorder(X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK27,sK28])],[f3545,f3546]) ).

fof(f3546,plain,
    ! [X0,X1] :
      ( ? [X2,X3] :
          ( ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X3),hAPP(X0,X2))
          & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) )
     => ( ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,sK28(X0,X1)),hAPP(X0,sK27(X0,X1)))
        & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK27(X0,X1),sK28(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f3545,plain,
    ! [X0,X1] :
      ( ( ( c_SEQ_Odecseq(X1,X0)
          | ? [X2,X3] :
              ( ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X3),hAPP(X0,X2))
              & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ) )
        & ( ! [X4,X5] :
              ( c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X5),hAPP(X0,X4))
              | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X5) )
          | ~ c_SEQ_Odecseq(X1,X0) ) )
      | ~ class_Orderings_Oorder(X1) ),
    inference(rectify,[],[f3544]) ).

fof(f3544,plain,
    ! [X0,X1] :
      ( ( ( c_SEQ_Odecseq(X1,X0)
          | ? [X2,X3] :
              ( ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X3),hAPP(X0,X2))
              & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ) )
        & ( ! [X2,X3] :
              ( c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X3),hAPP(X0,X2))
              | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) )
          | ~ c_SEQ_Odecseq(X1,X0) ) )
      | ~ class_Orderings_Oorder(X1) ),
    inference(nnf_transformation,[],[f2556]) ).

fof(f2556,plain,
    ! [X0,X1] :
      ( ( c_SEQ_Odecseq(X1,X0)
      <=> ! [X2,X3] :
            ( c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X3),hAPP(X0,X2))
            | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ) )
      | ~ class_Orderings_Oorder(X1) ),
    inference(ennf_transformation,[],[f1613]) ).

fof(f1613,plain,
    ! [X0,X1] :
      ( class_Orderings_Oorder(X1)
     => ( c_SEQ_Odecseq(X1,X0)
      <=> ! [X2,X3] :
            ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
           => c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X3),hAPP(X0,X2)) ) ) ),
    inference(rectify,[],[f793]) ).

fof(f793,axiom,
    ! [X74,X5] :
      ( class_Orderings_Oorder(X5)
     => ( c_SEQ_Odecseq(X5,X74)
      <=> ! [X44,X37] :
            ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X44,X37)
           => c_Orderings_Oord__class_Oless__eq(X5,hAPP(X74,X37),hAPP(X74,X44)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_decseq__def) ).

fof(f18930,plain,
    spl50_966,
    inference(avatar_split_clause,[],[f4537,f18928]) ).

fof(f18928,plain,
    ( spl50_966
  <=> ! [X4,X0,X5,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X5),hAPP(X0,X4))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X5)
        | ~ c_SEQ_Odecseq(X1,X0)
        | ~ class_Orderings_Oorder(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_966])]) ).

fof(f4537,plain,
    ! [X0,X1,X4,X5] :
      ( c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X5),hAPP(X0,X4))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X5)
      | ~ c_SEQ_Odecseq(X1,X0)
      | ~ class_Orderings_Oorder(X1) ),
    inference(cnf_transformation,[],[f3547]) ).

fof(f18926,plain,
    spl50_965,
    inference(avatar_split_clause,[],[f4412,f18924]) ).

fof(f18924,plain,
    ( spl50_965
  <=> ! [X0,X1] :
        ( c_Groups_Oone__class_Oone(X1) = c_Groups_Osgn__class_Osgn(X1,X0)
        | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
        | c_Groups_Ozero__class_Ozero(X1) = X0
        | ~ class_Groups_Osgn__if(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_965])]) ).

fof(f4412,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(X1) = c_Groups_Osgn__class_Osgn(X1,X0)
      | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
      | c_Groups_Ozero__class_Ozero(X1) = X0
      | ~ class_Groups_Osgn__if(X1) ),
    inference(cnf_transformation,[],[f2459]) ).

fof(f18922,plain,
    spl50_964,
    inference(avatar_split_clause,[],[f4387,f18920]) ).

fof(f18920,plain,
    ( spl50_964
  <=> ! [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))
        | c_Groups_Ozero__class_Ozero(X1) = X0
        | ~ class_Rings_Odivision__ring(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_964])]) ).

fof(f4387,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))
      | c_Groups_Ozero__class_Ozero(X1) = X0
      | ~ class_Rings_Odivision__ring(X1) ),
    inference(cnf_transformation,[],[f2441]) ).

fof(f2441,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))
      | c_Groups_Ozero__class_Ozero(X1) = X0
      | ~ class_Rings_Odivision__ring(X1) ),
    inference(flattening,[],[f2440]) ).

fof(f2440,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))
      | c_Groups_Ozero__class_Ozero(X1) = X0
      | ~ class_Rings_Odivision__ring(X1) ),
    inference(ennf_transformation,[],[f1503]) ).

fof(f1503,plain,
    ! [X0,X1] :
      ( class_Rings_Odivision__ring(X1)
     => ( c_Groups_Ozero__class_Ozero(X1) != X0
       => 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,[],[f344]) ).

fof(f344,axiom,
    ! [X4,X5] :
      ( class_Rings_Odivision__ring(X5)
     => ( c_Groups_Ozero__class_Ozero(X5) != X4
       => c_Rings_Oinverse__class_Oinverse(X5,c_Groups_Ouminus__class_Ouminus(X5,X4)) = c_Groups_Ouminus__class_Ouminus(X5,c_Rings_Oinverse__class_Oinverse(X5,X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__inverse__minus__eq) ).

fof(f18918,plain,
    spl50_963,
    inference(avatar_split_clause,[],[f4386,f18916]) ).

fof(f18916,plain,
    ( spl50_963
  <=> ! [X0,X1] :
        ( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(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,[spl50_963])]) ).

fof(f4386,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Rings_Oinverse__class_Oinverse(X1,X0)),X0)
      | c_Groups_Ozero__class_Ozero(X1) = X0
      | ~ class_Rings_Odivision__ring(X1) ),
    inference(cnf_transformation,[],[f2439]) ).

fof(f2439,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Rings_Oinverse__class_Oinverse(X1,X0)),X0)
      | c_Groups_Ozero__class_Ozero(X1) = X0
      | ~ class_Rings_Odivision__ring(X1) ),
    inference(flattening,[],[f2438]) ).

fof(f2438,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Rings_Oinverse__class_Oinverse(X1,X0)),X0)
      | c_Groups_Ozero__class_Ozero(X1) = X0
      | ~ class_Rings_Odivision__ring(X1) ),
    inference(ennf_transformation,[],[f1502]) ).

fof(f1502,plain,
    ! [X0,X1] :
      ( class_Rings_Odivision__ring(X1)
     => ( c_Groups_Ozero__class_Ozero(X1) != X0
       => c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Rings_Oinverse__class_Oinverse(X1,X0)),X0) ) ),
    inference(rectify,[],[f14]) ).

fof(f14,axiom,
    ! [X4,X5] :
      ( class_Rings_Odivision__ring(X5)
     => ( c_Groups_Ozero__class_Ozero(X5) != X4
       => c_Groups_Oone__class_Oone(X5) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Rings_Oinverse__class_Oinverse(X5,X4)),X4) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_left__inverse) ).

fof(f18914,plain,
    spl50_962,
    inference(avatar_split_clause,[],[f4385,f18912]) ).

fof(f18912,plain,
    ( spl50_962
  <=> ! [X0,X1] :
        ( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Rings_Oinverse__class_Oinverse(X1,X0))
        | c_Groups_Ozero__class_Ozero(X1) = X0
        | ~ class_Rings_Odivision__ring(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_962])]) ).

fof(f4385,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Rings_Oinverse__class_Oinverse(X1,X0))
      | c_Groups_Ozero__class_Ozero(X1) = X0
      | ~ class_Rings_Odivision__ring(X1) ),
    inference(cnf_transformation,[],[f2437]) ).

fof(f2437,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Rings_Oinverse__class_Oinverse(X1,X0))
      | c_Groups_Ozero__class_Ozero(X1) = X0
      | ~ class_Rings_Odivision__ring(X1) ),
    inference(flattening,[],[f2436]) ).

fof(f2436,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Rings_Oinverse__class_Oinverse(X1,X0))
      | c_Groups_Ozero__class_Ozero(X1) = X0
      | ~ class_Rings_Odivision__ring(X1) ),
    inference(ennf_transformation,[],[f1501]) ).

fof(f1501,plain,
    ! [X0,X1] :
      ( class_Rings_Odivision__ring(X1)
     => ( c_Groups_Ozero__class_Ozero(X1) != X0
       => c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Rings_Oinverse__class_Oinverse(X1,X0)) ) ),
    inference(rectify,[],[f12]) ).

fof(f12,axiom,
    ! [X4,X5] :
      ( class_Rings_Odivision__ring(X5)
     => ( c_Groups_Ozero__class_Ozero(X5) != X4
       => c_Groups_Oone__class_Oone(X5) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),c_Rings_Oinverse__class_Oinverse(X5,X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_right__inverse) ).

fof(f18910,plain,
    spl50_961,
    inference(avatar_split_clause,[],[f4378,f18908]) ).

fof(f18908,plain,
    ( spl50_961
  <=> ! [X0,X1] :
        ( c_RealVector_Onorm__class_Onorm(X1,c_Rings_Oinverse__class_Oinverse(X1,X0)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X0))
        | c_Groups_Ozero__class_Ozero(X1) = X0
        | ~ class_RealVector_Oreal__normed__div__algebra(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_961])]) ).

fof(f4378,plain,
    ! [X0,X1] :
      ( c_RealVector_Onorm__class_Onorm(X1,c_Rings_Oinverse__class_Oinverse(X1,X0)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X0))
      | c_Groups_Ozero__class_Ozero(X1) = X0
      | ~ class_RealVector_Oreal__normed__div__algebra(X1) ),
    inference(cnf_transformation,[],[f2428]) ).

fof(f2428,plain,
    ! [X0,X1] :
      ( c_RealVector_Onorm__class_Onorm(X1,c_Rings_Oinverse__class_Oinverse(X1,X0)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X0))
      | c_Groups_Ozero__class_Ozero(X1) = X0
      | ~ class_RealVector_Oreal__normed__div__algebra(X1) ),
    inference(flattening,[],[f2427]) ).

fof(f2427,plain,
    ! [X0,X1] :
      ( c_RealVector_Onorm__class_Onorm(X1,c_Rings_Oinverse__class_Oinverse(X1,X0)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X0))
      | c_Groups_Ozero__class_Ozero(X1) = X0
      | ~ class_RealVector_Oreal__normed__div__algebra(X1) ),
    inference(ennf_transformation,[],[f1495]) ).

fof(f1495,plain,
    ! [X0,X1] :
      ( class_RealVector_Oreal__normed__div__algebra(X1)
     => ( c_Groups_Ozero__class_Ozero(X1) != X0
       => c_RealVector_Onorm__class_Onorm(X1,c_Rings_Oinverse__class_Oinverse(X1,X0)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X0)) ) ),
    inference(rectify,[],[f9]) ).

fof(f9,axiom,
    ! [X4,X5] :
      ( class_RealVector_Oreal__normed__div__algebra(X5)
     => ( c_Groups_Ozero__class_Ozero(X5) != X4
       => c_RealVector_Onorm__class_Onorm(X5,c_Rings_Oinverse__class_Oinverse(X5,X4)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__norm__inverse) ).

fof(f18906,plain,
    spl50_960,
    inference(avatar_split_clause,[],[f4377,f18904]) ).

fof(f18904,plain,
    ( spl50_960
  <=> ! [X0,X1] :
        ( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Rings_Oinverse__class_Oinverse(X1,X0)),X0)
        | c_Groups_Ozero__class_Ozero(X1) = X0
        | ~ class_Fields_Ofield(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_960])]) ).

fof(f4377,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Rings_Oinverse__class_Oinverse(X1,X0)),X0)
      | c_Groups_Ozero__class_Ozero(X1) = X0
      | ~ class_Fields_Ofield(X1) ),
    inference(cnf_transformation,[],[f2426]) ).

fof(f2426,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Rings_Oinverse__class_Oinverse(X1,X0)),X0)
      | c_Groups_Ozero__class_Ozero(X1) = X0
      | ~ class_Fields_Ofield(X1) ),
    inference(flattening,[],[f2425]) ).

fof(f2425,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Rings_Oinverse__class_Oinverse(X1,X0)),X0)
      | c_Groups_Ozero__class_Ozero(X1) = X0
      | ~ class_Fields_Ofield(X1) ),
    inference(ennf_transformation,[],[f1494]) ).

fof(f1494,plain,
    ! [X0,X1] :
      ( class_Fields_Ofield(X1)
     => ( c_Groups_Ozero__class_Ozero(X1) != X0
       => c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Rings_Oinverse__class_Oinverse(X1,X0)),X0) ) ),
    inference(rectify,[],[f13]) ).

fof(f13,axiom,
    ! [X4,X5] :
      ( class_Fields_Ofield(X5)
     => ( c_Groups_Ozero__class_Ozero(X5) != X4
       => c_Groups_Oone__class_Oone(X5) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Rings_Oinverse__class_Oinverse(X5,X4)),X4) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_field__inverse) ).

fof(f18902,plain,
    ( ~ spl50_86
    | spl50_959
    | ~ spl50_445
    | ~ spl50_909 ),
    inference(avatar_split_clause,[],[f16107,f15960,f8306,f18900,f6476]) ).

fof(f18900,plain,
    ( spl50_959
  <=> ! [X0] :
        ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_959])]) ).

fof(f8306,plain,
    ( spl50_445
  <=> ! [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,[spl50_445])]) ).

fof(f15960,plain,
    ( spl50_909
  <=> ! [X0] :
        ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_909])]) ).

fof(f16107,plain,
    ( ! [X0] :
        ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))
        | ~ class_Orderings_Olinorder(tc_RealDef_Oreal) )
    | ~ spl50_445
    | ~ spl50_909 ),
    inference(resolution,[],[f15961,f8307]) ).

fof(f8307,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
        | ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
        | ~ class_Orderings_Olinorder(X2) )
    | ~ spl50_445 ),
    inference(avatar_component_clause,[],[f8306]) ).

fof(f15961,plain,
    ( ! [X0] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X0)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) )
    | ~ spl50_909 ),
    inference(avatar_component_clause,[],[f15960]) ).

fof(f18898,plain,
    spl50_958,
    inference(avatar_split_clause,[],[f4336,f18896]) ).

fof(f18896,plain,
    ( spl50_958
  <=> ! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)),X0) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_958])]) ).

fof(f4336,plain,
    ! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)),X0) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0)),
    inference(cnf_transformation,[],[f1467]) ).

fof(f1467,plain,
    ! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)),X0) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0)),
    inference(rectify,[],[f577]) ).

fof(f577,axiom,
    ! [X15,X14] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X14)),X15) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X14),X15)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__zminus) ).

fof(f18893,plain,
    spl50_957,
    inference(avatar_split_clause,[],[f4301,f18891]) ).

fof(f4301,plain,
    ! [X0] :
      ( c_Orderings_Oord__class_Oless(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),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(cnf_transformation,[],[f3491]) ).

fof(f3491,plain,
    ! [X0] :
      ( ( c_Orderings_Oord__class_Oless(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),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless(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),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
    inference(nnf_transformation,[],[f1433]) ).

fof(f1433,plain,
    ! [X0] :
      ( c_Orderings_Oord__class_Oless(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),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(rectify,[],[f599]) ).

fof(f599,axiom,
    ! [X33] :
      ( c_Orderings_Oord__class_Oless(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),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X33,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_odd__less__0) ).

fof(f18888,plain,
    spl50_956,
    inference(avatar_split_clause,[],[f4300,f18886]) ).

fof(f4300,plain,
    ! [X0] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | ~ c_Orderings_Oord__class_Oless(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),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(cnf_transformation,[],[f3491]) ).

fof(f18884,plain,
    spl50_955,
    inference(avatar_split_clause,[],[f4194,f18882]) ).

fof(f18882,plain,
    ( spl50_955
  <=> ! [X0] :
        ( c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,X0)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
        | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_955])]) ).

fof(f4194,plain,
    ! [X0] :
      ( c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,X0)
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
      | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 ),
    inference(cnf_transformation,[],[f2307]) ).

fof(f2307,plain,
    ! [X0] :
      ( ( ( ( c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,X0)
            | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) )
          & ( c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,X0)
            | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ) )
        | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 )
      & ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,X0)
        | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ) ),
    inference(ennf_transformation,[],[f1336]) ).

fof(f1336,plain,
    ! [X0] :
      ( ( 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_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,X0) )
          & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
           => c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,X0) ) ) )
      & ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0
       => c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,X0) ) ),
    inference(rectify,[],[f880]) ).

fof(f880,axiom,
    ! [X18] :
      ( ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X18
       => ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X18)
           => c_Groups_Osgn__class_Osgn(tc_Int_Oint,X18) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)) )
          & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X18)
           => c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,X18) ) ) )
      & ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X18
       => c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,X18) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zsgn__def) ).

fof(f18880,plain,
    spl50_954,
    inference(avatar_split_clause,[],[f4188,f18878]) ).

fof(f18878,plain,
    ( spl50_954
  <=> ! [X0] :
        ( c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X0)
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
        | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_954])]) ).

fof(f4188,plain,
    ! [X0] :
      ( c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X0)
      | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
      | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X0 ),
    inference(cnf_transformation,[],[f2305]) ).

fof(f2305,plain,
    ! [X0] :
      ( ( ( ( c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X0)
            | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) )
          & ( c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X0)
            | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ) )
        | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X0 )
      & ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X0)
        | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X0 ) ),
    inference(ennf_transformation,[],[f1334]) ).

fof(f1334,plain,
    ! [X0] :
      ( ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X0
       => ( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
           => c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X0) )
          & ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
           => c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X0) ) ) )
      & ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X0
       => c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X0) ) ),
    inference(rectify,[],[f881]) ).

fof(f881,axiom,
    ! [X9] :
      ( ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X9
       => ( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X9)
           => c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X9) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
          & ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X9)
           => c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X9) ) ) )
      & ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X9
       => c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X9) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__sgn__def) ).

fof(f18876,plain,
    ~ spl50_953,
    inference(avatar_split_clause,[],[f4117,f18873]) ).

fof(f18873,plain,
    ( spl50_953
  <=> c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_953])]) ).

fof(f4117,plain,
    ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))),
    inference(cnf_transformation,[],[f661]) ).

fof(f661,axiom,
    ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_th01) ).

fof(f18785,plain,
    ( spl50_952
    | ~ spl50_324
    | ~ spl50_947 ),
    inference(avatar_split_clause,[],[f17284,f17280,f7586,f18782]) ).

fof(f18782,plain,
    ( spl50_952
  <=> c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK19) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)),v_q____)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_952])]) ).

fof(f7586,plain,
    ( spl50_324
  <=> c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK19) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_324])]) ).

fof(f17280,plain,
    ( spl50_947
  <=> c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)),v_q____)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_947])]) ).

fof(f17284,plain,
    ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK19) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)),v_q____))
    | ~ spl50_324
    | ~ spl50_947 ),
    inference(forward_demodulation,[],[f17282,f7588]) ).

fof(f7588,plain,
    ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK19)
    | ~ spl50_324 ),
    inference(avatar_component_clause,[],[f7586]) ).

fof(f17282,plain,
    ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)),v_q____))
    | ~ spl50_947 ),
    inference(avatar_component_clause,[],[f17280]) ).

fof(f18138,plain,
    ( ~ spl50_201
    | spl50_951
    | ~ spl50_448
    | ~ spl50_845 ),
    inference(avatar_split_clause,[],[f14252,f13307,f8318,f18136,f7051]) ).

fof(f18136,plain,
    ( spl50_951
  <=> ! [X0] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_951])]) ).

fof(f8318,plain,
    ( spl50_448
  <=> ! [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,[spl50_448])]) ).

fof(f13307,plain,
    ( spl50_845
  <=> ! [X0] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_845])]) ).

fof(f14252,plain,
    ( ! [X0] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))
        | ~ class_Orderings_Opreorder(tc_RealDef_Oreal) )
    | ~ spl50_448
    | ~ spl50_845 ),
    inference(resolution,[],[f13308,f8319]) ).

fof(f8319,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) )
    | ~ spl50_448 ),
    inference(avatar_component_clause,[],[f8318]) ).

fof(f13308,plain,
    ( ! [X0] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X0)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) )
    | ~ spl50_845 ),
    inference(avatar_component_clause,[],[f13307]) ).

fof(f17340,plain,
    ( spl50_950
    | ~ spl50_358
    | ~ spl50_932 ),
    inference(avatar_split_clause,[],[f17255,f17208,f7741,f17338]) ).

fof(f7741,plain,
    ( spl50_358
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_358])]) ).

fof(f17208,plain,
    ( spl50_932
  <=> ! [X0] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_932])]) ).

fof(f17255,plain,
    ( ! [X0] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X0) )
    | ~ spl50_358
    | ~ spl50_932 ),
    inference(resolution,[],[f17209,f7742]) ).

fof(f7742,plain,
    ( ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) )
    | ~ spl50_358 ),
    inference(avatar_component_clause,[],[f7741]) ).

fof(f17209,plain,
    ( ! [X0] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
    | ~ spl50_932 ),
    inference(avatar_component_clause,[],[f17208]) ).

fof(f17317,plain,
    ( spl50_949
    | ~ spl50_189
    | ~ spl50_518
    | ~ spl50_914 ),
    inference(avatar_split_clause,[],[f17131,f17128,f8874,f6991,f17315]) ).

fof(f17315,plain,
    ( spl50_949
  <=> ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X0)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_949])]) ).

fof(f6991,plain,
    ( spl50_189
  <=> class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_189])]) ).

fof(f8874,plain,
    ( spl50_518
  <=> ! [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,[spl50_518])]) ).

fof(f17128,plain,
    ( spl50_914
  <=> ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X0)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_914])]) ).

fof(f17131,plain,
    ( ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X0))))
    | ~ spl50_189
    | ~ spl50_518
    | ~ spl50_914 ),
    inference(forward_demodulation,[],[f17129,f9396]) ).

fof(f9396,plain,
    ( ! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1)
    | ~ spl50_189
    | ~ spl50_518 ),
    inference(resolution,[],[f8875,f6993]) ).

fof(f6993,plain,
    ( class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)
    | ~ spl50_189 ),
    inference(avatar_component_clause,[],[f6991]) ).

fof(f8875,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Rings_Ocomm__semiring__1(X2)
        | c_Groups_Oplus__class_Oplus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X0,X1) )
    | ~ spl50_518 ),
    inference(avatar_component_clause,[],[f8874]) ).

fof(f17129,plain,
    ( ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X0)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0)))
    | ~ spl50_914 ),
    inference(avatar_component_clause,[],[f17128]) ).

fof(f17288,plain,
    spl50_948,
    inference(avatar_split_clause,[],[f5966,f17286]) ).

fof(f17286,plain,
    ( spl50_948
  <=> ! [X0,X1] :
        ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK33(X0,X1))) = X0
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_948])]) ).

fof(f5966,plain,
    ! [X0,X1] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK33(X0,X1))) = X0
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
    inference(forward_demodulation,[],[f5965,f4313]) ).

fof(f5965,plain,
    ! [X0,X1] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK33(X0,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X0
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
    inference(forward_demodulation,[],[f5629,f5594]) ).

fof(f5594,plain,
    ! [X0,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)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
    inference(definition_unfolding,[],[f4322,f4164,f4164]) ).

fof(f4322,plain,
    ! [X0,X1] : c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Nat_OSuc(X0)),
    inference(cnf_transformation,[],[f1453]) ).

fof(f1453,plain,
    ! [X0,X1] : c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Nat_OSuc(X0)),
    inference(rectify,[],[f939]) ).

fof(f939,axiom,
    ! [X3,X17] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,c_Nat_OSuc(X3)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc__right) ).

fof(f5629,plain,
    ! [X0,X1] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK33(X0,X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
    inference(definition_unfolding,[],[f4674,f4164]) ).

fof(f4674,plain,
    ! [X0,X1] :
      ( c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK33(X0,X1))) = X0
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
    inference(cnf_transformation,[],[f3594]) ).

fof(f3594,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
        | ! [X2] : c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) != X0 )
      & ( c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK33(X0,X1))) = X0
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK33])],[f3592,f3593]) ).

fof(f3593,plain,
    ! [X0,X1] :
      ( ? [X3] : c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)) = X0
     => c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK33(X0,X1))) = X0 ),
    introduced(choice_axiom,[]) ).

fof(f3592,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
        | ! [X2] : c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) != X0 )
      & ( ? [X3] : c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)) = X0
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
    inference(rectify,[],[f3591]) ).

fof(f3591,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
        | ! [X2] : c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) != X0 )
      & ( ? [X2] : c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) = X0
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
    inference(nnf_transformation,[],[f1708]) ).

fof(f1708,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
    <=> ? [X2] : c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) = X0 ),
    inference(rectify,[],[f963]) ).

fof(f963,axiom,
    ! [X16,X32] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X32,X16)
    <=> ? [X52] : c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X32,X52)) = X16 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__iff__Suc__add) ).

fof(f17283,plain,
    spl50_947,
    inference(avatar_split_clause,[],[f5907,f17280]) ).

fof(f5907,plain,
    c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)),v_q____)),
    inference(forward_demodulation,[],[f5906,f4106]) ).

fof(f4106,plain,
    c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_q____),
    inference(cnf_transformation,[],[f554]) ).

fof(f554,axiom,
    c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_q____),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_q_I1_J) ).

fof(f5906,plain,
    c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_q____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)),v_q____)),
    inference(forward_demodulation,[],[f4118,f4114]) ).

fof(f4118,plain,
    c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_q____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),
    inference(cnf_transformation,[],[f572]) ).

fof(f572,axiom,
    c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_q____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lgqr) ).

fof(f17278,plain,
    spl50_946,
    inference(avatar_split_clause,[],[f5682,f17276]) ).

fof(f17276,plain,
    ( spl50_946
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_946])]) ).

fof(f5682,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
    inference(definition_unfolding,[],[f5141,f4164]) ).

fof(f5141,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X2),X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
    inference(cnf_transformation,[],[f3031]) ).

fof(f3031,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X2),X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
    inference(flattening,[],[f3030]) ).

fof(f3030,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X2),X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
    inference(ennf_transformation,[],[f2011]) ).

fof(f2011,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X2),X0) ) ),
    inference(rectify,[],[f967]) ).

fof(f967,axiom,
    ! [X38,X39,X18] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X39)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X39,X38)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X18),X38) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__trans__Suc) ).

fof(f17274,plain,
    spl50_945,
    inference(avatar_split_clause,[],[f5647,f17272]) ).

fof(f17272,plain,
    ( spl50_945
  <=> ! [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,X1,c_Groups_Oone__class_Oone(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,[spl50_945])]) ).

fof(f5647,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,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(definition_unfolding,[],[f4692,f4164,f4164]) ).

fof(f4692,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(X1),c_Nat_OSuc(X0)) ),
    inference(cnf_transformation,[],[f3607]) ).

fof(f3607,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(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__eq(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X0)) ) ),
    inference(nnf_transformation,[],[f1715]) ).

fof(f1715,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X0))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
    inference(rectify,[],[f952]) ).

fof(f952,axiom,
    ! [X32,X16] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X16),c_Nat_OSuc(X32))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X16,X32) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__mono) ).

fof(f17270,plain,
    spl50_944,
    inference(avatar_split_clause,[],[f5617,f17268]) ).

fof(f17268,plain,
    ( spl50_944
  <=> ! [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,X1,c_Groups_Oone__class_Oone(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,[spl50_944])]) ).

fof(f5617,plain,
    ! [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,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(definition_unfolding,[],[f4608,f4164,f4164]) ).

fof(f4608,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X0)) ),
    inference(cnf_transformation,[],[f2640]) ).

fof(f2640,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X0)) ),
    inference(ennf_transformation,[],[f1672]) ).

fof(f1672,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X0))
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
    inference(rectify,[],[f964]) ).

fof(f964,axiom,
    ! [X3,X17] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X17),c_Nat_OSuc(X3))
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__less__SucD) ).

fof(f17266,plain,
    spl50_943,
    inference(avatar_split_clause,[],[f5444,f17264]) ).

fof(f17264,plain,
    ( spl50_943
  <=> ! [X2,X3,X0,X5,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X3,hAPP(X1,X5),hAPP(X0,X5))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0)
        | ~ class_Orderings_Oord(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_943])]) ).

fof(f5444,plain,
    ! [X2,X3,X0,X1,X5] :
      ( c_Orderings_Oord__class_Oless__eq(X3,hAPP(X1,X5),hAPP(X0,X5))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0)
      | ~ class_Orderings_Oord(X3) ),
    inference(cnf_transformation,[],[f3836]) ).

fof(f3836,plain,
    ! [X0,X1,X2,X3] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0)
          | ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(X1,sK42(X0,X1,X3)),hAPP(X0,sK42(X0,X1,X3))) )
        & ( ! [X5] : c_Orderings_Oord__class_Oless__eq(X3,hAPP(X1,X5),hAPP(X0,X5))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0) ) )
      | ~ class_Orderings_Oord(X3) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK42])],[f3834,f3835]) ).

fof(f3835,plain,
    ! [X0,X1,X3] :
      ( ? [X4] : ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(X1,X4),hAPP(X0,X4))
     => ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(X1,sK42(X0,X1,X3)),hAPP(X0,sK42(X0,X1,X3))) ),
    introduced(choice_axiom,[]) ).

fof(f3834,plain,
    ! [X0,X1,X2,X3] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0)
          | ? [X4] : ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(X1,X4),hAPP(X0,X4)) )
        & ( ! [X5] : c_Orderings_Oord__class_Oless__eq(X3,hAPP(X1,X5),hAPP(X0,X5))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0) ) )
      | ~ class_Orderings_Oord(X3) ),
    inference(rectify,[],[f3833]) ).

fof(f3833,plain,
    ! [X0,X1,X2,X3] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0)
          | ? [X4] : ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(X1,X4),hAPP(X0,X4)) )
        & ( ! [X4] : c_Orderings_Oord__class_Oless__eq(X3,hAPP(X1,X4),hAPP(X0,X4))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0) ) )
      | ~ class_Orderings_Oord(X3) ),
    inference(nnf_transformation,[],[f3305]) ).

fof(f3305,plain,
    ! [X0,X1,X2,X3] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0)
      <=> ! [X4] : c_Orderings_Oord__class_Oless__eq(X3,hAPP(X1,X4),hAPP(X0,X4)) )
      | ~ class_Orderings_Oord(X3) ),
    inference(ennf_transformation,[],[f2208]) ).

fof(f2208,plain,
    ! [X0,X1,X2,X3] :
      ( class_Orderings_Oord(X3)
     => ( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0)
      <=> ! [X4] : c_Orderings_Oord__class_Oless__eq(X3,hAPP(X1,X4),hAPP(X0,X4)) ) ),
    inference(rectify,[],[f712]) ).

fof(f712,axiom,
    ! [X0,X1,X5,X46] :
      ( class_Orderings_Oord(X46)
     => ( c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X46),X1,X0)
      <=> ! [X2] : c_Orderings_Oord__class_Oless__eq(X46,hAPP(X1,X2),hAPP(X0,X2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__fun__def) ).

fof(f17250,plain,
    spl50_942,
    inference(avatar_split_clause,[],[f5411,f17248]) ).

fof(f17248,plain,
    ( spl50_942
  <=> ! [X0,X3,X2,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X1
        | c_Polynomial_Osmult(X3,X2,X1) != c_Polynomial_OpCons(X3,X0,X1)
        | ~ class_Rings_Ocomm__semiring__0(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_942])]) ).

fof(f5411,plain,
    ! [X2,X3,X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X1
      | c_Polynomial_Osmult(X3,X2,X1) != c_Polynomial_OpCons(X3,X0,X1)
      | ~ class_Rings_Ocomm__semiring__0(X3) ),
    inference(cnf_transformation,[],[f3257]) ).

fof(f3257,plain,
    ! [X0,X1,X2,X3] :
      ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X1
      | c_Polynomial_Osmult(X3,X2,X1) != c_Polynomial_OpCons(X3,X0,X1)
      | ~ class_Rings_Ocomm__semiring__0(X3) ),
    inference(flattening,[],[f3256]) ).

fof(f3256,plain,
    ! [X0,X1,X2,X3] :
      ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X1
      | c_Polynomial_Osmult(X3,X2,X1) != c_Polynomial_OpCons(X3,X0,X1)
      | ~ class_Rings_Ocomm__semiring__0(X3) ),
    inference(ennf_transformation,[],[f2175]) ).

fof(f2175,plain,
    ! [X0,X1,X2,X3] :
      ( class_Rings_Ocomm__semiring__0(X3)
     => ( c_Polynomial_Osmult(X3,X2,X1) = c_Polynomial_OpCons(X3,X0,X1)
       => c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X1 ) ),
    inference(rectify,[],[f601]) ).

fof(f601,axiom,
    ! [X4,X54,X23,X5] :
      ( class_Rings_Ocomm__semiring__0(X5)
     => ( c_Polynomial_Osmult(X5,X23,X54) = c_Polynomial_OpCons(X5,X4,X54)
       => c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = X54 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_synthetic__div__unique__lemma) ).

fof(f17246,plain,
    spl50_941,
    inference(avatar_split_clause,[],[f5335,f17244]) ).

fof(f17244,plain,
    ( spl50_941
  <=> ! [X0,X3,X2,X1] :
        ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X2,X0))
        | ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_941])]) ).

fof(f5335,plain,
    ! [X2,X3,X0,X1] :
      ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X2,X0))
      | ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ),
    inference(cnf_transformation,[],[f3822]) ).

fof(f3822,plain,
    ! [X0,X1,X2,X3] :
      ( ( ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X2,X0))
          | ~ c_Orderings_Oord__class_Oless(X3,X1,X0) )
        & ( c_Orderings_Oord__class_Oless(X3,X1,X0)
          | ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X2,X0)) ) )
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ),
    inference(nnf_transformation,[],[f3159]) ).

fof(f3159,plain,
    ! [X0,X1,X2,X3] :
      ( ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X2,X0))
      <=> c_Orderings_Oord__class_Oless(X3,X1,X0) )
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ),
    inference(ennf_transformation,[],[f2109]) ).

fof(f2109,plain,
    ! [X0,X1,X2,X3] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X2,X0))
      <=> c_Orderings_Oord__class_Oless(X3,X1,X0) ) ),
    inference(rectify,[],[f225]) ).

fof(f225,axiom,
    ! [X21,X24,X25,X5] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X5)
     => ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,X25,X24),c_Groups_Oplus__class_Oplus(X5,X25,X21))
      <=> c_Orderings_Oord__class_Oless(X5,X24,X21) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__cancel__left) ).

fof(f17242,plain,
    spl50_940,
    inference(avatar_split_clause,[],[f5333,f17240]) ).

fof(f17240,plain,
    ( spl50_940
  <=> ! [X0,X3,X2,X1] :
        ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1))
        | ~ c_Orderings_Oord__class_Oless(X3,X2,X0)
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_940])]) ).

fof(f5333,plain,
    ! [X2,X3,X0,X1] :
      ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1))
      | ~ c_Orderings_Oord__class_Oless(X3,X2,X0)
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ),
    inference(cnf_transformation,[],[f3821]) ).

fof(f3821,plain,
    ! [X0,X1,X2,X3] :
      ( ( ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1))
          | ~ c_Orderings_Oord__class_Oless(X3,X2,X0) )
        & ( c_Orderings_Oord__class_Oless(X3,X2,X0)
          | ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1)) ) )
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ),
    inference(nnf_transformation,[],[f3158]) ).

fof(f3158,plain,
    ! [X0,X1,X2,X3] :
      ( ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1))
      <=> c_Orderings_Oord__class_Oless(X3,X2,X0) )
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ),
    inference(ennf_transformation,[],[f2108]) ).

fof(f2108,plain,
    ! [X0,X1,X2,X3] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1))
      <=> c_Orderings_Oord__class_Oless(X3,X2,X0) ) ),
    inference(rectify,[],[f224]) ).

fof(f224,axiom,
    ! [X21,X25,X24,X5] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X5)
     => ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,X24,X25),c_Groups_Oplus__class_Oplus(X5,X21,X25))
      <=> c_Orderings_Oord__class_Oless(X5,X24,X21) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__cancel__right) ).

fof(f17238,plain,
    spl50_939,
    inference(avatar_split_clause,[],[f5331,f17236]) ).

fof(f17236,plain,
    ( spl50_939
  <=> ! [X0,X3,X2,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X2,X0))
        | ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_939])]) ).

fof(f5331,plain,
    ! [X2,X3,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X2,X0))
      | ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ),
    inference(cnf_transformation,[],[f3820]) ).

fof(f3820,plain,
    ! [X0,X1,X2,X3] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X2,X0))
          | ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0) )
        & ( c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
          | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X2,X0)) ) )
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ),
    inference(nnf_transformation,[],[f3157]) ).

fof(f3157,plain,
    ! [X0,X1,X2,X3] :
      ( ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X2,X0))
      <=> c_Orderings_Oord__class_Oless__eq(X3,X1,X0) )
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ),
    inference(ennf_transformation,[],[f2107]) ).

fof(f2107,plain,
    ! [X0,X1,X2,X3] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X2,X0))
      <=> c_Orderings_Oord__class_Oless__eq(X3,X1,X0) ) ),
    inference(rectify,[],[f218]) ).

fof(f218,axiom,
    ! [X21,X24,X25,X5] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X5)
     => ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,X25,X24),c_Groups_Oplus__class_Oplus(X5,X25,X21))
      <=> c_Orderings_Oord__class_Oless__eq(X5,X24,X21) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__cancel__left) ).

fof(f17234,plain,
    spl50_938,
    inference(avatar_split_clause,[],[f5329,f17232]) ).

fof(f17232,plain,
    ( spl50_938
  <=> ! [X0,X3,X2,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1))
        | ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X0)
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_938])]) ).

fof(f5329,plain,
    ! [X2,X3,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1))
      | ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X0)
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ),
    inference(cnf_transformation,[],[f3819]) ).

fof(f3819,plain,
    ! [X0,X1,X2,X3] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1))
          | ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X0) )
        & ( c_Orderings_Oord__class_Oless__eq(X3,X2,X0)
          | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1)) ) )
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ),
    inference(nnf_transformation,[],[f3156]) ).

fof(f3156,plain,
    ! [X0,X1,X2,X3] :
      ( ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1))
      <=> c_Orderings_Oord__class_Oless__eq(X3,X2,X0) )
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ),
    inference(ennf_transformation,[],[f2106]) ).

fof(f2106,plain,
    ! [X0,X1,X2,X3] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1))
      <=> c_Orderings_Oord__class_Oless__eq(X3,X2,X0) ) ),
    inference(rectify,[],[f217]) ).

fof(f217,axiom,
    ! [X21,X25,X24,X5] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X5)
     => ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,X24,X25),c_Groups_Oplus__class_Oplus(X5,X21,X25))
      <=> c_Orderings_Oord__class_Oless__eq(X5,X24,X21) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__cancel__right) ).

fof(f17230,plain,
    spl50_937,
    inference(avatar_split_clause,[],[f5327,f17228]) ).

fof(f17228,plain,
    ( spl50_937
  <=> ! [X0,X3,X2,X1] :
        ( c_Orderings_Oord__class_Oless(X3,X2,X0)
        | ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1))
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_937])]) ).

fof(f5327,plain,
    ! [X2,X3,X0,X1] :
      ( c_Orderings_Oord__class_Oless(X3,X2,X0)
      | ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ),
    inference(cnf_transformation,[],[f3155]) ).

fof(f3155,plain,
    ! [X0,X1,X2,X3] :
      ( c_Orderings_Oord__class_Oless(X3,X2,X0)
      | ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ),
    inference(flattening,[],[f3154]) ).

fof(f3154,plain,
    ! [X0,X1,X2,X3] :
      ( c_Orderings_Oord__class_Oless(X3,X2,X0)
      | ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ),
    inference(ennf_transformation,[],[f2105]) ).

fof(f2105,plain,
    ! [X0,X1,X2,X3] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1))
       => c_Orderings_Oord__class_Oless(X3,X2,X0) ) ),
    inference(rectify,[],[f229]) ).

fof(f229,axiom,
    ! [X13,X23,X4,X5] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X5)
     => ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,X4,X23),c_Groups_Oplus__class_Oplus(X5,X13,X23))
       => c_Orderings_Oord__class_Oless(X5,X4,X13) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__imp__less__right) ).

fof(f17226,plain,
    spl50_936,
    inference(avatar_split_clause,[],[f5326,f17224]) ).

fof(f17224,plain,
    ( spl50_936
  <=> ! [X0,X3,X2,X1] :
        ( c_Orderings_Oord__class_Oless(X3,X1,X0)
        | ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X2,X0))
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_936])]) ).

fof(f5326,plain,
    ! [X2,X3,X0,X1] :
      ( c_Orderings_Oord__class_Oless(X3,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X2,X0))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ),
    inference(cnf_transformation,[],[f3153]) ).

fof(f3153,plain,
    ! [X0,X1,X2,X3] :
      ( c_Orderings_Oord__class_Oless(X3,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X2,X0))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ),
    inference(flattening,[],[f3152]) ).

fof(f3152,plain,
    ! [X0,X1,X2,X3] :
      ( c_Orderings_Oord__class_Oless(X3,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X2,X0))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ),
    inference(ennf_transformation,[],[f2104]) ).

fof(f2104,plain,
    ! [X0,X1,X2,X3] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X2,X0))
       => c_Orderings_Oord__class_Oless(X3,X1,X0) ) ),
    inference(rectify,[],[f230]) ).

fof(f230,axiom,
    ! [X13,X4,X23,X5] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X5)
     => ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,X23,X4),c_Groups_Oplus__class_Oplus(X5,X23,X13))
       => c_Orderings_Oord__class_Oless(X5,X4,X13) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__imp__less__left) ).

fof(f17222,plain,
    spl50_935,
    inference(avatar_split_clause,[],[f5325,f17220]) ).

fof(f17220,plain,
    ( spl50_935
  <=> ! [X0,X3,X2,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X3,X2,X0)
        | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1))
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_935])]) ).

fof(f5325,plain,
    ! [X2,X3,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X3,X2,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ),
    inference(cnf_transformation,[],[f3151]) ).

fof(f3151,plain,
    ! [X0,X1,X2,X3] :
      ( c_Orderings_Oord__class_Oless__eq(X3,X2,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ),
    inference(flattening,[],[f3150]) ).

fof(f3150,plain,
    ! [X0,X1,X2,X3] :
      ( c_Orderings_Oord__class_Oless__eq(X3,X2,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ),
    inference(ennf_transformation,[],[f2103]) ).

fof(f2103,plain,
    ! [X0,X1,X2,X3] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1))
       => c_Orderings_Oord__class_Oless__eq(X3,X2,X0) ) ),
    inference(rectify,[],[f222]) ).

fof(f222,axiom,
    ! [X13,X23,X4,X5] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X5)
     => ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,X4,X23),c_Groups_Oplus__class_Oplus(X5,X13,X23))
       => c_Orderings_Oord__class_Oless__eq(X5,X4,X13) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__imp__le__right) ).

fof(f17218,plain,
    spl50_934,
    inference(avatar_split_clause,[],[f5324,f17216]) ).

fof(f17216,plain,
    ( spl50_934
  <=> ! [X0,X3,X2,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
        | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X2,X0))
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_934])]) ).

fof(f5324,plain,
    ! [X2,X3,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X2,X0))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ),
    inference(cnf_transformation,[],[f3149]) ).

fof(f3149,plain,
    ! [X0,X1,X2,X3] :
      ( c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X2,X0))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ),
    inference(flattening,[],[f3148]) ).

fof(f3148,plain,
    ! [X0,X1,X2,X3] :
      ( c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X2,X0))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ),
    inference(ennf_transformation,[],[f2102]) ).

fof(f2102,plain,
    ! [X0,X1,X2,X3] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X2,X0))
       => c_Orderings_Oord__class_Oless__eq(X3,X1,X0) ) ),
    inference(rectify,[],[f223]) ).

fof(f223,axiom,
    ! [X13,X4,X23,X5] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X5)
     => ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,X23,X4),c_Groups_Oplus__class_Oplus(X5,X23,X13))
       => c_Orderings_Oord__class_Oless__eq(X5,X4,X13) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__imp__le__left) ).

fof(f17214,plain,
    spl50_933,
    inference(avatar_split_clause,[],[f5323,f17212]) ).

fof(f17212,plain,
    ( spl50_933
  <=> ! [X0,X3,X2,X1] :
        ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X0,X2),c_Groups_Oplus__class_Oplus(X3,X0,X1))
        | ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
        | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_933])]) ).

fof(f5323,plain,
    ! [X2,X3,X0,X1] :
      ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X0,X2),c_Groups_Oplus__class_Oplus(X3,X0,X1))
      | ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X3) ),
    inference(cnf_transformation,[],[f3147]) ).

fof(f3147,plain,
    ! [X0,X1,X2,X3] :
      ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X0,X2),c_Groups_Oplus__class_Oplus(X3,X0,X1))
      | ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X3) ),
    inference(flattening,[],[f3146]) ).

fof(f3146,plain,
    ! [X0,X1,X2,X3] :
      ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X0,X2),c_Groups_Oplus__class_Oplus(X3,X0,X1))
      | ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X3) ),
    inference(ennf_transformation,[],[f2101]) ).

fof(f2101,plain,
    ! [X0,X1,X2,X3] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(X3)
     => ( c_Orderings_Oord__class_Oless(X3,X2,X1)
       => c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X0,X2),c_Groups_Oplus__class_Oplus(X3,X0,X1)) ) ),
    inference(rectify,[],[f227]) ).

fof(f227,axiom,
    ! [X23,X13,X4,X5] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(X5)
     => ( c_Orderings_Oord__class_Oless(X5,X4,X13)
       => c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,X23,X4),c_Groups_Oplus__class_Oplus(X5,X23,X13)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__left__mono) ).

fof(f17210,plain,
    ( ~ spl50_205
    | spl50_932
    | ~ spl50_833
    | ~ spl50_844 ),
    inference(avatar_split_clause,[],[f14849,f13070,f12405,f17208,f7071]) ).

fof(f7071,plain,
    ( spl50_205
  <=> class_Orderings_Oorder(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_205])]) ).

fof(f12405,plain,
    ( spl50_833
  <=> ! [X0,X3,X2,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X3,X0,X1)
        | ~ c_Orderings_Oord__class_Oless__eq(X3,X0,X2)
        | ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
        | ~ class_Orderings_Oorder(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_833])]) ).

fof(f13070,plain,
    ( spl50_844
  <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_844])]) ).

fof(f14849,plain,
    ( ! [X0] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | ~ class_Orderings_Oorder(tc_RealDef_Oreal) )
    | ~ spl50_833
    | ~ spl50_844 ),
    inference(resolution,[],[f12406,f13072]) ).

fof(f13072,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    | ~ spl50_844 ),
    inference(avatar_component_clause,[],[f13070]) ).

fof(f12406,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
        | ~ c_Orderings_Oord__class_Oless__eq(X3,X0,X2)
        | c_Orderings_Oord__class_Oless__eq(X3,X0,X1)
        | ~ class_Orderings_Oorder(X3) )
    | ~ spl50_833 ),
    inference(avatar_component_clause,[],[f12405]) ).

fof(f17206,plain,
    spl50_931,
    inference(avatar_split_clause,[],[f5322,f17204]) ).

fof(f17204,plain,
    ( spl50_931
  <=> ! [X0,X3,X2,X1] :
        ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X0),c_Groups_Oplus__class_Oplus(X3,X1,X0))
        | ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
        | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_931])]) ).

fof(f5322,plain,
    ! [X2,X3,X0,X1] :
      ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X0),c_Groups_Oplus__class_Oplus(X3,X1,X0))
      | ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X3) ),
    inference(cnf_transformation,[],[f3145]) ).

fof(f3145,plain,
    ! [X0,X1,X2,X3] :
      ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X0),c_Groups_Oplus__class_Oplus(X3,X1,X0))
      | ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X3) ),
    inference(flattening,[],[f3144]) ).

fof(f3144,plain,
    ! [X0,X1,X2,X3] :
      ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X0),c_Groups_Oplus__class_Oplus(X3,X1,X0))
      | ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X3) ),
    inference(ennf_transformation,[],[f2100]) ).

fof(f2100,plain,
    ! [X0,X1,X2,X3] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(X3)
     => ( c_Orderings_Oord__class_Oless(X3,X2,X1)
       => c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X0),c_Groups_Oplus__class_Oplus(X3,X1,X0)) ) ),
    inference(rectify,[],[f226]) ).

fof(f226,axiom,
    ! [X23,X13,X4,X5] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(X5)
     => ( c_Orderings_Oord__class_Oless(X5,X4,X13)
       => c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,X4,X23),c_Groups_Oplus__class_Oplus(X5,X13,X23)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__right__mono) ).

fof(f17202,plain,
    spl50_930,
    inference(avatar_split_clause,[],[f5319,f17200]) ).

fof(f17200,plain,
    ( spl50_930
  <=> ! [X0,X3,X2,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X0,X2),c_Groups_Oplus__class_Oplus(X3,X0,X1))
        | ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
        | ~ class_Groups_Oordered__ab__semigroup__add(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_930])]) ).

fof(f5319,plain,
    ! [X2,X3,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X0,X2),c_Groups_Oplus__class_Oplus(X3,X0,X1))
      | ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
      | ~ class_Groups_Oordered__ab__semigroup__add(X3) ),
    inference(cnf_transformation,[],[f3139]) ).

fof(f3139,plain,
    ! [X0,X1,X2,X3] :
      ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X0,X2),c_Groups_Oplus__class_Oplus(X3,X0,X1))
      | ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
      | ~ class_Groups_Oordered__ab__semigroup__add(X3) ),
    inference(flattening,[],[f3138]) ).

fof(f3138,plain,
    ! [X0,X1,X2,X3] :
      ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X0,X2),c_Groups_Oplus__class_Oplus(X3,X0,X1))
      | ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
      | ~ class_Groups_Oordered__ab__semigroup__add(X3) ),
    inference(ennf_transformation,[],[f2097]) ).

fof(f2097,plain,
    ! [X0,X1,X2,X3] :
      ( class_Groups_Oordered__ab__semigroup__add(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
       => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X0,X2),c_Groups_Oplus__class_Oplus(X3,X0,X1)) ) ),
    inference(rectify,[],[f220]) ).

fof(f220,axiom,
    ! [X23,X13,X4,X5] :
      ( class_Groups_Oordered__ab__semigroup__add(X5)
     => ( c_Orderings_Oord__class_Oless__eq(X5,X4,X13)
       => c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,X23,X4),c_Groups_Oplus__class_Oplus(X5,X23,X13)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__mono) ).

fof(f17198,plain,
    spl50_929,
    inference(avatar_split_clause,[],[f5318,f17196]) ).

fof(f17196,plain,
    ( spl50_929
  <=> ! [X0,X3,X2,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X0),c_Groups_Oplus__class_Oplus(X3,X1,X0))
        | ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
        | ~ class_Groups_Oordered__ab__semigroup__add(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_929])]) ).

fof(f5318,plain,
    ! [X2,X3,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X0),c_Groups_Oplus__class_Oplus(X3,X1,X0))
      | ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
      | ~ class_Groups_Oordered__ab__semigroup__add(X3) ),
    inference(cnf_transformation,[],[f3137]) ).

fof(f3137,plain,
    ! [X0,X1,X2,X3] :
      ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X0),c_Groups_Oplus__class_Oplus(X3,X1,X0))
      | ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
      | ~ class_Groups_Oordered__ab__semigroup__add(X3) ),
    inference(flattening,[],[f3136]) ).

fof(f3136,plain,
    ! [X0,X1,X2,X3] :
      ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X0),c_Groups_Oplus__class_Oplus(X3,X1,X0))
      | ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
      | ~ class_Groups_Oordered__ab__semigroup__add(X3) ),
    inference(ennf_transformation,[],[f2096]) ).

fof(f2096,plain,
    ! [X0,X1,X2,X3] :
      ( class_Groups_Oordered__ab__semigroup__add(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
       => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X0),c_Groups_Oplus__class_Oplus(X3,X1,X0)) ) ),
    inference(rectify,[],[f219]) ).

fof(f219,axiom,
    ! [X23,X13,X4,X5] :
      ( class_Groups_Oordered__ab__semigroup__add(X5)
     => ( c_Orderings_Oord__class_Oless__eq(X5,X4,X13)
       => c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,X4,X23),c_Groups_Oplus__class_Oplus(X5,X13,X23)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__right__mono) ).

fof(f17194,plain,
    spl50_928,
    inference(avatar_split_clause,[],[f5229,f17192]) ).

fof(f17192,plain,
    ( spl50_928
  <=> ! [X2,X0,X1] :
        ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0)))
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_928])]) ).

fof(f5229,plain,
    ! [X2,X0,X1] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0)))
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X1) ),
    inference(cnf_transformation,[],[f3779]) ).

fof(f3779,plain,
    ! [X0,X1,X2] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0)))
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X1) )
      & ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X1)
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0))) ) ),
    inference(nnf_transformation,[],[f2055]) ).

fof(f2055,plain,
    ! [X0,X1,X2] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0)))
    <=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X1) ),
    inference(rectify,[],[f857]) ).

fof(f857,axiom,
    ! [X32,X16,X36] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X36,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X16,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X36),X32)))
    <=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,X36,X16) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__reduce) ).

fof(f17190,plain,
    spl50_927,
    inference(avatar_split_clause,[],[f5228,f17188]) ).

fof(f17188,plain,
    ( spl50_927
  <=> ! [X2,X0,X1] :
        ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X1)
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_927])]) ).

fof(f5228,plain,
    ! [X2,X0,X1] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X1)
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0))) ),
    inference(cnf_transformation,[],[f3779]) ).

fof(f17186,plain,
    spl50_926,
    inference(avatar_split_clause,[],[f5213,f17184]) ).

fof(f17184,plain,
    ( spl50_926
  <=> ! [X2,X0,X1] :
        ( sP8(X0,X1,X2)
        | ~ hBOOL(hAPP(X0,sK41(X0,X1,X2)))
        | ~ hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_926])]) ).

fof(f5213,plain,
    ! [X2,X0,X1] :
      ( sP8(X0,X1,X2)
      | ~ hBOOL(hAPP(X0,sK41(X0,X1,X2)))
      | ~ hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(cnf_transformation,[],[f3771]) ).

fof(f17182,plain,
    spl50_925,
    inference(avatar_split_clause,[],[f5205,f17180]) ).

fof(f17180,plain,
    ( spl50_925
  <=> ! [X2,X0,X1] :
        ( sP7(X0,X1,X2)
        | ~ hBOOL(hAPP(X0,sK40(X0,X1,X2)))
        | ~ hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_925])]) ).

fof(f5205,plain,
    ! [X2,X0,X1] :
      ( sP7(X0,X1,X2)
      | ~ hBOOL(hAPP(X0,sK40(X0,X1,X2)))
      | ~ hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(cnf_transformation,[],[f3765]) ).

fof(f17178,plain,
    spl50_924,
    inference(avatar_split_clause,[],[f5054,f17176]) ).

fof(f17176,plain,
    ( spl50_924
  <=> ! [X2,X0,X1] :
        ( c_Rings_Odvd__class_Odvd(X2,X0,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),X1))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
        | ~ class_Rings_Ocomm__semiring__1(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_924])]) ).

fof(f5054,plain,
    ! [X2,X0,X1] :
      ( c_Rings_Odvd__class_Odvd(X2,X0,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),X1))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
      | ~ class_Rings_Ocomm__semiring__1(X2) ),
    inference(cnf_transformation,[],[f2930]) ).

fof(f2930,plain,
    ! [X0,X1,X2] :
      ( c_Rings_Odvd__class_Odvd(X2,X0,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),X1))
      | ( c_Groups_Oone__class_Oone(X2) != X0
        & ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) )
      | ~ class_Rings_Ocomm__semiring__1(X2) ),
    inference(flattening,[],[f2929]) ).

fof(f2929,plain,
    ! [X0,X1,X2] :
      ( c_Rings_Odvd__class_Odvd(X2,X0,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),X1))
      | ( c_Groups_Oone__class_Oone(X2) != X0
        & ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) )
      | ~ class_Rings_Ocomm__semiring__1(X2) ),
    inference(ennf_transformation,[],[f1944]) ).

fof(f1944,plain,
    ! [X0,X1,X2] :
      ( class_Rings_Ocomm__semiring__1(X2)
     => ( ( c_Groups_Oone__class_Oone(X2) = X0
          | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) )
       => c_Rings_Odvd__class_Odvd(X2,X0,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),X1)) ) ),
    inference(rectify,[],[f847]) ).

fof(f847,axiom,
    ! [X9,X3,X5] :
      ( class_Rings_Ocomm__semiring__1(X5)
     => ( ( c_Groups_Oone__class_Oone(X5) = X9
          | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3) )
       => c_Rings_Odvd__class_Odvd(X5,X9,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X9),X3)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__power) ).

fof(f17174,plain,
    spl50_923,
    inference(avatar_split_clause,[],[f4993,f17172]) ).

fof(f17172,plain,
    ( spl50_923
  <=> ! [X2,X0,X1] :
        ( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),c_Polynomial_Omonom(X2,X1,X0)) = c_Polynomial_Omonom(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)
        | ~ class_Groups_Oab__group__add(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_923])]) ).

fof(f4993,plain,
    ! [X2,X0,X1] :
      ( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),c_Polynomial_Omonom(X2,X1,X0)) = c_Polynomial_Omonom(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)
      | ~ class_Groups_Oab__group__add(X2) ),
    inference(cnf_transformation,[],[f2867]) ).

fof(f2867,plain,
    ! [X0,X1,X2] :
      ( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),c_Polynomial_Omonom(X2,X1,X0)) = c_Polynomial_Omonom(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)
      | ~ class_Groups_Oab__group__add(X2) ),
    inference(ennf_transformation,[],[f1895]) ).

fof(f1895,plain,
    ! [X0,X1,X2] :
      ( class_Groups_Oab__group__add(X2)
     => c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),c_Polynomial_Omonom(X2,X1,X0)) = c_Polynomial_Omonom(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0) ),
    inference(rectify,[],[f668]) ).

fof(f668,axiom,
    ! [X3,X4,X5] :
      ( class_Groups_Oab__group__add(X5)
     => c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X5),c_Polynomial_Omonom(X5,X4,X3)) = c_Polynomial_Omonom(X5,c_Groups_Ouminus__class_Ouminus(X5,X4),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__monom) ).

fof(f17170,plain,
    spl50_922,
    inference(avatar_split_clause,[],[f4926,f17168]) ).

fof(f17168,plain,
    ( spl50_922
  <=> ! [X2,X0,X1] :
        ( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),c_Polynomial_Osmult(X2,X1,X0)) = c_Polynomial_Osmult(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)
        | ~ class_Rings_Ocomm__ring(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_922])]) ).

fof(f4926,plain,
    ! [X2,X0,X1] :
      ( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),c_Polynomial_Osmult(X2,X1,X0)) = c_Polynomial_Osmult(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)
      | ~ class_Rings_Ocomm__ring(X2) ),
    inference(cnf_transformation,[],[f2793]) ).

fof(f2793,plain,
    ! [X0,X1,X2] :
      ( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),c_Polynomial_Osmult(X2,X1,X0)) = c_Polynomial_Osmult(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)
      | ~ class_Rings_Ocomm__ring(X2) ),
    inference(ennf_transformation,[],[f1850]) ).

fof(f1850,plain,
    ! [X0,X1,X2] :
      ( class_Rings_Ocomm__ring(X2)
     => c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),c_Polynomial_Osmult(X2,X1,X0)) = c_Polynomial_Osmult(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0) ),
    inference(rectify,[],[f655]) ).

fof(f655,axiom,
    ! [X54,X4,X5] :
      ( class_Rings_Ocomm__ring(X5)
     => c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X5),c_Polynomial_Osmult(X5,X4,X54)) = c_Polynomial_Osmult(X5,c_Groups_Ouminus__class_Ouminus(X5,X4),X54) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__minus__left) ).

fof(f17159,plain,
    spl50_921,
    inference(avatar_split_clause,[],[f4902,f17157]) ).

fof(f17157,plain,
    ( spl50_921
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
        | c_Polynomial_Opos__poly(X2,X0)
        | ~ c_Polynomial_Opos__poly(X2,c_Polynomial_OpCons(X2,X1,X0))
        | ~ class_Rings_Olinordered__idom(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_921])]) ).

fof(f4902,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
      | c_Polynomial_Opos__poly(X2,X0)
      | ~ c_Polynomial_Opos__poly(X2,c_Polynomial_OpCons(X2,X1,X0))
      | ~ class_Rings_Olinordered__idom(X2) ),
    inference(cnf_transformation,[],[f3684]) ).

fof(f3684,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,[],[f3683]) ).

fof(f3683,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,[],[f2770]) ).

fof(f2770,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,[],[f1833]) ).

fof(f1833,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,[],[f784]) ).

fof(f784,axiom,
    ! [X64,X24,X5] :
      ( class_Rings_Olinordered__idom(X5)
     => ( c_Polynomial_Opos__poly(X5,c_Polynomial_OpCons(X5,X24,X64))
      <=> ( ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X24)
            & c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = X64 )
          | c_Polynomial_Opos__poly(X5,X64) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__poly__pCons) ).

fof(f17155,plain,
    spl50_920,
    inference(avatar_split_clause,[],[f4901,f17153]) ).

fof(f17153,plain,
    ( spl50_920
  <=> ! [X2,X0,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) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_920])]) ).

fof(f4901,plain,
    ! [X2,X0,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(cnf_transformation,[],[f3684]) ).

fof(f17151,plain,
    spl50_919,
    inference(avatar_split_clause,[],[f4829,f17149]) ).

fof(f17149,plain,
    ( spl50_919
  <=> ! [X2,X0,X1] :
        ( c_Rings_Oinverse__class_Oinverse(X2,X1) = X0
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) != c_Groups_Oone__class_Oone(X2)
        | ~ class_Rings_Odivision__ring(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_919])]) ).

fof(f4829,plain,
    ! [X2,X0,X1] :
      ( c_Rings_Oinverse__class_Oinverse(X2,X1) = X0
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) != c_Groups_Oone__class_Oone(X2)
      | ~ class_Rings_Odivision__ring(X2) ),
    inference(cnf_transformation,[],[f2723]) ).

fof(f2723,plain,
    ! [X0,X1,X2] :
      ( c_Rings_Oinverse__class_Oinverse(X2,X1) = X0
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) != c_Groups_Oone__class_Oone(X2)
      | ~ class_Rings_Odivision__ring(X2) ),
    inference(flattening,[],[f2722]) ).

fof(f2722,plain,
    ! [X0,X1,X2] :
      ( c_Rings_Oinverse__class_Oinverse(X2,X1) = X0
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) != c_Groups_Oone__class_Oone(X2)
      | ~ class_Rings_Odivision__ring(X2) ),
    inference(ennf_transformation,[],[f1795]) ).

fof(f1795,plain,
    ! [X0,X1,X2] :
      ( class_Rings_Odivision__ring(X2)
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) = c_Groups_Oone__class_Oone(X2)
       => c_Rings_Oinverse__class_Oinverse(X2,X1) = X0 ) ),
    inference(rectify,[],[f167]) ).

fof(f167,axiom,
    ! [X13,X4,X5] :
      ( class_Rings_Odivision__ring(X5)
     => ( c_Groups_Oone__class_Oone(X5) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X13)
       => c_Rings_Oinverse__class_Oinverse(X5,X4) = X13 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__unique) ).

fof(f17147,plain,
    spl50_918,
    inference(avatar_split_clause,[],[f4613,f17145]) ).

fof(f17145,plain,
    ( spl50_918
  <=> ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) != X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_918])]) ).

fof(f4613,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
      | c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) != X1 ),
    inference(cnf_transformation,[],[f2650]) ).

fof(f2650,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
      | c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) != X1 ),
    inference(flattening,[],[f2649]) ).

fof(f2649,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
      | c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) != X1 ),
    inference(ennf_transformation,[],[f1677]) ).

fof(f1677,plain,
    ! [X0,X1] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) = X1
     => ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0 ) ),
    inference(rectify,[],[f435]) ).

fof(f435,axiom,
    ! [X3,X17] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X3) = X17
     => ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X17
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) = X3 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__eq__self__implies__10) ).

fof(f17143,plain,
    spl50_917,
    inference(avatar_split_clause,[],[f4450,f17141]) ).

fof(f17141,plain,
    ( spl50_917
  <=> ! [X0,X1] :
        ( c_Polynomial_Opos__poly(X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X0))
        | c_Polynomial_Opos__poly(X1,X0)
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X0
        | ~ class_Rings_Olinordered__idom(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_917])]) ).

fof(f4450,plain,
    ! [X0,X1] :
      ( c_Polynomial_Opos__poly(X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X0))
      | c_Polynomial_Opos__poly(X1,X0)
      | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X0
      | ~ class_Rings_Olinordered__idom(X1) ),
    inference(cnf_transformation,[],[f2480]) ).

fof(f2480,plain,
    ! [X0,X1] :
      ( c_Polynomial_Opos__poly(X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X0))
      | c_Polynomial_Opos__poly(X1,X0)
      | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X0
      | ~ class_Rings_Olinordered__idom(X1) ),
    inference(flattening,[],[f2479]) ).

fof(f2479,plain,
    ! [X0,X1] :
      ( c_Polynomial_Opos__poly(X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X0))
      | c_Polynomial_Opos__poly(X1,X0)
      | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X0
      | ~ class_Rings_Olinordered__idom(X1) ),
    inference(ennf_transformation,[],[f1540]) ).

fof(f1540,plain,
    ! [X0,X1] :
      ( class_Rings_Olinordered__idom(X1)
     => ( c_Polynomial_Opos__poly(X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X0))
        | c_Polynomial_Opos__poly(X1,X0)
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X0 ) ),
    inference(rectify,[],[f791]) ).

fof(f791,axiom,
    ! [X54,X5] :
      ( class_Rings_Olinordered__idom(X5)
     => ( c_Polynomial_Opos__poly(X5,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X5),X54))
        | c_Polynomial_Opos__poly(X5,X54)
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = X54 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__poly__total) ).

fof(f17139,plain,
    spl50_916,
    inference(avatar_split_clause,[],[f4333,f17137]) ).

fof(f17137,plain,
    ( spl50_916
  <=> ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X0)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_916])]) ).

fof(f4333,plain,
    ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X0)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0)),
    inference(cnf_transformation,[],[f1464]) ).

fof(f1464,plain,
    ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X0)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0)),
    inference(rectify,[],[f493]) ).

fof(f493,axiom,
    ! [X4,X13] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X13,X4)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X13)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X4)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__mod__triangle__ineq2) ).

fof(f17135,plain,
    spl50_915,
    inference(avatar_split_clause,[],[f4332,f17133]) ).

fof(f17133,plain,
    ( spl50_915
  <=> ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_915])]) ).

fof(f4332,plain,
    ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),X0)),
    inference(cnf_transformation,[],[f1463]) ).

fof(f1463,plain,
    ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),X0)),
    inference(rectify,[],[f472]) ).

fof(f472,axiom,
    ! [X9,X6] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X6),X6)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X9),X9)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__minus__mult__self__le) ).

fof(f17130,plain,
    spl50_914,
    inference(avatar_split_clause,[],[f4331,f17128]) ).

fof(f4331,plain,
    ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X0)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0))),
    inference(cnf_transformation,[],[f1462]) ).

fof(f1462,plain,
    ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X0)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0))),
    inference(rectify,[],[f20]) ).

fof(f20,axiom,
    ! [X14,X15] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X15),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X15,X14)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X14))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__mod__triangle__sub) ).

fof(f17126,plain,
    spl50_913,
    inference(avatar_split_clause,[],[f4182,f17124]) ).

fof(f17124,plain,
    ( spl50_913
  <=> ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_913])]) ).

fof(f4182,plain,
    ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),X0))),
    inference(cnf_transformation,[],[f1330]) ).

fof(f1330,plain,
    ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),X0))),
    inference(rectify,[],[f444]) ).

fof(f444,axiom,
    ! [X43] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),X43))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_c) ).

fof(f17122,plain,
    spl50_912,
    inference(avatar_split_clause,[],[f4116,f17119]) ).

fof(f17119,plain,
    ( spl50_912
  <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_912])]) ).

fof(f4116,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
    inference(cnf_transformation,[],[f265]) ).

fof(f265,axiom,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wm1) ).

fof(f17117,plain,
    ( ~ spl50_201
    | spl50_911
    | ~ spl50_831
    | ~ spl50_844 ),
    inference(avatar_split_clause,[],[f14721,f13070,f12397,f17115,f7051]) ).

fof(f12397,plain,
    ( spl50_831
  <=> ! [X0,X3,X2,X1] :
        ( c_Orderings_Oord__class_Oless(X3,X2,X0)
        | ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
        | ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
        | ~ class_Orderings_Opreorder(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_831])]) ).

fof(f14721,plain,
    ( ! [X0] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))
        | ~ class_Orderings_Opreorder(tc_RealDef_Oreal) )
    | ~ spl50_831
    | ~ spl50_844 ),
    inference(resolution,[],[f12398,f13072]) ).

fof(f12398,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
        | c_Orderings_Oord__class_Oless(X3,X2,X0)
        | ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
        | ~ class_Orderings_Opreorder(X3) )
    | ~ spl50_831 ),
    inference(avatar_component_clause,[],[f12397]) ).

fof(f16788,plain,
    ( spl50_910
    | ~ spl50_362
    | ~ spl50_909 ),
    inference(avatar_split_clause,[],[f16103,f15960,f7757,f16786]) ).

fof(f16786,plain,
    ( spl50_910
  <=> ! [X0] :
        ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_910])]) ).

fof(f7757,plain,
    ( spl50_362
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_362])]) ).

fof(f16103,plain,
    ( ! [X0] :
        ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X0) )
    | ~ spl50_362
    | ~ spl50_909 ),
    inference(resolution,[],[f15961,f7758]) ).

fof(f7758,plain,
    ( ! [X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) )
    | ~ spl50_362 ),
    inference(avatar_component_clause,[],[f7757]) ).

fof(f15962,plain,
    ( ~ spl50_201
    | spl50_909
    | ~ spl50_830
    | ~ spl50_844 ),
    inference(avatar_split_clause,[],[f14655,f13070,f12388,f15960,f7051]) ).

fof(f12388,plain,
    ( spl50_830
  <=> ! [X0,X3,X2,X1] :
        ( c_Orderings_Oord__class_Oless(X3,X2,X0)
        | ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
        | ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
        | ~ class_Orderings_Opreorder(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_830])]) ).

fof(f14655,plain,
    ( ! [X0] :
        ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X0)
        | ~ class_Orderings_Opreorder(tc_RealDef_Oreal) )
    | ~ spl50_830
    | ~ spl50_844 ),
    inference(resolution,[],[f12389,f13072]) ).

fof(f12389,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
        | ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
        | c_Orderings_Oord__class_Oless(X3,X2,X0)
        | ~ class_Orderings_Opreorder(X3) )
    | ~ spl50_830 ),
    inference(avatar_component_clause,[],[f12388]) ).

fof(f15538,plain,
    spl50_908,
    inference(avatar_split_clause,[],[f6019,f15536]) ).

fof(f15536,plain,
    ( spl50_908
  <=> ! [X2,X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X0) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_908])]) ).

fof(f6019,plain,
    ! [X2,X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X0) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)),
    inference(forward_demodulation,[],[f4779,f4778]) ).

fof(f4778,plain,
    ! [X2,X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X0) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)),
    inference(cnf_transformation,[],[f1746]) ).

fof(f1746,plain,
    ! [X0,X1,X2] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X0) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)),
    inference(rectify,[],[f456]) ).

fof(f456,axiom,
    ! [X38,X39,X18] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,X39),X38) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X39,X38)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__diff__left) ).

fof(f4779,plain,
    ! [X2,X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X0) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0),X1),
    inference(cnf_transformation,[],[f1747]) ).

fof(f1747,plain,
    ! [X0,X1,X2] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X0) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0),X1),
    inference(rectify,[],[f561]) ).

fof(f561,axiom,
    ! [X38,X39,X18] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,X39),X38) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,X38),X39),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__commute) ).

fof(f15534,plain,
    ~ spl50_907,
    inference(avatar_split_clause,[],[f5905,f15531]) ).

fof(f15531,plain,
    ( spl50_907
  <=> c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)),v_q____))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_907])]) ).

fof(f5905,plain,
    ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)),v_q____))),
    inference(forward_demodulation,[],[f4115,f4114]) ).

fof(f4115,plain,
    ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____))),
    inference(cnf_transformation,[],[f573]) ).

fof(f573,axiom,
    ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rnc) ).

fof(f15529,plain,
    spl50_906,
    inference(avatar_split_clause,[],[f5800,f15527]) ).

fof(f15527,plain,
    ( spl50_906
  <=> ! [X2,X1] :
        ( c_Polynomial_Opos__poly(X2,c_Polynomial_OpCons(X2,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))
        | ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
        | ~ class_Rings_Olinordered__idom(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_906])]) ).

fof(f5800,plain,
    ! [X2,X1] :
      ( c_Polynomial_Opos__poly(X2,c_Polynomial_OpCons(X2,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))
      | ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
      | ~ class_Rings_Olinordered__idom(X2) ),
    inference(equality_resolution,[],[f4904]) ).

fof(f4904,plain,
    ! [X2,X0,X1] :
      ( 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
      | ~ class_Rings_Olinordered__idom(X2) ),
    inference(cnf_transformation,[],[f3684]) ).

fof(f15525,plain,
    spl50_905,
    inference(avatar_split_clause,[],[f5606,f15523]) ).

fof(f15523,plain,
    ( spl50_905
  <=> ! [X0,X1] :
        ( 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__eq(tc_Nat_Onat,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_905])]) ).

fof(f5606,plain,
    ! [X0,X1] :
      ( 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__eq(tc_Nat_Onat,X1,X0) ),
    inference(definition_unfolding,[],[f4573,f4164]) ).

fof(f4573,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
    inference(cnf_transformation,[],[f3552]) ).

fof(f3552,plain,
    ! [X0,X1] :
      ( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1))
          | X0 != X1 )
        & ( X0 = X1
          | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1)) ) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
    inference(nnf_transformation,[],[f2599]) ).

fof(f2599,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1))
      <=> X0 = X1 )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
    inference(ennf_transformation,[],[f1642]) ).

fof(f1642,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1))
      <=> X0 = X1 ) ),
    inference(rectify,[],[f981]) ).

fof(f981,axiom,
    ! [X16,X32] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X32,X16)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X16,c_Nat_OSuc(X32))
      <=> X16 = X32 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__less__Suc__eq) ).

fof(f15521,plain,
    spl50_904,
    inference(avatar_split_clause,[],[f5599,f15519]) ).

fof(f15519,plain,
    ( spl50_904
  <=> ! [X0,X1] :
        ( 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(tc_Nat_Onat,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_904])]) ).

fof(f5599,plain,
    ! [X0,X1] :
      ( 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(tc_Nat_Onat,X1,X0) ),
    inference(definition_unfolding,[],[f4548,f4164]) ).

fof(f4548,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
    inference(cnf_transformation,[],[f2568]) ).

fof(f2568,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
    inference(flattening,[],[f2567]) ).

fof(f2567,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
    inference(ennf_transformation,[],[f1621]) ).

fof(f1621,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
       => X0 = X1 ) ),
    inference(rectify,[],[f970]) ).

fof(f970,axiom,
    ! [X17,X3] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X17)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,c_Nat_OSuc(X17))
       => X3 = X17 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__antisym) ).

fof(f15517,plain,
    spl50_903,
    inference(avatar_split_clause,[],[f5439,f15515]) ).

fof(f15515,plain,
    ( spl50_903
  <=> ! [X0,X3,X2,X1] :
        ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,X3),X1),X0) = c_Groups_Ouminus__class_Ouminus(X3,hAPP(X1,X0))
        | ~ class_Groups_Ouminus(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_903])]) ).

fof(f5439,plain,
    ! [X2,X3,X0,X1] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,X3),X1),X0) = c_Groups_Ouminus__class_Ouminus(X3,hAPP(X1,X0))
      | ~ class_Groups_Ouminus(X3) ),
    inference(cnf_transformation,[],[f3296]) ).

fof(f3296,plain,
    ! [X0,X1,X2,X3] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,X3),X1),X0) = c_Groups_Ouminus__class_Ouminus(X3,hAPP(X1,X0))
      | ~ class_Groups_Ouminus(X3) ),
    inference(ennf_transformation,[],[f2203]) ).

fof(f2203,plain,
    ! [X0,X1,X2,X3] :
      ( class_Groups_Ouminus(X3)
     => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,X3),X1),X0) = c_Groups_Ouminus__class_Ouminus(X3,hAPP(X1,X0)) ),
    inference(rectify,[],[f801]) ).

fof(f801,axiom,
    ! [X12,X79,X46,X5] :
      ( class_Groups_Ouminus(X5)
     => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X46,X5),X79),X12) = c_Groups_Ouminus__class_Ouminus(X5,hAPP(X79,X12)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_uminus__apply) ).

fof(f15513,plain,
    spl50_902,
    inference(avatar_split_clause,[],[f5438,f15511]) ).

fof(f15511,plain,
    ( spl50_902
  <=> ! [X0,X3,X2,X1] :
        ( c_Rings_Odvd__class_Odvd(X3,X2,X0)
        | ~ c_Rings_Odvd__class_Odvd(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0)
        | ~ class_Rings_Ocomm__semiring__1(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_902])]) ).

fof(f5438,plain,
    ! [X2,X3,X0,X1] :
      ( c_Rings_Odvd__class_Odvd(X3,X2,X0)
      | ~ c_Rings_Odvd__class_Odvd(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0)
      | ~ class_Rings_Ocomm__semiring__1(X3) ),
    inference(cnf_transformation,[],[f3295]) ).

fof(f3295,plain,
    ! [X0,X1,X2,X3] :
      ( c_Rings_Odvd__class_Odvd(X3,X2,X0)
      | ~ c_Rings_Odvd__class_Odvd(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0)
      | ~ class_Rings_Ocomm__semiring__1(X3) ),
    inference(flattening,[],[f3294]) ).

fof(f3294,plain,
    ! [X0,X1,X2,X3] :
      ( c_Rings_Odvd__class_Odvd(X3,X2,X0)
      | ~ c_Rings_Odvd__class_Odvd(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0)
      | ~ class_Rings_Ocomm__semiring__1(X3) ),
    inference(ennf_transformation,[],[f2202]) ).

fof(f2202,plain,
    ! [X0,X1,X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => ( c_Rings_Odvd__class_Odvd(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0)
       => c_Rings_Odvd__class_Odvd(X3,X2,X0) ) ),
    inference(rectify,[],[f825]) ).

fof(f825,axiom,
    ! [X23,X13,X4,X5] :
      ( class_Rings_Ocomm__semiring__1(X5)
     => ( c_Rings_Odvd__class_Odvd(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X13),X23)
       => c_Rings_Odvd__class_Odvd(X5,X4,X23) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult__left) ).

fof(f15509,plain,
    spl50_901,
    inference(avatar_split_clause,[],[f5437,f15507]) ).

fof(f15507,plain,
    ( spl50_901
  <=> ! [X0,X3,X2,X1] :
        ( c_Rings_Odvd__class_Odvd(X3,X1,X0)
        | ~ c_Rings_Odvd__class_Odvd(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0)
        | ~ class_Rings_Ocomm__semiring__1(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_901])]) ).

fof(f5437,plain,
    ! [X2,X3,X0,X1] :
      ( c_Rings_Odvd__class_Odvd(X3,X1,X0)
      | ~ c_Rings_Odvd__class_Odvd(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0)
      | ~ class_Rings_Ocomm__semiring__1(X3) ),
    inference(cnf_transformation,[],[f3293]) ).

fof(f3293,plain,
    ! [X0,X1,X2,X3] :
      ( c_Rings_Odvd__class_Odvd(X3,X1,X0)
      | ~ c_Rings_Odvd__class_Odvd(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0)
      | ~ class_Rings_Ocomm__semiring__1(X3) ),
    inference(flattening,[],[f3292]) ).

fof(f3292,plain,
    ! [X0,X1,X2,X3] :
      ( c_Rings_Odvd__class_Odvd(X3,X1,X0)
      | ~ c_Rings_Odvd__class_Odvd(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0)
      | ~ class_Rings_Ocomm__semiring__1(X3) ),
    inference(ennf_transformation,[],[f2201]) ).

fof(f2201,plain,
    ! [X0,X1,X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => ( c_Rings_Odvd__class_Odvd(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0)
       => c_Rings_Odvd__class_Odvd(X3,X1,X0) ) ),
    inference(rectify,[],[f824]) ).

fof(f824,axiom,
    ! [X23,X13,X4,X5] :
      ( class_Rings_Ocomm__semiring__1(X5)
     => ( c_Rings_Odvd__class_Odvd(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X13),X23)
       => c_Rings_Odvd__class_Odvd(X5,X13,X23) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult__right) ).

fof(f15505,plain,
    spl50_900,
    inference(avatar_split_clause,[],[f5436,f15503]) ).

fof(f15503,plain,
    ( spl50_900
  <=> ! [X0,X3,X2,X1] :
        ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),X1,X0)
        | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X1),X0)
        | ~ class_Rings_Ocomm__semiring__1(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_900])]) ).

fof(f5436,plain,
    ! [X2,X3,X0,X1] :
      ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),X1,X0)
      | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X1),X0)
      | ~ class_Rings_Ocomm__semiring__1(X3) ),
    inference(cnf_transformation,[],[f3291]) ).

fof(f3291,plain,
    ! [X0,X1,X2,X3] :
      ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),X1,X0)
      | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X1),X0)
      | ~ class_Rings_Ocomm__semiring__1(X3) ),
    inference(flattening,[],[f3290]) ).

fof(f3290,plain,
    ! [X0,X1,X2,X3] :
      ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),X1,X0)
      | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X1),X0)
      | ~ class_Rings_Ocomm__semiring__1(X3) ),
    inference(ennf_transformation,[],[f2200]) ).

fof(f2200,plain,
    ! [X0,X1,X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X1),X0)
       => c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),X1,X0) ) ),
    inference(rectify,[],[f810]) ).

fof(f810,axiom,
    ! [X53,X54,X4,X5] :
      ( class_Rings_Ocomm__semiring__1(X5)
     => ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5),c_Polynomial_Osmult(X5,X4,X54),X53)
       => c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5),X54,X53) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__dvd__cancel) ).

fof(f15501,plain,
    spl50_899,
    inference(avatar_split_clause,[],[f5435,f15499]) ).

fof(f15499,plain,
    ( spl50_899
  <=> ! [X0,X3,X2,X1] :
        ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),X2,c_Polynomial_Osmult(X3,X0,X1))
        | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),X2,X1)
        | ~ class_Rings_Ocomm__semiring__1(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_899])]) ).

fof(f5435,plain,
    ! [X2,X3,X0,X1] :
      ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),X2,c_Polynomial_Osmult(X3,X0,X1))
      | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),X2,X1)
      | ~ class_Rings_Ocomm__semiring__1(X3) ),
    inference(cnf_transformation,[],[f3289]) ).

fof(f3289,plain,
    ! [X0,X1,X2,X3] :
      ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),X2,c_Polynomial_Osmult(X3,X0,X1))
      | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),X2,X1)
      | ~ class_Rings_Ocomm__semiring__1(X3) ),
    inference(flattening,[],[f3288]) ).

fof(f3288,plain,
    ! [X0,X1,X2,X3] :
      ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),X2,c_Polynomial_Osmult(X3,X0,X1))
      | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),X2,X1)
      | ~ class_Rings_Ocomm__semiring__1(X3) ),
    inference(ennf_transformation,[],[f2199]) ).

fof(f2199,plain,
    ! [X0,X1,X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),X2,X1)
       => c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),X2,c_Polynomial_Osmult(X3,X0,X1)) ) ),
    inference(rectify,[],[f811]) ).

fof(f811,axiom,
    ! [X4,X53,X54,X5] :
      ( class_Rings_Ocomm__semiring__1(X5)
     => ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5),X54,X53)
       => c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5),X54,c_Polynomial_Osmult(X5,X4,X53)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__smult) ).

fof(f15497,plain,
    spl50_898,
    inference(avatar_split_clause,[],[f5431,f15495]) ).

fof(f15495,plain,
    ( spl50_898
  <=> ! [X0,X3,X2,X1] :
        ( c_Rings_Odvd__class_Odvd(X3,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
        | ~ c_Rings_Odvd__class_Odvd(X3,X2,X1)
        | ~ class_Rings_Ocomm__semiring__1(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_898])]) ).

fof(f5431,plain,
    ! [X2,X3,X0,X1] :
      ( c_Rings_Odvd__class_Odvd(X3,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
      | ~ c_Rings_Odvd__class_Odvd(X3,X2,X1)
      | ~ class_Rings_Ocomm__semiring__1(X3) ),
    inference(cnf_transformation,[],[f3281]) ).

fof(f3281,plain,
    ! [X0,X1,X2,X3] :
      ( c_Rings_Odvd__class_Odvd(X3,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
      | ~ c_Rings_Odvd__class_Odvd(X3,X2,X1)
      | ~ class_Rings_Ocomm__semiring__1(X3) ),
    inference(flattening,[],[f3280]) ).

fof(f3280,plain,
    ! [X0,X1,X2,X3] :
      ( c_Rings_Odvd__class_Odvd(X3,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
      | ~ c_Rings_Odvd__class_Odvd(X3,X2,X1)
      | ~ class_Rings_Ocomm__semiring__1(X3) ),
    inference(ennf_transformation,[],[f2195]) ).

fof(f2195,plain,
    ! [X0,X1,X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => ( c_Rings_Odvd__class_Odvd(X3,X2,X1)
       => c_Rings_Odvd__class_Odvd(X3,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1)) ) ),
    inference(rectify,[],[f828]) ).

fof(f828,axiom,
    ! [X13,X23,X4,X5] :
      ( class_Rings_Ocomm__semiring__1(X5)
     => ( c_Rings_Odvd__class_Odvd(X5,X4,X23)
       => c_Rings_Odvd__class_Odvd(X5,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),X23)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult) ).

fof(f15493,plain,
    spl50_897,
    inference(avatar_split_clause,[],[f5430,f15491]) ).

fof(f15491,plain,
    ( spl50_897
  <=> ! [X0,X3,X2,X1] :
        ( c_Rings_Odvd__class_Odvd(X3,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0))
        | ~ c_Rings_Odvd__class_Odvd(X3,X2,X1)
        | ~ class_Rings_Ocomm__semiring__1(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_897])]) ).

fof(f5430,plain,
    ! [X2,X3,X0,X1] :
      ( c_Rings_Odvd__class_Odvd(X3,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0))
      | ~ c_Rings_Odvd__class_Odvd(X3,X2,X1)
      | ~ class_Rings_Ocomm__semiring__1(X3) ),
    inference(cnf_transformation,[],[f3279]) ).

fof(f3279,plain,
    ! [X0,X1,X2,X3] :
      ( c_Rings_Odvd__class_Odvd(X3,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0))
      | ~ c_Rings_Odvd__class_Odvd(X3,X2,X1)
      | ~ class_Rings_Ocomm__semiring__1(X3) ),
    inference(flattening,[],[f3278]) ).

fof(f3278,plain,
    ! [X0,X1,X2,X3] :
      ( c_Rings_Odvd__class_Odvd(X3,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0))
      | ~ c_Rings_Odvd__class_Odvd(X3,X2,X1)
      | ~ class_Rings_Ocomm__semiring__1(X3) ),
    inference(ennf_transformation,[],[f2194]) ).

fof(f2194,plain,
    ! [X0,X1,X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => ( c_Rings_Odvd__class_Odvd(X3,X2,X1)
       => c_Rings_Odvd__class_Odvd(X3,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)) ) ),
    inference(rectify,[],[f829]) ).

fof(f829,axiom,
    ! [X23,X13,X4,X5] :
      ( class_Rings_Ocomm__semiring__1(X5)
     => ( c_Rings_Odvd__class_Odvd(X5,X4,X13)
       => c_Rings_Odvd__class_Odvd(X5,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),X23)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult2) ).

fof(f15489,plain,
    spl50_896,
    inference(avatar_split_clause,[],[f5307,f15487]) ).

fof(f15487,plain,
    ( spl50_896
  <=> ! [X2,X0,X1,X3] :
        ( c_Orderings_Oord__class_Oless(X2,X3,c_Groups_Ozero__class_Ozero(X2))
        | c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X3)
        | ~ sP13(X0,X1,X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_896])]) ).

fof(f5307,plain,
    ! [X2,X3,X0,X1] :
      ( c_Orderings_Oord__class_Oless(X2,X3,c_Groups_Ozero__class_Ozero(X2))
      | c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X3)
      | ~ sP13(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f3818]) ).

fof(f3818,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,[],[f3817]) ).

fof(f3817,plain,
    ! [X1,X0,X3,X2] :
      ( ( sP13(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) )
        | ~ sP13(X1,X0,X3,X2) ) ),
    inference(flattening,[],[f3816]) ).

fof(f3816,plain,
    ! [X1,X0,X3,X2] :
      ( ( sP13(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) )
        | ~ sP13(X1,X0,X3,X2) ) ),
    inference(nnf_transformation,[],[f3461]) ).

fof(f3461,plain,
    ! [X1,X0,X3,X2] :
      ( sP13(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,[sP13])]) ).

fof(f15485,plain,
    spl50_895,
    inference(avatar_split_clause,[],[f5298,f15483]) ).

fof(f15483,plain,
    ( spl50_895
  <=> ! [X2,X0,X1,X3] :
        ( c_Orderings_Oord__class_Oless(X2,X3,c_Groups_Ozero__class_Ozero(X2))
        | c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X3)
        | ~ sP11(X0,X1,X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_895])]) ).

fof(f5298,plain,
    ! [X2,X3,X0,X1] :
      ( c_Orderings_Oord__class_Oless(X2,X3,c_Groups_Ozero__class_Ozero(X2))
      | c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X3)
      | ~ sP11(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f3813]) ).

fof(f3813,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,[],[f3812]) ).

fof(f3812,plain,
    ! [X2,X0,X3,X1] :
      ( ( sP11(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) )
        | ~ sP11(X2,X0,X3,X1) ) ),
    inference(flattening,[],[f3811]) ).

fof(f3811,plain,
    ! [X2,X0,X3,X1] :
      ( ( sP11(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) )
        | ~ sP11(X2,X0,X3,X1) ) ),
    inference(nnf_transformation,[],[f3458]) ).

fof(f3458,plain,
    ! [X2,X0,X3,X1] :
      ( sP11(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,[sP11])]) ).

fof(f15481,plain,
    spl50_894,
    inference(avatar_split_clause,[],[f5212,f15479]) ).

fof(f15479,plain,
    ( spl50_894
  <=> ! [X2,X0,X1] :
        ( sP8(X0,X1,X2)
        | ~ hBOOL(hAPP(X0,sK41(X0,X1,X2)))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_894])]) ).

fof(f5212,plain,
    ! [X2,X0,X1] :
      ( sP8(X0,X1,X2)
      | ~ hBOOL(hAPP(X0,sK41(X0,X1,X2)))
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(cnf_transformation,[],[f3771]) ).

fof(f15457,plain,
    spl50_893,
    inference(avatar_split_clause,[],[f5204,f15455]) ).

fof(f15455,plain,
    ( spl50_893
  <=> ! [X2,X0,X1] :
        ( sP7(X0,X1,X2)
        | ~ hBOOL(hAPP(X0,sK40(X0,X1,X2)))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_893])]) ).

fof(f5204,plain,
    ! [X2,X0,X1] :
      ( sP7(X0,X1,X2)
      | ~ hBOOL(hAPP(X0,sK40(X0,X1,X2)))
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(cnf_transformation,[],[f3765]) ).

fof(f15453,plain,
    spl50_892,
    inference(avatar_split_clause,[],[f5165,f15451]) ).

fof(f15451,plain,
    ( spl50_892
  <=> ! [X2,X0,X1] :
        ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X1)
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X0)
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_892])]) ).

fof(f5165,plain,
    ! [X2,X0,X1] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X1)
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X0)
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0)) ),
    inference(cnf_transformation,[],[f3056]) ).

fof(f3056,plain,
    ! [X0,X1,X2] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X1)
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X0)
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0)) ),
    inference(flattening,[],[f3055]) ).

fof(f3055,plain,
    ! [X0,X1,X2] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X1)
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X0)
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0)) ),
    inference(ennf_transformation,[],[f2027]) ).

fof(f2027,plain,
    ! [X0,X1,X2] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0))
     => ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X0)
       => c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X1) ) ),
    inference(rectify,[],[f861]) ).

fof(f861,axiom,
    ! [X3,X17,X38] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X38,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X17,X3))
     => ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X38,X3)
       => c_Rings_Odvd__class_Odvd(tc_Int_Oint,X38,X17) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__zdiffD) ).

fof(f15449,plain,
    spl50_891,
    inference(avatar_split_clause,[],[f5098,f15447]) ).

fof(f15447,plain,
    ( spl50_891
  <=> ! [X2,X0,X1] :
        ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X0)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_891])]) ).

fof(f5098,plain,
    ! [X2,X0,X1] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X0)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
    inference(cnf_transformation,[],[f2983]) ).

fof(f2983,plain,
    ! [X0,X1,X2] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X0)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
    inference(flattening,[],[f2982]) ).

fof(f2982,plain,
    ! [X0,X1,X2] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X0)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
    inference(ennf_transformation,[],[f1974]) ).

fof(f1974,plain,
    ! [X0,X1,X2] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X0)
       => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) ) ),
    inference(rectify,[],[f860]) ).

fof(f860,axiom,
    ! [X3,X17,X38] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X38,X17)
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X38,X3)
       => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X38,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X3)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__diff__nat) ).

fof(f15445,plain,
    spl50_890,
    inference(avatar_split_clause,[],[f5048,f15443]) ).

fof(f5048,plain,
    ! [X2,X0,X1] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1)
      | ~ class_Rings_Ocomm__semiring__1(X2) ),
    inference(cnf_transformation,[],[f2923]) ).

fof(f2923,plain,
    ! [X0,X1,X2] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1)
      | ~ class_Rings_Ocomm__semiring__1(X2) ),
    inference(ennf_transformation,[],[f1938]) ).

fof(f1938,plain,
    ! [X0,X1,X2] :
      ( class_Rings_Ocomm__semiring__1(X2)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1) ),
    inference(rectify,[],[f507]) ).

fof(f507,axiom,
    ! [X13,X4,X5] :
      ( class_Rings_Ocomm__semiring__1(X5)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X13) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).

fof(f15441,plain,
    spl50_889,
    inference(avatar_split_clause,[],[f5042,f15439]) ).

fof(f15439,plain,
    ( spl50_889
  <=> ! [X2,X0,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
        | c_Polynomial_OpCons(X2,X1,X0) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
        | ~ class_Groups_Ozero(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_889])]) ).

fof(f5042,plain,
    ! [X2,X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
      | c_Polynomial_OpCons(X2,X1,X0) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
      | ~ class_Groups_Ozero(X2) ),
    inference(cnf_transformation,[],[f3720]) ).

fof(f3720,plain,
    ! [X0,X1,X2] :
      ( ( ( c_Polynomial_OpCons(X2,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
          | 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_Polynomial_OpCons(X2,X1,X0) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ) )
      | ~ class_Groups_Ozero(X2) ),
    inference(flattening,[],[f3719]) ).

fof(f3719,plain,
    ! [X0,X1,X2] :
      ( ( ( c_Polynomial_OpCons(X2,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
          | 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_Polynomial_OpCons(X2,X1,X0) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ) )
      | ~ class_Groups_Ozero(X2) ),
    inference(nnf_transformation,[],[f2918]) ).

fof(f2918,plain,
    ! [X0,X1,X2] :
      ( ( c_Polynomial_OpCons(X2,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
      <=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
          & c_Groups_Ozero__class_Ozero(X2) = X1 ) )
      | ~ class_Groups_Ozero(X2) ),
    inference(ennf_transformation,[],[f1933]) ).

fof(f1933,plain,
    ! [X0,X1,X2] :
      ( class_Groups_Ozero(X2)
     => ( c_Polynomial_OpCons(X2,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
      <=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
          & c_Groups_Ozero__class_Ozero(X2) = X1 ) ) ),
    inference(rectify,[],[f603]) ).

fof(f603,axiom,
    ! [X64,X24,X5] :
      ( class_Groups_Ozero(X5)
     => ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = c_Polynomial_OpCons(X5,X24,X64)
      <=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = X64
          & c_Groups_Ozero__class_Ozero(X5) = X24 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pCons__eq__0__iff) ).

fof(f15437,plain,
    spl50_888,
    inference(avatar_split_clause,[],[f4909,f15435]) ).

fof(f4909,plain,
    ! [X2,X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X2) != hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)
      | c_Groups_Ozero__class_Ozero(X2) = X1
      | ~ class_Rings_Oring__1__no__zero__divisors(X2) ),
    inference(cnf_transformation,[],[f2774]) ).

fof(f2774,plain,
    ! [X0,X1,X2] :
      ( c_Groups_Ozero__class_Ozero(X2) != hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)
      | c_Groups_Ozero__class_Ozero(X2) = X1
      | ~ class_Rings_Oring__1__no__zero__divisors(X2) ),
    inference(flattening,[],[f2773]) ).

fof(f2773,plain,
    ! [X0,X1,X2] :
      ( c_Groups_Ozero__class_Ozero(X2) != hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)
      | c_Groups_Ozero__class_Ozero(X2) = X1
      | ~ class_Rings_Oring__1__no__zero__divisors(X2) ),
    inference(ennf_transformation,[],[f1836]) ).

fof(f1836,plain,
    ! [X0,X1,X2] :
      ( class_Rings_Oring__1__no__zero__divisors(X2)
     => ( c_Groups_Ozero__class_Ozero(X2) != X1
       => c_Groups_Ozero__class_Ozero(X2) != hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0) ) ),
    inference(rectify,[],[f107]) ).

fof(f107,axiom,
    ! [X3,X4,X5] :
      ( class_Rings_Oring__1__no__zero__divisors(X5)
     => ( c_Groups_Ozero__class_Ozero(X5) != X4
       => c_Groups_Ozero__class_Ozero(X5) != hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X3) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_field__power__not__zero) ).

fof(f15433,plain,
    spl50_887,
    inference(avatar_split_clause,[],[f4892,f15431]) ).

fof(f15431,plain,
    ( spl50_887
  <=> ! [X2,X0,X1] :
        ( c_Polynomial_Opos__poly(X2,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),X1,X0))
        | ~ c_Polynomial_Opos__poly(X2,X0)
        | ~ c_Polynomial_Opos__poly(X2,X1)
        | ~ class_Rings_Olinordered__idom(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_887])]) ).

fof(f4892,plain,
    ! [X2,X0,X1] :
      ( c_Polynomial_Opos__poly(X2,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),X1,X0))
      | ~ c_Polynomial_Opos__poly(X2,X0)
      | ~ c_Polynomial_Opos__poly(X2,X1)
      | ~ class_Rings_Olinordered__idom(X2) ),
    inference(cnf_transformation,[],[f2761]) ).

fof(f2761,plain,
    ! [X0,X1,X2] :
      ( c_Polynomial_Opos__poly(X2,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),X1,X0))
      | ~ c_Polynomial_Opos__poly(X2,X0)
      | ~ c_Polynomial_Opos__poly(X2,X1)
      | ~ class_Rings_Olinordered__idom(X2) ),
    inference(flattening,[],[f2760]) ).

fof(f2760,plain,
    ! [X0,X1,X2] :
      ( c_Polynomial_Opos__poly(X2,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),X1,X0))
      | ~ c_Polynomial_Opos__poly(X2,X0)
      | ~ c_Polynomial_Opos__poly(X2,X1)
      | ~ class_Rings_Olinordered__idom(X2) ),
    inference(ennf_transformation,[],[f1827]) ).

fof(f1827,plain,
    ! [X0,X1,X2] :
      ( class_Rings_Olinordered__idom(X2)
     => ( c_Polynomial_Opos__poly(X2,X1)
       => ( c_Polynomial_Opos__poly(X2,X0)
         => c_Polynomial_Opos__poly(X2,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),X1,X0)) ) ) ),
    inference(rectify,[],[f786]) ).

fof(f786,axiom,
    ! [X53,X54,X5] :
      ( class_Rings_Olinordered__idom(X5)
     => ( c_Polynomial_Opos__poly(X5,X54)
       => ( c_Polynomial_Opos__poly(X5,X53)
         => c_Polynomial_Opos__poly(X5,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X5),X54,X53)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__poly__add) ).

fof(f15429,plain,
    spl50_886,
    inference(avatar_split_clause,[],[f4830,f15427]) ).

fof(f15427,plain,
    ( spl50_886
  <=> ! [X2,X0,X1] :
        ( c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0)) = c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ominus__class_Ominus(X2,X0,X1))
        | ~ class_RealVector_Oreal__normed__vector(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_886])]) ).

fof(f4830,plain,
    ! [X2,X0,X1] :
      ( c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0)) = c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ominus__class_Ominus(X2,X0,X1))
      | ~ class_RealVector_Oreal__normed__vector(X2) ),
    inference(cnf_transformation,[],[f2724]) ).

fof(f2724,plain,
    ! [X0,X1,X2] :
      ( c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0)) = c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ominus__class_Ominus(X2,X0,X1))
      | ~ class_RealVector_Oreal__normed__vector(X2) ),
    inference(ennf_transformation,[],[f1796]) ).

fof(f1796,plain,
    ! [X0,X1,X2] :
      ( class_RealVector_Oreal__normed__vector(X2)
     => c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0)) = c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ominus__class_Ominus(X2,X0,X1)) ),
    inference(rectify,[],[f320]) ).

fof(f320,axiom,
    ! [X13,X4,X5] :
      ( class_RealVector_Oreal__normed__vector(X5)
     => c_RealVector_Onorm__class_Onorm(X5,c_Groups_Ominus__class_Ominus(X5,X4,X13)) = c_RealVector_Onorm__class_Onorm(X5,c_Groups_Ominus__class_Ominus(X5,X13,X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__minus__commute) ).

fof(f15425,plain,
    spl50_885,
    inference(avatar_split_clause,[],[f4783,f15423]) ).

fof(f15423,plain,
    ( spl50_885
  <=> ! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_885])]) ).

fof(f4783,plain,
    ! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X0),
    inference(cnf_transformation,[],[f1751]) ).

fof(f1751,plain,
    ! [X0,X1,X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X0),
    inference(rectify,[],[f362]) ).

fof(f362,axiom,
    ! [X38,X3,X17] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X3),X38) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X38)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__assoc) ).

fof(f15421,plain,
    spl50_884,
    inference(avatar_split_clause,[],[f4782,f15419]) ).

fof(f15419,plain,
    ( spl50_884
  <=> ! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_884])]) ).

fof(f4782,plain,
    ! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)),
    inference(cnf_transformation,[],[f1750]) ).

fof(f1750,plain,
    ! [X0,X1,X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)),
    inference(rectify,[],[f363]) ).

fof(f363,axiom,
    ! [X14,X7,X9] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X9,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,X14)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X9,X14)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__commute) ).

fof(f15409,plain,
    spl50_883,
    inference(avatar_split_clause,[],[f4781,f15407]) ).

fof(f15407,plain,
    ( spl50_883
  <=> ! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_883])]) ).

fof(f4781,plain,
    ! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1),X0),
    inference(cnf_transformation,[],[f1749]) ).

fof(f1749,plain,
    ! [X0,X1,X2] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1),X0),
    inference(rectify,[],[f614]) ).

fof(f614,axiom,
    ! [X40,X41,X42] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X42,X41),X40) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X42,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X41,X40)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__assoc) ).

fof(f15405,plain,
    spl50_882,
    inference(avatar_split_clause,[],[f4780,f15403]) ).

fof(f15403,plain,
    ( spl50_882
  <=> ! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_882])]) ).

fof(f4780,plain,
    ! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X0)),
    inference(cnf_transformation,[],[f1748]) ).

fof(f1748,plain,
    ! [X0,X1,X2] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X0)),
    inference(rectify,[],[f616]) ).

fof(f616,axiom,
    ! [X14,X7,X9] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X9,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X7,X14)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X7,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X9,X14)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__left__commute) ).

fof(f15401,plain,
    spl50_881,
    inference(avatar_split_clause,[],[f4778,f15399]) ).

fof(f15399,plain,
    ( spl50_881
  <=> ! [X2,X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X0) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_881])]) ).

fof(f15397,plain,
    spl50_880,
    inference(avatar_split_clause,[],[f4777,f15395]) ).

fof(f15395,plain,
    ( spl50_880
  <=> ! [X2,X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0) = c_Groups_Ominus__class_Ominus(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,[spl50_880])]) ).

fof(f4777,plain,
    ! [X2,X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0) = c_Groups_Ominus__class_Ominus(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,[],[f1745]) ).

fof(f1745,plain,
    ! [X0,X1,X2] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)),
    inference(rectify,[],[f455]) ).

fof(f455,axiom,
    ! [X3,X17,X38] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X3) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X38,X17),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X38,X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__cancel) ).

fof(f15393,plain,
    spl50_879,
    inference(avatar_split_clause,[],[f4776,f15391]) ).

fof(f15391,plain,
    ( spl50_879
  <=> ! [X2,X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_879])]) ).

fof(f4776,plain,
    ! [X2,X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)),
    inference(cnf_transformation,[],[f1744]) ).

fof(f1744,plain,
    ! [X0,X1,X2] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)),
    inference(rectify,[],[f454]) ).

fof(f454,axiom,
    ! [X3,X38,X17] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X3) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X38),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X38)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__cancel2) ).

fof(f15389,plain,
    spl50_878,
    inference(avatar_split_clause,[],[f4767,f15387]) ).

fof(f15387,plain,
    ( spl50_878
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,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_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_878])]) ).

fof(f4767,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,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_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ),
    inference(cnf_transformation,[],[f3648]) ).

fof(f15385,plain,
    spl50_877,
    inference(avatar_split_clause,[],[f4766,f15383]) ).

fof(f15383,plain,
    ( spl50_877
  <=> ! [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_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_877])]) ).

fof(f4766,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_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ),
    inference(cnf_transformation,[],[f3648]) ).

fof(f15381,plain,
    spl50_876,
    inference(avatar_split_clause,[],[f4762,f15379]) ).

fof(f15379,plain,
    ( spl50_876
  <=> ! [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) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_876])]) ).

fof(f4762,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) ),
    inference(cnf_transformation,[],[f3644]) ).

fof(f15377,plain,
    spl50_875,
    inference(avatar_split_clause,[],[f4735,f15375]) ).

fof(f15375,plain,
    ( spl50_875
  <=> ! [X0,X1] :
        ( 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))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_875])]) ).

fof(f4735,plain,
    ! [X0,X1] :
      ( 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(cnf_transformation,[],[f3628]) ).

fof(f3628,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,[],[f3627]) ).

fof(f3627,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,[],[f1730]) ).

fof(f1730,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,[],[f617]) ).

fof(f617,axiom,
    ! [X33,X63] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X63,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X33,c_Groups_Oone__class_Oone(tc_Int_Oint)))
    <=> ( X33 = X63
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X63,X33) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__add1__eq) ).

fof(f15373,plain,
    spl50_874,
    inference(avatar_split_clause,[],[f4614,f15371]) ).

fof(f15371,plain,
    ( spl50_874
  <=> ! [X0,X1] :
        ( c_RealVector_Onorm__class_Onorm(X1,c_Rings_Oinverse__class_Oinverse(X1,X0)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X0))
        | ~ class_Rings_Odivision__ring__inverse__zero(X1)
        | ~ class_RealVector_Oreal__normed__div__algebra(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_874])]) ).

fof(f4614,plain,
    ! [X0,X1] :
      ( c_RealVector_Onorm__class_Onorm(X1,c_Rings_Oinverse__class_Oinverse(X1,X0)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X0))
      | ~ class_Rings_Odivision__ring__inverse__zero(X1)
      | ~ class_RealVector_Oreal__normed__div__algebra(X1) ),
    inference(cnf_transformation,[],[f2652]) ).

fof(f2652,plain,
    ! [X0,X1] :
      ( c_RealVector_Onorm__class_Onorm(X1,c_Rings_Oinverse__class_Oinverse(X1,X0)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X0))
      | ~ class_Rings_Odivision__ring__inverse__zero(X1)
      | ~ class_RealVector_Oreal__normed__div__algebra(X1) ),
    inference(flattening,[],[f2651]) ).

fof(f2651,plain,
    ! [X0,X1] :
      ( c_RealVector_Onorm__class_Onorm(X1,c_Rings_Oinverse__class_Oinverse(X1,X0)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X0))
      | ~ class_Rings_Odivision__ring__inverse__zero(X1)
      | ~ class_RealVector_Oreal__normed__div__algebra(X1) ),
    inference(ennf_transformation,[],[f1678]) ).

fof(f1678,plain,
    ! [X0,X1] :
      ( ( class_Rings_Odivision__ring__inverse__zero(X1)
        & class_RealVector_Oreal__normed__div__algebra(X1) )
     => c_RealVector_Onorm__class_Onorm(X1,c_Rings_Oinverse__class_Oinverse(X1,X0)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X0)) ),
    inference(rectify,[],[f173]) ).

fof(f173,axiom,
    ! [X4,X5] :
      ( ( class_Rings_Odivision__ring__inverse__zero(X5)
        & class_RealVector_Oreal__normed__div__algebra(X5) )
     => c_RealVector_Onorm__class_Onorm(X5,c_Rings_Oinverse__class_Oinverse(X5,X4)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__inverse) ).

fof(f15369,plain,
    ( ~ spl50_873
    | ~ spl50_365
    | ~ spl50_850 ),
    inference(avatar_split_clause,[],[f15197,f15103,f7769,f15366]) ).

fof(f15366,plain,
    ( spl50_873
  <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK19) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_873])]) ).

fof(f7769,plain,
    ( spl50_365
  <=> ! [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,[spl50_365])]) ).

fof(f15103,plain,
    ( spl50_850
  <=> c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK19) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_s____)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_850])]) ).

fof(f15197,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK19)
    | ~ spl50_365
    | ~ spl50_850 ),
    inference(superposition,[],[f7770,f15105]) ).

fof(f15105,plain,
    ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK19) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_s____)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ spl50_850 ),
    inference(avatar_component_clause,[],[f15103]) ).

fof(f7770,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))
    | ~ spl50_365 ),
    inference(avatar_component_clause,[],[f7769]) ).

fof(f15364,plain,
    spl50_872,
    inference(avatar_split_clause,[],[f4586,f15362]) ).

fof(f15362,plain,
    ( spl50_872
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X0))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_872])]) ).

fof(f4586,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X0))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(cnf_transformation,[],[f2612]) ).

fof(f2612,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X0))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(ennf_transformation,[],[f1654]) ).

fof(f1654,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_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X0)) ),
    inference(rectify,[],[f689]) ).

fof(f689,axiom,
    ! [X3,X9] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X9)
     => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X9),X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).

fof(f15360,plain,
    spl50_871,
    inference(avatar_split_clause,[],[f4515,f15358]) ).

fof(f15358,plain,
    ( spl50_871
  <=> ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_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,[spl50_871])]) ).

fof(f4515,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X0)
      | ~ class_Rings_Ocomm__semiring__0(X1) ),
    inference(cnf_transformation,[],[f2533]) ).

fof(f2533,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X0)
      | ~ class_Rings_Ocomm__semiring__0(X1) ),
    inference(ennf_transformation,[],[f1591]) ).

fof(f1591,plain,
    ! [X0,X1] :
      ( class_Rings_Ocomm__semiring__0(X1)
     => c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X0) ),
    inference(rectify,[],[f632]) ).

fof(f632,axiom,
    ! [X53,X5] :
      ( class_Rings_Ocomm__semiring__0(X5)
     => c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X5)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))),X53) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__poly__0__left) ).

fof(f15356,plain,
    spl50_870,
    inference(avatar_split_clause,[],[f4514,f15354]) ).

fof(f15354,plain,
    ( spl50_870
  <=> ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
        | ~ class_Rings_Ocomm__semiring__0(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_870])]) ).

fof(f4514,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
      | ~ class_Rings_Ocomm__semiring__0(X1) ),
    inference(cnf_transformation,[],[f2532]) ).

fof(f2532,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
      | ~ class_Rings_Ocomm__semiring__0(X1) ),
    inference(ennf_transformation,[],[f1590]) ).

fof(f1590,plain,
    ! [X0,X1] :
      ( class_Rings_Ocomm__semiring__0(X1)
     => c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) ),
    inference(rectify,[],[f634]) ).

fof(f634,axiom,
    ! [X54,X5] :
      ( class_Rings_Ocomm__semiring__0(X5)
     => c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X5)),X54),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__poly__0__right) ).

fof(f15352,plain,
    spl50_869,
    inference(avatar_split_clause,[],[f4471,f15350]) ).

fof(f15350,plain,
    ( spl50_869
  <=> ! [X0,X1] :
        ( c_Groups_Ouminus__class_Ouminus(X1,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))),X0)
        | ~ class_Rings_Ocomm__ring__1(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_869])]) ).

fof(f4471,plain,
    ! [X0,X1] :
      ( c_Groups_Ouminus__class_Ouminus(X1,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))),X0)
      | ~ class_Rings_Ocomm__ring__1(X1) ),
    inference(cnf_transformation,[],[f2494]) ).

fof(f2494,plain,
    ! [X0,X1] :
      ( c_Groups_Ouminus__class_Ouminus(X1,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))),X0)
      | ~ class_Rings_Ocomm__ring__1(X1) ),
    inference(ennf_transformation,[],[f1552]) ).

fof(f1552,plain,
    ! [X0,X1] :
      ( class_Rings_Ocomm__ring__1(X1)
     => c_Groups_Ouminus__class_Ouminus(X1,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))),X0) ),
    inference(rectify,[],[f547]) ).

fof(f547,axiom,
    ! [X9,X5] :
      ( class_Rings_Ocomm__ring__1(X5)
     => c_Groups_Ouminus__class_Ouminus(X5,X9) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ouminus__class_Ouminus(X5,c_Groups_Oone__class_Oone(X5))),X9) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J) ).

fof(f15348,plain,
    spl50_868,
    inference(avatar_split_clause,[],[f4466,f15346]) ).

fof(f15346,plain,
    ( spl50_868
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X0,X0),c_Groups_Ozero__class_Ozero(X1))
        | ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
        | ~ class_Rings_Olinordered__idom(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_868])]) ).

fof(f4466,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X0,X0),c_Groups_Ozero__class_Ozero(X1))
      | ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
      | ~ class_Rings_Olinordered__idom(X1) ),
    inference(cnf_transformation,[],[f3536]) ).

fof(f3536,plain,
    ! [X0,X1] :
      ( ( ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X0,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_Ozero__class_Ozero(X1))
          | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X0,X0),c_Groups_Ozero__class_Ozero(X1)) ) )
      | ~ class_Rings_Olinordered__idom(X1) ),
    inference(nnf_transformation,[],[f2491]) ).

fof(f2491,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X0,X0),c_Groups_Ozero__class_Ozero(X1))
      <=> c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1)) )
      | ~ class_Rings_Olinordered__idom(X1) ),
    inference(ennf_transformation,[],[f1549]) ).

fof(f1549,plain,
    ! [X0,X1] :
      ( class_Rings_Olinordered__idom(X1)
     => ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X0,X0),c_Groups_Ozero__class_Ozero(X1))
      <=> c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ) ),
    inference(rectify,[],[f551]) ).

fof(f551,axiom,
    ! [X24,X5] :
      ( class_Rings_Olinordered__idom(X5)
     => ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,X24,X24),c_Groups_Ozero__class_Ozero(X5))
      <=> c_Orderings_Oord__class_Oless(X5,X24,c_Groups_Ozero__class_Ozero(X5)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_even__less__0__iff) ).

fof(f15344,plain,
    spl50_867,
    inference(avatar_split_clause,[],[f4465,f15342]) ).

fof(f15342,plain,
    ( spl50_867
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
        | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X0,X0),c_Groups_Ozero__class_Ozero(X1))
        | ~ class_Rings_Olinordered__idom(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_867])]) ).

fof(f4465,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
      | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X0,X0),c_Groups_Ozero__class_Ozero(X1))
      | ~ class_Rings_Olinordered__idom(X1) ),
    inference(cnf_transformation,[],[f3536]) ).

fof(f15340,plain,
    spl50_866,
    inference(avatar_split_clause,[],[f4463,f15338]) ).

fof(f15338,plain,
    ( spl50_866
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
        | c_Groups_Osgn__class_Osgn(X1,X0) != c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))
        | ~ class_Rings_Olinordered__idom(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_866])]) ).

fof(f4463,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
      | c_Groups_Osgn__class_Osgn(X1,X0) != c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))
      | ~ class_Rings_Olinordered__idom(X1) ),
    inference(cnf_transformation,[],[f3535]) ).

fof(f3535,plain,
    ! [X0,X1] :
      ( ( ( c_Groups_Osgn__class_Osgn(X1,X0) = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))
          | ~ 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_Groups_Osgn__class_Osgn(X1,X0) != c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1)) ) )
      | ~ class_Rings_Olinordered__idom(X1) ),
    inference(nnf_transformation,[],[f2490]) ).

fof(f2490,plain,
    ! [X0,X1] :
      ( ( c_Groups_Osgn__class_Osgn(X1,X0) = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))
      <=> c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1)) )
      | ~ class_Rings_Olinordered__idom(X1) ),
    inference(ennf_transformation,[],[f1548]) ).

fof(f1548,plain,
    ! [X0,X1] :
      ( class_Rings_Olinordered__idom(X1)
     => ( c_Groups_Osgn__class_Osgn(X1,X0) = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))
      <=> c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ) ),
    inference(rectify,[],[f849]) ).

fof(f849,axiom,
    ! [X24,X5] :
      ( class_Rings_Olinordered__idom(X5)
     => ( c_Groups_Ouminus__class_Ouminus(X5,c_Groups_Oone__class_Oone(X5)) = c_Groups_Osgn__class_Osgn(X5,X24)
      <=> c_Orderings_Oord__class_Oless(X5,X24,c_Groups_Ozero__class_Ozero(X5)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__1__neg) ).

fof(f15336,plain,
    spl50_865,
    inference(avatar_split_clause,[],[f4451,f15334]) ).

fof(f15334,plain,
    ( spl50_865
  <=> ! [X0,X1] :
        ( c_Groups_Osgn__class_Osgn(X1,X0) = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))
        | ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
        | ~ class_Rings_Olinordered__idom(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_865])]) ).

fof(f4451,plain,
    ! [X0,X1] :
      ( c_Groups_Osgn__class_Osgn(X1,X0) = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))
      | ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
      | ~ class_Rings_Olinordered__idom(X1) ),
    inference(cnf_transformation,[],[f2482]) ).

fof(f2482,plain,
    ! [X0,X1] :
      ( c_Groups_Osgn__class_Osgn(X1,X0) = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))
      | ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
      | ~ class_Rings_Olinordered__idom(X1) ),
    inference(flattening,[],[f2481]) ).

fof(f2481,plain,
    ! [X0,X1] :
      ( c_Groups_Osgn__class_Osgn(X1,X0) = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))
      | ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
      | ~ class_Rings_Olinordered__idom(X1) ),
    inference(ennf_transformation,[],[f1541]) ).

fof(f1541,plain,
    ! [X0,X1] :
      ( class_Rings_Olinordered__idom(X1)
     => ( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
       => c_Groups_Osgn__class_Osgn(X1,X0) = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1)) ) ),
    inference(rectify,[],[f850]) ).

fof(f850,axiom,
    ! [X4,X5] :
      ( class_Rings_Olinordered__idom(X5)
     => ( c_Orderings_Oord__class_Oless(X5,X4,c_Groups_Ozero__class_Ozero(X5))
       => c_Groups_Ouminus__class_Ouminus(X5,c_Groups_Oone__class_Oone(X5)) = c_Groups_Osgn__class_Osgn(X5,X4) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__neg) ).

fof(f15332,plain,
    spl50_864,
    inference(avatar_split_clause,[],[f4437,f15330]) ).

fof(f15330,plain,
    ( spl50_864
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X0,X0),c_Groups_Ozero__class_Ozero(X1))
        | ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
        | ~ class_Groups_Olinordered__ab__group__add(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_864])]) ).

fof(f4437,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X0,X0),c_Groups_Ozero__class_Ozero(X1))
      | ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
      | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(cnf_transformation,[],[f3525]) ).

fof(f3525,plain,
    ! [X0,X1] :
      ( ( ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X0,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_Ozero__class_Ozero(X1))
          | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X0,X0),c_Groups_Ozero__class_Ozero(X1)) ) )
      | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(nnf_transformation,[],[f2472]) ).

fof(f2472,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X0,X0),c_Groups_Ozero__class_Ozero(X1))
      <=> c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1)) )
      | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(ennf_transformation,[],[f1533]) ).

fof(f1533,plain,
    ! [X0,X1] :
      ( class_Groups_Olinordered__ab__group__add(X1)
     => ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X0,X0),c_Groups_Ozero__class_Ozero(X1))
      <=> c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ) ),
    inference(rectify,[],[f249]) ).

fof(f249,axiom,
    ! [X24,X5] :
      ( class_Groups_Olinordered__ab__group__add(X5)
     => ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,X24,X24),c_Groups_Ozero__class_Ozero(X5))
      <=> c_Orderings_Oord__class_Oless(X5,X24,c_Groups_Ozero__class_Ozero(X5)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__add__less__zero__iff__single__add__less__zero) ).

fof(f15328,plain,
    spl50_863,
    inference(avatar_split_clause,[],[f4436,f15326]) ).

fof(f15326,plain,
    ( spl50_863
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
        | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X0,X0),c_Groups_Ozero__class_Ozero(X1))
        | ~ class_Groups_Olinordered__ab__group__add(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_863])]) ).

fof(f4436,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
      | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X0,X0),c_Groups_Ozero__class_Ozero(X1))
      | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(cnf_transformation,[],[f3525]) ).

fof(f15324,plain,
    ( spl50_862
    | ~ spl50_336
    | ~ spl50_842 ),
    inference(avatar_split_clause,[],[f15109,f12450,f7635,f15321]) ).

fof(f15321,plain,
    ( spl50_862
  <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK47,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK19)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_862])]) ).

fof(f7635,plain,
    ( spl50_336
  <=> ! [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,[spl50_336])]) ).

fof(f12450,plain,
    ( spl50_842
  <=> c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK19) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK47,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK49))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_842])]) ).

fof(f15109,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK47,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK19))
    | ~ spl50_336
    | ~ spl50_842 ),
    inference(superposition,[],[f7636,f12452]) ).

fof(f12452,plain,
    ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK19) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK47,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK49)))
    | ~ spl50_842 ),
    inference(avatar_component_clause,[],[f12450]) ).

fof(f7636,plain,
    ( ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
    | ~ spl50_336 ),
    inference(avatar_component_clause,[],[f7635]) ).

fof(f15319,plain,
    spl50_861,
    inference(avatar_split_clause,[],[f4435,f15317]) ).

fof(f15317,plain,
    ( spl50_861
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(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,[spl50_861])]) ).

fof(f4435,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(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,[],[f3524]) ).

fof(f3524,plain,
    ! [X0,X1] :
      ( ( ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(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_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X0,X0)) ) )
      | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(nnf_transformation,[],[f2471]) ).

fof(f2471,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(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,[],[f1532]) ).

fof(f1532,plain,
    ! [X0,X1] :
      ( class_Groups_Olinordered__ab__group__add(X1)
     => ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X0,X0))
      <=> c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) ) ),
    inference(rectify,[],[f248]) ).

fof(f248,axiom,
    ! [X24,X5] :
      ( class_Groups_Olinordered__ab__group__add(X5)
     => ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),c_Groups_Oplus__class_Oplus(X5,X24,X24))
      <=> c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X24) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__double__add__iff__zero__less__single__add) ).

fof(f15315,plain,
    spl50_860,
    inference(avatar_split_clause,[],[f4434,f15313]) ).

fof(f15313,plain,
    ( spl50_860
  <=> ! [X0,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),c_Groups_Oplus__class_Oplus(X1,X0,X0))
        | ~ class_Groups_Olinordered__ab__group__add(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_860])]) ).

fof(f4434,plain,
    ! [X0,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),c_Groups_Oplus__class_Oplus(X1,X0,X0))
      | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(cnf_transformation,[],[f3524]) ).

fof(f15311,plain,
    spl50_859,
    inference(avatar_split_clause,[],[f4433,f15309]) ).

fof(f15309,plain,
    ( spl50_859
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X0,X0),c_Groups_Ozero__class_Ozero(X1))
        | ~ 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,[spl50_859])]) ).

fof(f4433,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X0,X0),c_Groups_Ozero__class_Ozero(X1))
      | ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
      | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(cnf_transformation,[],[f3523]) ).

fof(f3523,plain,
    ! [X0,X1] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X0,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_Ozero__class_Ozero(X1))
          | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X0,X0),c_Groups_Ozero__class_Ozero(X1)) ) )
      | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(nnf_transformation,[],[f2470]) ).

fof(f2470,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X0,X0),c_Groups_Ozero__class_Ozero(X1))
      <=> c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1)) )
      | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(ennf_transformation,[],[f1531]) ).

fof(f1531,plain,
    ! [X0,X1] :
      ( class_Groups_Olinordered__ab__group__add(X1)
     => ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X0,X0),c_Groups_Ozero__class_Ozero(X1))
      <=> c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ) ),
    inference(rectify,[],[f242]) ).

fof(f242,axiom,
    ! [X24,X5] :
      ( class_Groups_Olinordered__ab__group__add(X5)
     => ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,X24,X24),c_Groups_Ozero__class_Ozero(X5))
      <=> c_Orderings_Oord__class_Oless__eq(X5,X24,c_Groups_Ozero__class_Ozero(X5)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__add__le__zero__iff__single__add__le__zero) ).

fof(f15307,plain,
    spl50_858,
    inference(avatar_split_clause,[],[f4432,f15305]) ).

fof(f15305,plain,
    ( spl50_858
  <=> ! [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_Oplus__class_Oplus(X1,X0,X0),c_Groups_Ozero__class_Ozero(X1))
        | ~ class_Groups_Olinordered__ab__group__add(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_858])]) ).

fof(f4432,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_Oplus__class_Oplus(X1,X0,X0),c_Groups_Ozero__class_Ozero(X1))
      | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(cnf_transformation,[],[f3523]) ).

fof(f15303,plain,
    spl50_857,
    inference(avatar_split_clause,[],[f4431,f15301]) ).

fof(f15301,plain,
    ( spl50_857
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(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,[spl50_857])]) ).

fof(f4431,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(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,[],[f3522]) ).

fof(f3522,plain,
    ! [X0,X1] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(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_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X0,X0)) ) )
      | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(nnf_transformation,[],[f2469]) ).

fof(f2469,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(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,[],[f1530]) ).

fof(f1530,plain,
    ! [X0,X1] :
      ( class_Groups_Olinordered__ab__group__add(X1)
     => ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X0,X0))
      <=> c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0) ) ),
    inference(rectify,[],[f241]) ).

fof(f241,axiom,
    ! [X24,X5] :
      ( class_Groups_Olinordered__ab__group__add(X5)
     => ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),c_Groups_Oplus__class_Oplus(X5,X24,X24))
      <=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X24) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__double__add__iff__zero__le__single__add) ).

fof(f15299,plain,
    spl50_856,
    inference(avatar_split_clause,[],[f4430,f15297]) ).

fof(f15297,plain,
    ( spl50_856
  <=> ! [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),c_Groups_Oplus__class_Oplus(X1,X0,X0))
        | ~ class_Groups_Olinordered__ab__group__add(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_856])]) ).

fof(f4430,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_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X0,X0))
      | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(cnf_transformation,[],[f3522]) ).

fof(f15295,plain,
    spl50_855,
    inference(avatar_split_clause,[],[f4330,f15293]) ).

fof(f15293,plain,
    ( spl50_855
  <=> ! [X0,X1] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_855])]) ).

fof(f4330,plain,
    ! [X0,X1] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)),
    inference(cnf_transformation,[],[f1461]) ).

fof(f1461,plain,
    ! [X0,X1] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)),
    inference(rectify,[],[f629]) ).

fof(f629,axiom,
    ! [X15,X14] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X14,X15)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X14),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X15)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zminus__zadd__distrib) ).

fof(f15291,plain,
    spl50_854,
    inference(avatar_split_clause,[],[f4276,f15289]) ).

fof(f15289,plain,
    ( spl50_854
  <=> ! [X0] :
        ( c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X0)),X0)
        | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_854])]) ).

fof(f4276,plain,
    ! [X0] :
      ( c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X0)),X0)
      | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X0 ),
    inference(cnf_transformation,[],[f2388]) ).

fof(f2388,plain,
    ! [X0] :
      ( c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X0)),X0)
      | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X0 ),
    inference(ennf_transformation,[],[f1417]) ).

fof(f1417,plain,
    ! [X0] :
      ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X0
     => c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X0)),X0) ),
    inference(rectify,[],[f258]) ).

fof(f258,axiom,
    ! [X9] :
      ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X9
     => c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X9)),X9) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__inverse__left) ).

fof(f15287,plain,
    spl50_853,
    inference(avatar_split_clause,[],[f4193,f15285]) ).

fof(f15285,plain,
    ( spl50_853
  <=> ! [X0] :
        ( c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
        | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_853])]) ).

fof(f4193,plain,
    ! [X0] :
      ( c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
      | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 ),
    inference(cnf_transformation,[],[f2307]) ).

fof(f15283,plain,
    spl50_852,
    inference(avatar_split_clause,[],[f4181,f15281]) ).

fof(f15281,plain,
    ( spl50_852
  <=> ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),X0)) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_852])]) ).

fof(f4181,plain,
    ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),X0)) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),
    inference(cnf_transformation,[],[f1329]) ).

fof(f1329,plain,
    ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),X0)) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),
    inference(rectify,[],[f705]) ).

fof(f705,axiom,
    ! [X9] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),X9)) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X9),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__i__mult__minus) ).

fof(f15279,plain,
    ( ~ spl50_851
    | ~ spl50_334
    | ~ spl50_842 ),
    inference(avatar_split_clause,[],[f15107,f12450,f7627,f15276]) ).

fof(f15276,plain,
    ( spl50_851
  <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK19),sK47) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_851])]) ).

fof(f7627,plain,
    ( spl50_334
  <=> ! [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,[spl50_334])]) ).

fof(f15107,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK19),sK47)
    | ~ spl50_334
    | ~ spl50_842 ),
    inference(superposition,[],[f7628,f12452]) ).

fof(f7628,plain,
    ( ! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X1)
    | ~ spl50_334 ),
    inference(avatar_component_clause,[],[f7627]) ).

fof(f15106,plain,
    ( spl50_850
    | ~ spl50_324
    | ~ spl50_395
    | ~ spl50_841 ),
    inference(avatar_split_clause,[],[f12448,f12443,f7922,f7586,f15103]) ).

fof(f7922,plain,
    ( spl50_395
  <=> ! [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,[spl50_395])]) ).

fof(f12443,plain,
    ( spl50_841
  <=> c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_s____),v_k____),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_841])]) ).

fof(f12448,plain,
    ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK19) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_s____)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ spl50_324
    | ~ spl50_395
    | ~ spl50_841 ),
    inference(forward_demodulation,[],[f12447,f7588]) ).

fof(f12447,plain,
    ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_s____)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ spl50_395
    | ~ spl50_841 ),
    inference(forward_demodulation,[],[f12445,f7923]) ).

fof(f7923,plain,
    ( ! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)
    | ~ spl50_395 ),
    inference(avatar_component_clause,[],[f7922]) ).

fof(f12445,plain,
    ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_s____),v_k____),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ spl50_841 ),
    inference(avatar_component_clause,[],[f12443]) ).

fof(f14891,plain,
    ( spl50_849
    | ~ spl50_472
    | ~ spl50_763 ),
    inference(avatar_split_clause,[],[f13241,f12116,f8684,f14889]) ).

fof(f14889,plain,
    ( spl50_849
  <=> ! [X0] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | sP2(tc_RealDef_Oreal,X0,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_849])]) ).

fof(f8684,plain,
    ( spl50_472
  <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_472])]) ).

fof(f12116,plain,
    ( spl50_763
  <=> ! [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,[spl50_763])]) ).

fof(f13241,plain,
    ( ! [X0] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | sP2(tc_RealDef_Oreal,X0,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))) )
    | ~ spl50_472
    | ~ spl50_763 ),
    inference(resolution,[],[f12117,f8686]) ).

fof(f8686,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    | ~ spl50_472 ),
    inference(avatar_component_clause,[],[f8684]) ).

fof(f12117,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,X1,c_Groups_Ozero__class_Ozero(X0))
        | sP2(X0,X1,X2) )
    | ~ spl50_763 ),
    inference(avatar_component_clause,[],[f12116]) ).

fof(f14002,plain,
    ( spl50_848
    | ~ spl50_763
    | ~ spl50_844 ),
    inference(avatar_split_clause,[],[f13239,f13070,f12116,f14000]) ).

fof(f14000,plain,
    ( spl50_848
  <=> ! [X0] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | sP2(tc_RealDef_Oreal,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_848])]) ).

fof(f13239,plain,
    ( ! [X0] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | sP2(tc_RealDef_Oreal,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))) )
    | ~ spl50_763
    | ~ spl50_844 ),
    inference(resolution,[],[f12117,f13072]) ).

fof(f13599,plain,
    ( ~ spl50_846
    | spl50_847
    | ~ spl50_231
    | ~ spl50_774 ),
    inference(avatar_split_clause,[],[f13432,f12160,f7194,f13597,f13593]) ).

fof(f13593,plain,
    ( spl50_846
  <=> class_Groups_Oordered__ab__group__add(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_846])]) ).

fof(f13597,plain,
    ( spl50_847
  <=> ! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_847])]) ).

fof(f7194,plain,
    ( spl50_231
  <=> ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_231])]) ).

fof(f12160,plain,
    ( spl50_774
  <=> ! [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,[spl50_774])]) ).

fof(f13432,plain,
    ( ! [X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
        | ~ class_Groups_Oordered__ab__group__add(tc_Nat_Onat) )
    | ~ spl50_231
    | ~ spl50_774 ),
    inference(resolution,[],[f12161,f7195]) ).

fof(f7195,plain,
    ( ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ spl50_231 ),
    inference(avatar_component_clause,[],[f7194]) ).

fof(f12161,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) )
    | ~ spl50_774 ),
    inference(avatar_component_clause,[],[f12160]) ).

fof(f13309,plain,
    ( spl50_845
    | ~ spl50_622
    | ~ spl50_844 ),
    inference(avatar_split_clause,[],[f13195,f13070,f9967,f13307]) ).

fof(f9967,plain,
    ( spl50_622
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X0)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_622])]) ).

fof(f13195,plain,
    ( ! [X0] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X0) )
    | ~ spl50_622
    | ~ spl50_844 ),
    inference(resolution,[],[f13072,f9968]) ).

fof(f9968,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X0) )
    | ~ spl50_622 ),
    inference(avatar_component_clause,[],[f9967]) ).

fof(f13073,plain,
    ( ~ spl50_1
    | spl50_844
    | ~ spl50_472
    | ~ spl50_716 ),
    inference(avatar_split_clause,[],[f12599,f11928,f8684,f13070,f6051]) ).

fof(f6051,plain,
    ( spl50_1
  <=> class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1])]) ).

fof(f11928,plain,
    ( spl50_716
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
        | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Ozero__class_Ozero(X1))
        | ~ class_Fields_Olinordered__field__inverse__zero(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_716])]) ).

fof(f12599,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    | ~ class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal)
    | ~ spl50_472
    | ~ spl50_716 ),
    inference(resolution,[],[f11929,f8686]) ).

fof(f11929,plain,
    ( ! [X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Ozero__class_Ozero(X1))
        | c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
        | ~ class_Fields_Olinordered__field__inverse__zero(X1) )
    | ~ spl50_716 ),
    inference(avatar_component_clause,[],[f11928]) ).

fof(f12742,plain,
    ( ~ spl50_1
    | ~ spl50_843
    | spl50_298
    | ~ spl50_721 ),
    inference(avatar_split_clause,[],[f12683,f11948,f7469,f12739,f6051]) ).

fof(f7469,plain,
    ( spl50_298
  <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_298])]) ).

fof(f11948,plain,
    ( spl50_721
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
        | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
        | ~ class_Fields_Olinordered__field__inverse__zero(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_721])]) ).

fof(f12683,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))
    | ~ class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal)
    | spl50_298
    | ~ spl50_721 ),
    inference(resolution,[],[f11949,f7471]) ).

fof(f7471,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))))
    | spl50_298 ),
    inference(avatar_component_clause,[],[f7469]) ).

fof(f11949,plain,
    ( ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
        | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
        | ~ class_Fields_Olinordered__field__inverse__zero(X1) )
    | ~ spl50_721 ),
    inference(avatar_component_clause,[],[f11948]) ).

fof(f12453,plain,
    spl50_842,
    inference(avatar_split_clause,[],[f6049,f12450]) ).

fof(f6049,plain,
    c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK19) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK47,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK49))),
    inference(forward_demodulation,[],[f6048,f4130]) ).

fof(f4130,plain,
    c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK19),
    inference(cnf_transformation,[],[f3473]) ).

fof(f3473,plain,
    ( ! [X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X1)) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,sK19),X1)
    & c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK19) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f2303,f3472]) ).

fof(f3472,plain,
    ( ? [X0] :
        ( ! [X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X1)) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X0),X1)
        & c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,X0) )
   => ( ! [X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X1)) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,sK19),X1)
      & c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK19) ) ),
    introduced(choice_axiom,[]) ).

fof(f2303,plain,
    ? [X0] :
      ( ! [X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X1)) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X0),X1)
      & c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,X0) ),
    inference(ennf_transformation,[],[f1279]) ).

fof(f1279,plain,
    ~ ! [X0] :
        ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,X0)
       => ~ ! [X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X1)) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X0),X1) ),
    inference(rectify,[],[f771]) ).

fof(f771,axiom,
    ~ ! [X65] :
        ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,X65)
       => ~ ! [X2] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X2)) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X65),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_Bq_O_A_091_124_Apsize_Aq_A_061_Apsize_Ap_059_AALL_Ax_O_Apoly_Aq_Ax_A_061_Apoly_Ap_A_Ic_A_L_Ax_J_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).

fof(f6048,plain,
    c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK47,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK49))),
    inference(forward_demodulation,[],[f6047,f5907]) ).

fof(f6047,plain,
    c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)),v_q____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK47,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK49))),
    inference(forward_demodulation,[],[f6046,f4114]) ).

fof(f6046,plain,
    c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK47,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK49))),
    inference(forward_demodulation,[],[f6045,f4313]) ).

fof(f6045,plain,
    c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK47,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK49),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
    inference(forward_demodulation,[],[f6044,f4782]) ).

fof(f6044,plain,
    c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK49),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK47,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
    inference(forward_demodulation,[],[f5564,f4783]) ).

fof(f5564,plain,
    c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK49),sK47),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(cnf_transformation,[],[f3874]) ).

fof(f3874,plain,
    ( ! [X3] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X3) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X3),sK47)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,sK48,sK49)),X3)))
    & c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK49),sK47),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != sK47
    & c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != sK48 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK47,sK48,sK49])],[f2295,f3873,f3872]) ).

fof(f3872,plain,
    ( ? [X0,X1] :
        ( ? [X2] :
            ( ! [X3] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X3) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X3),X0)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X1,X2)),X3)))
            & c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,X2),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
        & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
        & c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != X1 )
   => ( ? [X2] :
          ( ! [X3] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X3) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X3),sK47)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,sK48,X2)),X3)))
          & c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,X2),sK47),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
      & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != sK47
      & c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != sK48 ) ),
    introduced(choice_axiom,[]) ).

fof(f3873,plain,
    ( ? [X2] :
        ( ! [X3] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X3) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X3),sK47)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,sK48,X2)),X3)))
        & c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,X2),sK47),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
   => ( ! [X3] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X3) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X3),sK47)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,sK48,sK49)),X3)))
      & c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK49),sK47),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
    introduced(choice_axiom,[]) ).

fof(f2295,plain,
    ? [X0,X1] :
      ( ? [X2] :
          ( ! [X3] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X3) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X3),X0)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X1,X2)),X3)))
          & c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,X2),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
      & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
      & c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != X1 ),
    inference(rectify,[],[f708]) ).

fof(f708,axiom,
    ? [X52,X71] :
      ( ? [X65] :
          ( ! [X34] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X34) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X34),X52)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X71,X65)),X34)))
          & c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,X65),X52),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
      & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X52
      & c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != X71 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096EX_Ak_Aa_Aqa_O_Aa_A_126_061_A0_A_G_Ak_A_126_061_A0_A_G_Apsize_Aqa_A_L_Ak_A_L_A1_A_061_Apsize_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_A_G_A_IALL_Az_O_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_Az_A_061_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_A0_A_L_Az_A_094_Ak_A_K_Apoly_A_IpCons_Aa_Aqa_J_Az_J_096) ).

fof(f12446,plain,
    spl50_841,
    inference(avatar_split_clause,[],[f5911,f12443]) ).

fof(f5911,plain,
    c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_s____),v_k____),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(forward_demodulation,[],[f5910,f5907]) ).

fof(f5910,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_s____),v_k____),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)),v_q____)),
    inference(forward_demodulation,[],[f4122,f4114]) ).

fof(f4122,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_s____),v_k____),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),
    inference(cnf_transformation,[],[f560]) ).

fof(f560,axiom,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_s____),v_k____),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_kas_I3_J) ).

fof(f12435,plain,
    spl50_840,
    inference(avatar_split_clause,[],[f5889,f12433]) ).

fof(f12433,plain,
    ( spl50_840
  <=> ! [X4,X3,X2,X1] :
        ( X2 = X3
        | c_Groups_Ominus__class_Ominus(X4,X3,X2) != c_Groups_Ominus__class_Ominus(X4,X1,X1)
        | ~ class_Groups_Oab__group__add(X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_840])]) ).

fof(f5889,plain,
    ! [X2,X3,X1,X4] :
      ( X2 = X3
      | c_Groups_Ominus__class_Ominus(X4,X3,X2) != c_Groups_Ominus__class_Ominus(X4,X1,X1)
      | ~ class_Groups_Oab__group__add(X4) ),
    inference(equality_resolution,[],[f5497]) ).

fof(f5497,plain,
    ! [X2,X3,X0,X1,X4] :
      ( X2 = X3
      | X0 != X1
      | c_Groups_Ominus__class_Ominus(X4,X3,X2) != c_Groups_Ominus__class_Ominus(X4,X1,X0)
      | ~ class_Groups_Oab__group__add(X4) ),
    inference(cnf_transformation,[],[f3846]) ).

fof(f3846,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ( ( X2 = X3
          | X0 != X1 )
        & ( X0 = X1
          | X2 != X3 ) )
      | c_Groups_Ominus__class_Ominus(X4,X3,X2) != c_Groups_Ominus__class_Ominus(X4,X1,X0)
      | ~ class_Groups_Oab__group__add(X4) ),
    inference(nnf_transformation,[],[f3385]) ).

fof(f3385,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ( X2 = X3
      <=> X0 = X1 )
      | c_Groups_Ominus__class_Ominus(X4,X3,X2) != c_Groups_Ominus__class_Ominus(X4,X1,X0)
      | ~ class_Groups_Oab__group__add(X4) ),
    inference(flattening,[],[f3384]) ).

fof(f3384,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ( X2 = X3
      <=> X0 = X1 )
      | c_Groups_Ominus__class_Ominus(X4,X3,X2) != c_Groups_Ominus__class_Ominus(X4,X1,X0)
      | ~ class_Groups_Oab__group__add(X4) ),
    inference(ennf_transformation,[],[f2252]) ).

fof(f2252,plain,
    ! [X0,X1,X2,X3,X4] :
      ( class_Groups_Oab__group__add(X4)
     => ( c_Groups_Ominus__class_Ominus(X4,X3,X2) = c_Groups_Ominus__class_Ominus(X4,X1,X0)
       => ( X2 = X3
        <=> X0 = X1 ) ) ),
    inference(rectify,[],[f275]) ).

fof(f275,axiom,
    ! [X45,X25,X21,X24,X5] :
      ( class_Groups_Oab__group__add(X5)
     => ( c_Groups_Ominus__class_Ominus(X5,X24,X21) = c_Groups_Ominus__class_Ominus(X5,X25,X45)
       => ( X21 = X24
        <=> X25 = X45 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__eq__diff__eq) ).

fof(f12431,plain,
    spl50_839,
    inference(avatar_split_clause,[],[f5869,f12429]) ).

fof(f12429,plain,
    ( spl50_839
  <=> ! [X2,X1,X3] :
        ( sP9(c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X1,X2,X3)
        | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2),X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_839])]) ).

fof(f5869,plain,
    ! [X2,X3,X1] :
      ( sP9(c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X1,X2,X3)
      | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2),X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))) ),
    inference(equality_resolution,[],[f5273]) ).

fof(f5273,plain,
    ! [X2,X3,X0,X1] :
      ( sP9(X0,X1,X2,X3)
      | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2),X1,X0)
      | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X0 ),
    inference(cnf_transformation,[],[f3804]) ).

fof(f3804,plain,
    ! [X0,X1,X2,X3] :
      ( ( sP9(X0,X1,X2,X3)
        | ( ~ 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 ) )
      & ( ( ( 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,[],[f3803]) ).

fof(f3803,plain,
    ! [X0,X1,X3,X2] :
      ( ( sP9(X0,X1,X3,X2)
        | ( ~ 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 ) )
      & ( ( ( 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,[],[f3802]) ).

fof(f3802,plain,
    ! [X0,X1,X3,X2] :
      ( ( sP9(X0,X1,X3,X2)
        | ( ~ 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 ) )
      & ( ( ( 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,[],[f3455]) ).

fof(f3455,plain,
    ! [X0,X1,X3,X2] :
      ( sP9(X0,X1,X3,X2)
    <=> ( ( 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(f12427,plain,
    spl50_838,
    inference(avatar_split_clause,[],[f5507,f12425]) ).

fof(f12425,plain,
    ( spl50_838
  <=> ! [X4,X0,X3,X2,X1] :
        ( X0 = X2
        | c_Polynomial_OpCons(X4,X3,X2) != c_Polynomial_OpCons(X4,X1,X0)
        | ~ class_Groups_Ozero(X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_838])]) ).

fof(f5507,plain,
    ! [X2,X3,X0,X1,X4] :
      ( X0 = X2
      | c_Polynomial_OpCons(X4,X3,X2) != c_Polynomial_OpCons(X4,X1,X0)
      | ~ class_Groups_Ozero(X4) ),
    inference(cnf_transformation,[],[f3852]) ).

fof(f3852,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ( ( c_Polynomial_OpCons(X4,X3,X2) = c_Polynomial_OpCons(X4,X1,X0)
          | X0 != X2
          | X1 != X3 )
        & ( ( X0 = X2
            & X1 = X3 )
          | c_Polynomial_OpCons(X4,X3,X2) != c_Polynomial_OpCons(X4,X1,X0) ) )
      | ~ class_Groups_Ozero(X4) ),
    inference(flattening,[],[f3851]) ).

fof(f3851,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ( ( c_Polynomial_OpCons(X4,X3,X2) = c_Polynomial_OpCons(X4,X1,X0)
          | X0 != X2
          | X1 != X3 )
        & ( ( X0 = X2
            & X1 = X3 )
          | c_Polynomial_OpCons(X4,X3,X2) != c_Polynomial_OpCons(X4,X1,X0) ) )
      | ~ class_Groups_Ozero(X4) ),
    inference(nnf_transformation,[],[f3390]) ).

fof(f3390,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ( c_Polynomial_OpCons(X4,X3,X2) = c_Polynomial_OpCons(X4,X1,X0)
      <=> ( X0 = X2
          & X1 = X3 ) )
      | ~ class_Groups_Ozero(X4) ),
    inference(ennf_transformation,[],[f2257]) ).

fof(f2257,plain,
    ! [X0,X1,X2,X3,X4] :
      ( class_Groups_Ozero(X4)
     => ( c_Polynomial_OpCons(X4,X3,X2) = c_Polynomial_OpCons(X4,X1,X0)
      <=> ( X0 = X2
          & X1 = X3 ) ) ),
    inference(rectify,[],[f609]) ).

fof(f609,axiom,
    ! [X66,X21,X64,X24,X5] :
      ( class_Groups_Ozero(X5)
     => ( c_Polynomial_OpCons(X5,X24,X64) = c_Polynomial_OpCons(X5,X21,X66)
      <=> ( X64 = X66
          & X21 = X24 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pCons__eq__iff) ).

fof(f12423,plain,
    spl50_837,
    inference(avatar_split_clause,[],[f5506,f12421]) ).

fof(f12421,plain,
    ( spl50_837
  <=> ! [X2,X4,X0,X3,X1] :
        ( X1 = X3
        | c_Polynomial_OpCons(X4,X3,X2) != c_Polynomial_OpCons(X4,X1,X0)
        | ~ class_Groups_Ozero(X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_837])]) ).

fof(f5506,plain,
    ! [X2,X3,X0,X1,X4] :
      ( X1 = X3
      | c_Polynomial_OpCons(X4,X3,X2) != c_Polynomial_OpCons(X4,X1,X0)
      | ~ class_Groups_Ozero(X4) ),
    inference(cnf_transformation,[],[f3852]) ).

fof(f12419,plain,
    spl50_836,
    inference(avatar_split_clause,[],[f5460,f12417]) ).

fof(f12417,plain,
    ( spl50_836
  <=> ! [X0,X3,X2,X1] :
        ( c_Orderings_Oord__class_Oless(X3,X0,X1)
        | ~ c_Orderings_Oord__class_Oless(X3,X0,X2)
        | ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
        | ~ class_Orderings_Oorder(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_836])]) ).

fof(f5460,plain,
    ! [X2,X3,X0,X1] :
      ( c_Orderings_Oord__class_Oless(X3,X0,X1)
      | ~ c_Orderings_Oord__class_Oless(X3,X0,X2)
      | ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
      | ~ class_Orderings_Oorder(X3) ),
    inference(cnf_transformation,[],[f3330]) ).

fof(f3330,plain,
    ! [X0,X1,X2,X3] :
      ( c_Orderings_Oord__class_Oless(X3,X0,X1)
      | ~ c_Orderings_Oord__class_Oless(X3,X0,X2)
      | ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
      | ~ class_Orderings_Oorder(X3) ),
    inference(flattening,[],[f3329]) ).

fof(f3329,plain,
    ! [X0,X1,X2,X3] :
      ( c_Orderings_Oord__class_Oless(X3,X0,X1)
      | ~ c_Orderings_Oord__class_Oless(X3,X0,X2)
      | ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
      | ~ class_Orderings_Oorder(X3) ),
    inference(ennf_transformation,[],[f2221]) ).

fof(f2221,plain,
    ! [X0,X1,X2,X3] :
      ( class_Orderings_Oorder(X3)
     => ( c_Orderings_Oord__class_Oless(X3,X2,X1)
       => ( c_Orderings_Oord__class_Oless(X3,X0,X2)
         => c_Orderings_Oord__class_Oless(X3,X0,X1) ) ) ),
    inference(rectify,[],[f730]) ).

fof(f730,axiom,
    ! [X14,X9,X7,X5] :
      ( class_Orderings_Oorder(X5)
     => ( c_Orderings_Oord__class_Oless(X5,X7,X9)
       => ( c_Orderings_Oord__class_Oless(X5,X14,X7)
         => c_Orderings_Oord__class_Oless(X5,X14,X9) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I10_J) ).

fof(f12415,plain,
    spl50_835,
    inference(avatar_split_clause,[],[f5459,f12413]) ).

fof(f12413,plain,
    ( spl50_835
  <=> ! [X0,X3,X2,X1] :
        ( c_Orderings_Oord__class_Oless(X3,X0,X1)
        | ~ c_Orderings_Oord__class_Oless__eq(X3,X0,X2)
        | ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
        | ~ class_Orderings_Oorder(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_835])]) ).

fof(f5459,plain,
    ! [X2,X3,X0,X1] :
      ( c_Orderings_Oord__class_Oless(X3,X0,X1)
      | ~ c_Orderings_Oord__class_Oless__eq(X3,X0,X2)
      | ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
      | ~ class_Orderings_Oorder(X3) ),
    inference(cnf_transformation,[],[f3328]) ).

fof(f3328,plain,
    ! [X0,X1,X2,X3] :
      ( c_Orderings_Oord__class_Oless(X3,X0,X1)
      | ~ c_Orderings_Oord__class_Oless__eq(X3,X0,X2)
      | ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
      | ~ class_Orderings_Oorder(X3) ),
    inference(flattening,[],[f3327]) ).

fof(f3327,plain,
    ! [X0,X1,X2,X3] :
      ( c_Orderings_Oord__class_Oless(X3,X0,X1)
      | ~ c_Orderings_Oord__class_Oless__eq(X3,X0,X2)
      | ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
      | ~ class_Orderings_Oorder(X3) ),
    inference(ennf_transformation,[],[f2220]) ).

fof(f2220,plain,
    ! [X0,X1,X2,X3] :
      ( class_Orderings_Oorder(X3)
     => ( c_Orderings_Oord__class_Oless(X3,X2,X1)
       => ( c_Orderings_Oord__class_Oless__eq(X3,X0,X2)
         => c_Orderings_Oord__class_Oless(X3,X0,X1) ) ) ),
    inference(rectify,[],[f751]) ).

fof(f751,axiom,
    ! [X14,X9,X7,X5] :
      ( class_Orderings_Oorder(X5)
     => ( c_Orderings_Oord__class_Oless(X5,X7,X9)
       => ( c_Orderings_Oord__class_Oless__eq(X5,X14,X7)
         => c_Orderings_Oord__class_Oless(X5,X14,X9) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I7_J) ).

fof(f12411,plain,
    spl50_834,
    inference(avatar_split_clause,[],[f5457,f12409]) ).

fof(f12409,plain,
    ( spl50_834
  <=> ! [X0,X3,X2,X1] :
        ( c_Orderings_Oord__class_Oless(X3,X0,X1)
        | ~ c_Orderings_Oord__class_Oless(X3,X0,X2)
        | ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
        | ~ class_Orderings_Oorder(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_834])]) ).

fof(f5457,plain,
    ! [X2,X3,X0,X1] :
      ( c_Orderings_Oord__class_Oless(X3,X0,X1)
      | ~ c_Orderings_Oord__class_Oless(X3,X0,X2)
      | ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
      | ~ class_Orderings_Oorder(X3) ),
    inference(cnf_transformation,[],[f3324]) ).

fof(f3324,plain,
    ! [X0,X1,X2,X3] :
      ( c_Orderings_Oord__class_Oless(X3,X0,X1)
      | ~ c_Orderings_Oord__class_Oless(X3,X0,X2)
      | ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
      | ~ class_Orderings_Oorder(X3) ),
    inference(flattening,[],[f3323]) ).

fof(f3323,plain,
    ! [X0,X1,X2,X3] :
      ( c_Orderings_Oord__class_Oless(X3,X0,X1)
      | ~ c_Orderings_Oord__class_Oless(X3,X0,X2)
      | ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
      | ~ class_Orderings_Oorder(X3) ),
    inference(ennf_transformation,[],[f2218]) ).

fof(f2218,plain,
    ! [X0,X1,X2,X3] :
      ( class_Orderings_Oorder(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
       => ( c_Orderings_Oord__class_Oless(X3,X0,X2)
         => c_Orderings_Oord__class_Oless(X3,X0,X1) ) ) ),
    inference(rectify,[],[f749]) ).

fof(f749,axiom,
    ! [X14,X9,X7,X5] :
      ( class_Orderings_Oorder(X5)
     => ( c_Orderings_Oord__class_Oless__eq(X5,X7,X9)
       => ( c_Orderings_Oord__class_Oless(X5,X14,X7)
         => c_Orderings_Oord__class_Oless(X5,X14,X9) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I8_J) ).

fof(f12407,plain,
    spl50_833,
    inference(avatar_split_clause,[],[f5456,f12405]) ).

fof(f5456,plain,
    ! [X2,X3,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X3,X0,X1)
      | ~ c_Orderings_Oord__class_Oless__eq(X3,X0,X2)
      | ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
      | ~ class_Orderings_Oorder(X3) ),
    inference(cnf_transformation,[],[f3322]) ).

fof(f3322,plain,
    ! [X0,X1,X2,X3] :
      ( c_Orderings_Oord__class_Oless__eq(X3,X0,X1)
      | ~ c_Orderings_Oord__class_Oless__eq(X3,X0,X2)
      | ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
      | ~ class_Orderings_Oorder(X3) ),
    inference(flattening,[],[f3321]) ).

fof(f3321,plain,
    ! [X0,X1,X2,X3] :
      ( c_Orderings_Oord__class_Oless__eq(X3,X0,X1)
      | ~ c_Orderings_Oord__class_Oless__eq(X3,X0,X2)
      | ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
      | ~ class_Orderings_Oorder(X3) ),
    inference(ennf_transformation,[],[f2217]) ).

fof(f2217,plain,
    ! [X0,X1,X2,X3] :
      ( class_Orderings_Oorder(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
       => ( c_Orderings_Oord__class_Oless__eq(X3,X0,X2)
         => c_Orderings_Oord__class_Oless__eq(X3,X0,X1) ) ) ),
    inference(rectify,[],[f725]) ).

fof(f725,axiom,
    ! [X14,X9,X7,X5] :
      ( class_Orderings_Oorder(X5)
     => ( c_Orderings_Oord__class_Oless__eq(X5,X7,X9)
       => ( c_Orderings_Oord__class_Oless__eq(X5,X14,X7)
         => c_Orderings_Oord__class_Oless__eq(X5,X14,X9) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I6_J) ).

fof(f12403,plain,
    spl50_832,
    inference(avatar_split_clause,[],[f5452,f12401]) ).

fof(f12401,plain,
    ( spl50_832
  <=> ! [X0,X3,X2,X1] :
        ( c_Orderings_Oord__class_Oless(X3,X2,X0)
        | ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
        | ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
        | ~ class_Orderings_Opreorder(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_832])]) ).

fof(f5452,plain,
    ! [X2,X3,X0,X1] :
      ( c_Orderings_Oord__class_Oless(X3,X2,X0)
      | ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
      | ~ class_Orderings_Opreorder(X3) ),
    inference(cnf_transformation,[],[f3314]) ).

fof(f3314,plain,
    ! [X0,X1,X2,X3] :
      ( c_Orderings_Oord__class_Oless(X3,X2,X0)
      | ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
      | ~ class_Orderings_Opreorder(X3) ),
    inference(flattening,[],[f3313]) ).

fof(f3313,plain,
    ! [X0,X1,X2,X3] :
      ( c_Orderings_Oord__class_Oless(X3,X2,X0)
      | ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
      | ~ class_Orderings_Opreorder(X3) ),
    inference(ennf_transformation,[],[f2213]) ).

fof(f2213,plain,
    ! [X0,X1,X2,X3] :
      ( class_Orderings_Opreorder(X3)
     => ( c_Orderings_Oord__class_Oless(X3,X2,X1)
       => ( c_Orderings_Oord__class_Oless(X3,X1,X0)
         => c_Orderings_Oord__class_Oless(X3,X2,X0) ) ) ),
    inference(rectify,[],[f731]) ).

fof(f731,axiom,
    ! [X14,X7,X9,X5] :
      ( class_Orderings_Opreorder(X5)
     => ( c_Orderings_Oord__class_Oless(X5,X9,X7)
       => ( c_Orderings_Oord__class_Oless(X5,X7,X14)
         => c_Orderings_Oord__class_Oless(X5,X9,X14) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__trans) ).

fof(f12399,plain,
    spl50_831,
    inference(avatar_split_clause,[],[f5451,f12397]) ).

fof(f5451,plain,
    ! [X2,X3,X0,X1] :
      ( c_Orderings_Oord__class_Oless(X3,X2,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
      | ~ class_Orderings_Opreorder(X3) ),
    inference(cnf_transformation,[],[f3312]) ).

fof(f3312,plain,
    ! [X0,X1,X2,X3] :
      ( c_Orderings_Oord__class_Oless(X3,X2,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
      | ~ class_Orderings_Opreorder(X3) ),
    inference(flattening,[],[f3311]) ).

fof(f3311,plain,
    ! [X0,X1,X2,X3] :
      ( c_Orderings_Oord__class_Oless(X3,X2,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
      | ~ class_Orderings_Opreorder(X3) ),
    inference(ennf_transformation,[],[f2212]) ).

fof(f2212,plain,
    ! [X0,X1,X2,X3] :
      ( class_Orderings_Opreorder(X3)
     => ( c_Orderings_Oord__class_Oless(X3,X2,X1)
       => ( c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
         => c_Orderings_Oord__class_Oless(X3,X2,X0) ) ) ),
    inference(rectify,[],[f752]) ).

fof(f752,axiom,
    ! [X14,X7,X9,X5] :
      ( class_Orderings_Opreorder(X5)
     => ( c_Orderings_Oord__class_Oless(X5,X9,X7)
       => ( c_Orderings_Oord__class_Oless__eq(X5,X7,X14)
         => c_Orderings_Oord__class_Oless(X5,X9,X14) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__le__trans) ).

fof(f12390,plain,
    spl50_830,
    inference(avatar_split_clause,[],[f5450,f12388]) ).

fof(f5450,plain,
    ! [X2,X3,X0,X1] :
      ( c_Orderings_Oord__class_Oless(X3,X2,X0)
      | ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
      | ~ class_Orderings_Opreorder(X3) ),
    inference(cnf_transformation,[],[f3310]) ).

fof(f3310,plain,
    ! [X0,X1,X2,X3] :
      ( c_Orderings_Oord__class_Oless(X3,X2,X0)
      | ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
      | ~ class_Orderings_Opreorder(X3) ),
    inference(flattening,[],[f3309]) ).

fof(f3309,plain,
    ! [X0,X1,X2,X3] :
      ( c_Orderings_Oord__class_Oless(X3,X2,X0)
      | ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
      | ~ class_Orderings_Opreorder(X3) ),
    inference(ennf_transformation,[],[f2211]) ).

fof(f2211,plain,
    ! [X0,X1,X2,X3] :
      ( class_Orderings_Opreorder(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
       => ( c_Orderings_Oord__class_Oless(X3,X1,X0)
         => c_Orderings_Oord__class_Oless(X3,X2,X0) ) ) ),
    inference(rectify,[],[f750]) ).

fof(f750,axiom,
    ! [X14,X7,X9,X5] :
      ( class_Orderings_Opreorder(X5)
     => ( c_Orderings_Oord__class_Oless__eq(X5,X9,X7)
       => ( c_Orderings_Oord__class_Oless(X5,X7,X14)
         => c_Orderings_Oord__class_Oless(X5,X9,X14) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__less__trans) ).

fof(f12386,plain,
    spl50_829,
    inference(avatar_split_clause,[],[f5449,f12384]) ).

fof(f12384,plain,
    ( spl50_829
  <=> ! [X0,X3,X2,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X3,X2,X0)
        | ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
        | ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
        | ~ class_Orderings_Opreorder(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_829])]) ).

fof(f5449,plain,
    ! [X2,X3,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X3,X2,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
      | ~ class_Orderings_Opreorder(X3) ),
    inference(cnf_transformation,[],[f3308]) ).

fof(f3308,plain,
    ! [X0,X1,X2,X3] :
      ( c_Orderings_Oord__class_Oless__eq(X3,X2,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
      | ~ class_Orderings_Opreorder(X3) ),
    inference(flattening,[],[f3307]) ).

fof(f3307,plain,
    ! [X0,X1,X2,X3] :
      ( c_Orderings_Oord__class_Oless__eq(X3,X2,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
      | ~ class_Orderings_Opreorder(X3) ),
    inference(ennf_transformation,[],[f2210]) ).

fof(f2210,plain,
    ! [X0,X1,X2,X3] :
      ( class_Orderings_Opreorder(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
       => ( c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
         => c_Orderings_Oord__class_Oless__eq(X3,X2,X0) ) ) ),
    inference(rectify,[],[f723]) ).

fof(f723,axiom,
    ! [X14,X7,X9,X5] :
      ( class_Orderings_Opreorder(X5)
     => ( c_Orderings_Oord__class_Oless__eq(X5,X9,X7)
       => ( c_Orderings_Oord__class_Oless__eq(X5,X7,X14)
         => c_Orderings_Oord__class_Oless__eq(X5,X9,X14) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__trans) ).

fof(f12382,plain,
    spl50_828,
    inference(avatar_split_clause,[],[f5447,f12380]) ).

fof(f12380,plain,
    ( spl50_828
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X0,X1)
        | ~ c_Orderings_Oord__class_Oless(tc_fun(X2,X3),X1,X0)
        | ~ class_Orderings_Oord(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_828])]) ).

fof(f5447,plain,
    ! [X2,X3,X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X0,X1)
      | ~ c_Orderings_Oord__class_Oless(tc_fun(X2,X3),X1,X0)
      | ~ class_Orderings_Oord(X3) ),
    inference(cnf_transformation,[],[f3838]) ).

fof(f12378,plain,
    spl50_827,
    inference(avatar_split_clause,[],[f5446,f12376]) ).

fof(f12376,plain,
    ( spl50_827
  <=> ! [X0,X3,X2,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0)
        | ~ c_Orderings_Oord__class_Oless(tc_fun(X2,X3),X1,X0)
        | ~ class_Orderings_Oord(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_827])]) ).

fof(f5446,plain,
    ! [X2,X3,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0)
      | ~ c_Orderings_Oord__class_Oless(tc_fun(X2,X3),X1,X0)
      | ~ class_Orderings_Oord(X3) ),
    inference(cnf_transformation,[],[f3838]) ).

fof(f12374,plain,
    spl50_826,
    inference(avatar_split_clause,[],[f5433,f12372]) ).

fof(f12372,plain,
    ( spl50_826
  <=> ! [X0,X3,X2,X1] :
        ( c_Rings_Odvd__class_Odvd(X3,X2,X0)
        | ~ c_Rings_Odvd__class_Odvd(X3,X1,X0)
        | ~ c_Rings_Odvd__class_Odvd(X3,X2,X1)
        | ~ class_Rings_Ocomm__semiring__1(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_826])]) ).

fof(f5433,plain,
    ! [X2,X3,X0,X1] :
      ( c_Rings_Odvd__class_Odvd(X3,X2,X0)
      | ~ c_Rings_Odvd__class_Odvd(X3,X1,X0)
      | ~ c_Rings_Odvd__class_Odvd(X3,X2,X1)
      | ~ class_Rings_Ocomm__semiring__1(X3) ),
    inference(cnf_transformation,[],[f3285]) ).

fof(f3285,plain,
    ! [X0,X1,X2,X3] :
      ( c_Rings_Odvd__class_Odvd(X3,X2,X0)
      | ~ c_Rings_Odvd__class_Odvd(X3,X1,X0)
      | ~ c_Rings_Odvd__class_Odvd(X3,X2,X1)
      | ~ class_Rings_Ocomm__semiring__1(X3) ),
    inference(flattening,[],[f3284]) ).

fof(f3284,plain,
    ! [X0,X1,X2,X3] :
      ( c_Rings_Odvd__class_Odvd(X3,X2,X0)
      | ~ c_Rings_Odvd__class_Odvd(X3,X1,X0)
      | ~ c_Rings_Odvd__class_Odvd(X3,X2,X1)
      | ~ class_Rings_Ocomm__semiring__1(X3) ),
    inference(ennf_transformation,[],[f2197]) ).

fof(f2197,plain,
    ! [X0,X1,X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => ( c_Rings_Odvd__class_Odvd(X3,X2,X1)
       => ( c_Rings_Odvd__class_Odvd(X3,X1,X0)
         => c_Rings_Odvd__class_Odvd(X3,X2,X0) ) ) ),
    inference(rectify,[],[f815]) ).

fof(f815,axiom,
    ! [X23,X13,X4,X5] :
      ( class_Rings_Ocomm__semiring__1(X5)
     => ( c_Rings_Odvd__class_Odvd(X5,X4,X13)
       => ( c_Rings_Odvd__class_Odvd(X5,X13,X23)
         => c_Rings_Odvd__class_Odvd(X5,X4,X23) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__trans) ).

fof(f12370,plain,
    spl50_825,
    inference(avatar_split_clause,[],[f5392,f12368]) ).

fof(f12368,plain,
    ( spl50_825
  <=> ! [X0,X3,X2,X1] :
        ( X0 = X2
        | c_Polynomial_Omonom(X3,X2,X1) != c_Polynomial_Omonom(X3,X0,X1)
        | ~ class_Groups_Ozero(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_825])]) ).

fof(f5392,plain,
    ! [X2,X3,X0,X1] :
      ( X0 = X2
      | c_Polynomial_Omonom(X3,X2,X1) != c_Polynomial_Omonom(X3,X0,X1)
      | ~ class_Groups_Ozero(X3) ),
    inference(cnf_transformation,[],[f3832]) ).

fof(f3832,plain,
    ! [X0,X1,X2,X3] :
      ( ( ( c_Polynomial_Omonom(X3,X2,X1) = c_Polynomial_Omonom(X3,X0,X1)
          | X0 != X2 )
        & ( X0 = X2
          | c_Polynomial_Omonom(X3,X2,X1) != c_Polynomial_Omonom(X3,X0,X1) ) )
      | ~ class_Groups_Ozero(X3) ),
    inference(nnf_transformation,[],[f3238]) ).

fof(f3238,plain,
    ! [X0,X1,X2,X3] :
      ( ( c_Polynomial_Omonom(X3,X2,X1) = c_Polynomial_Omonom(X3,X0,X1)
      <=> X0 = X2 )
      | ~ class_Groups_Ozero(X3) ),
    inference(ennf_transformation,[],[f2157]) ).

fof(f2157,plain,
    ! [X0,X1,X2,X3] :
      ( class_Groups_Ozero(X3)
     => ( c_Polynomial_Omonom(X3,X2,X1) = c_Polynomial_Omonom(X3,X0,X1)
      <=> X0 = X2 ) ),
    inference(rectify,[],[f666]) ).

fof(f666,axiom,
    ! [X21,X16,X24,X5] :
      ( class_Groups_Ozero(X5)
     => ( c_Polynomial_Omonom(X5,X24,X16) = c_Polynomial_Omonom(X5,X21,X16)
      <=> X21 = X24 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_monom__eq__iff) ).

fof(f12366,plain,
    spl50_824,
    inference(avatar_split_clause,[],[f5384,f12364]) ).

fof(f12364,plain,
    ( spl50_824
  <=> ! [X0,X3,X2,X1] :
        ( X0 = X2
        | c_Groups_Oplus__class_Oplus(X3,X2,X1) != c_Groups_Oplus__class_Oplus(X3,X0,X1)
        | ~ class_Groups_Ocancel__semigroup__add(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_824])]) ).

fof(f5384,plain,
    ! [X2,X3,X0,X1] :
      ( X0 = X2
      | c_Groups_Oplus__class_Oplus(X3,X2,X1) != c_Groups_Oplus__class_Oplus(X3,X0,X1)
      | ~ class_Groups_Ocancel__semigroup__add(X3) ),
    inference(cnf_transformation,[],[f3232]) ).

fof(f3232,plain,
    ! [X0,X1,X2,X3] :
      ( X0 = X2
      | c_Groups_Oplus__class_Oplus(X3,X2,X1) != c_Groups_Oplus__class_Oplus(X3,X0,X1)
      | ~ class_Groups_Ocancel__semigroup__add(X3) ),
    inference(flattening,[],[f3231]) ).

fof(f3231,plain,
    ! [X0,X1,X2,X3] :
      ( X0 = X2
      | c_Groups_Oplus__class_Oplus(X3,X2,X1) != c_Groups_Oplus__class_Oplus(X3,X0,X1)
      | ~ class_Groups_Ocancel__semigroup__add(X3) ),
    inference(ennf_transformation,[],[f2151]) ).

fof(f2151,plain,
    ! [X0,X1,X2,X3] :
      ( class_Groups_Ocancel__semigroup__add(X3)
     => ( c_Groups_Oplus__class_Oplus(X3,X2,X1) = c_Groups_Oplus__class_Oplus(X3,X0,X1)
       => X0 = X2 ) ),
    inference(rectify,[],[f200]) ).

fof(f200,axiom,
    ! [X23,X4,X13,X5] :
      ( class_Groups_Ocancel__semigroup__add(X5)
     => ( c_Groups_Oplus__class_Oplus(X5,X13,X4) = c_Groups_Oplus__class_Oplus(X5,X23,X4)
       => X13 = X23 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__right__imp__eq) ).

fof(f12362,plain,
    spl50_823,
    inference(avatar_split_clause,[],[f5383,f12360]) ).

fof(f12360,plain,
    ( spl50_823
  <=> ! [X0,X3,X2,X1] :
        ( X0 = X1
        | c_Groups_Oplus__class_Oplus(X3,X2,X1) != c_Groups_Oplus__class_Oplus(X3,X2,X0)
        | ~ class_Groups_Ocancel__semigroup__add(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_823])]) ).

fof(f5383,plain,
    ! [X2,X3,X0,X1] :
      ( X0 = X1
      | c_Groups_Oplus__class_Oplus(X3,X2,X1) != c_Groups_Oplus__class_Oplus(X3,X2,X0)
      | ~ class_Groups_Ocancel__semigroup__add(X3) ),
    inference(cnf_transformation,[],[f3230]) ).

fof(f3230,plain,
    ! [X0,X1,X2,X3] :
      ( X0 = X1
      | c_Groups_Oplus__class_Oplus(X3,X2,X1) != c_Groups_Oplus__class_Oplus(X3,X2,X0)
      | ~ class_Groups_Ocancel__semigroup__add(X3) ),
    inference(flattening,[],[f3229]) ).

fof(f3229,plain,
    ! [X0,X1,X2,X3] :
      ( X0 = X1
      | c_Groups_Oplus__class_Oplus(X3,X2,X1) != c_Groups_Oplus__class_Oplus(X3,X2,X0)
      | ~ class_Groups_Ocancel__semigroup__add(X3) ),
    inference(ennf_transformation,[],[f2150]) ).

fof(f2150,plain,
    ! [X0,X1,X2,X3] :
      ( class_Groups_Ocancel__semigroup__add(X3)
     => ( c_Groups_Oplus__class_Oplus(X3,X2,X1) = c_Groups_Oplus__class_Oplus(X3,X2,X0)
       => X0 = X1 ) ),
    inference(rectify,[],[f198]) ).

fof(f198,axiom,
    ! [X23,X13,X4,X5] :
      ( class_Groups_Ocancel__semigroup__add(X5)
     => ( c_Groups_Oplus__class_Oplus(X5,X4,X13) = c_Groups_Oplus__class_Oplus(X5,X4,X23)
       => X13 = X23 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__imp__eq) ).

fof(f12358,plain,
    spl50_822,
    inference(avatar_split_clause,[],[f5380,f12356]) ).

fof(f12356,plain,
    ( spl50_822
  <=> ! [X0,X3,X2,X1] :
        ( X0 = X1
        | c_Groups_Oplus__class_Oplus(X3,X2,X1) != c_Groups_Oplus__class_Oplus(X3,X2,X0)
        | ~ class_Groups_Ocancel__ab__semigroup__add(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_822])]) ).

fof(f5380,plain,
    ! [X2,X3,X0,X1] :
      ( X0 = X1
      | c_Groups_Oplus__class_Oplus(X3,X2,X1) != c_Groups_Oplus__class_Oplus(X3,X2,X0)
      | ~ class_Groups_Ocancel__ab__semigroup__add(X3) ),
    inference(cnf_transformation,[],[f3225]) ).

fof(f3225,plain,
    ! [X0,X1,X2,X3] :
      ( X0 = X1
      | c_Groups_Oplus__class_Oplus(X3,X2,X1) != c_Groups_Oplus__class_Oplus(X3,X2,X0)
      | ~ class_Groups_Ocancel__ab__semigroup__add(X3) ),
    inference(flattening,[],[f3224]) ).

fof(f3224,plain,
    ! [X0,X1,X2,X3] :
      ( X0 = X1
      | c_Groups_Oplus__class_Oplus(X3,X2,X1) != c_Groups_Oplus__class_Oplus(X3,X2,X0)
      | ~ class_Groups_Ocancel__ab__semigroup__add(X3) ),
    inference(ennf_transformation,[],[f2147]) ).

fof(f2147,plain,
    ! [X0,X1,X2,X3] :
      ( class_Groups_Ocancel__ab__semigroup__add(X3)
     => ( c_Groups_Oplus__class_Oplus(X3,X2,X1) = c_Groups_Oplus__class_Oplus(X3,X2,X0)
       => X0 = X1 ) ),
    inference(rectify,[],[f199]) ).

fof(f199,axiom,
    ! [X23,X13,X4,X5] :
      ( class_Groups_Ocancel__ab__semigroup__add(X5)
     => ( c_Groups_Oplus__class_Oplus(X5,X4,X13) = c_Groups_Oplus__class_Oplus(X5,X4,X23)
       => X13 = X23 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__imp__eq) ).

fof(f12354,plain,
    spl50_821,
    inference(avatar_split_clause,[],[f5312,f12352]) ).

fof(f12352,plain,
    ( spl50_821
  <=> ! [X0,X3,X2,X1] :
        ( 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)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_821])]) ).

fof(f5312,plain,
    ! [X2,X3,X0,X1] :
      ( 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)) ),
    inference(cnf_transformation,[],[f3818]) ).

fof(f12346,plain,
    spl50_820,
    inference(avatar_split_clause,[],[f5311,f12344]) ).

fof(f12344,plain,
    ( spl50_820
  <=> ! [X0,X3,X2,X1] :
        ( sP13(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,[spl50_820])]) ).

fof(f5311,plain,
    ! [X2,X3,X0,X1] :
      ( sP13(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,[],[f3818]) ).

fof(f12342,plain,
    spl50_819,
    inference(avatar_split_clause,[],[f5309,f12340]) ).

fof(f12340,plain,
    ( spl50_819
  <=> ! [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,[spl50_819])]) ).

fof(f5309,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,[],[f3818]) ).

fof(f12338,plain,
    spl50_818,
    inference(avatar_split_clause,[],[f5308,f12336]) ).

fof(f12336,plain,
    ( spl50_818
  <=> ! [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,[spl50_818])]) ).

fof(f5308,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,[],[f3818]) ).

fof(f12334,plain,
    spl50_817,
    inference(avatar_split_clause,[],[f5303,f12332]) ).

fof(f12332,plain,
    ( spl50_817
  <=> ! [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,[spl50_817])]) ).

fof(f5303,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,[],[f3813]) ).

fof(f12330,plain,
    spl50_816,
    inference(avatar_split_clause,[],[f5302,f12328]) ).

fof(f12328,plain,
    ( spl50_816
  <=> ! [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,[spl50_816])]) ).

fof(f5302,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,[],[f3813]) ).

fof(f12326,plain,
    spl50_815,
    inference(avatar_split_clause,[],[f5300,f12324]) ).

fof(f12324,plain,
    ( spl50_815
  <=> ! [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,[spl50_815])]) ).

fof(f5300,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,[],[f3813]) ).

fof(f12322,plain,
    spl50_814,
    inference(avatar_split_clause,[],[f5299,f12320]) ).

fof(f12320,plain,
    ( spl50_814
  <=> ! [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,[spl50_814])]) ).

fof(f5299,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,[],[f3813]) ).

fof(f12318,plain,
    spl50_813,
    inference(avatar_split_clause,[],[f5272,f12316]) ).

fof(f12316,plain,
    ( spl50_813
  <=> ! [X0,X3,X2,X1] :
        ( sP9(X0,X1,X2,X3)
        | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2),X1,X0)
        | c_Groups_Ozero__class_Ozero(X2) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_813])]) ).

fof(f5272,plain,
    ! [X2,X3,X0,X1] :
      ( sP9(X0,X1,X2,X3)
      | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2),X1,X0)
      | c_Groups_Ozero__class_Ozero(X2) = X3 ),
    inference(cnf_transformation,[],[f3804]) ).

fof(f12314,plain,
    spl50_812,
    inference(avatar_split_clause,[],[f5269,f12312]) ).

fof(f12312,plain,
    ( spl50_812
  <=> ! [X0,X3,X2,X1] :
        ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2),X1,X0)
        | c_Groups_Ozero__class_Ozero(X2) = X3
        | ~ sP9(X0,X1,X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_812])]) ).

fof(f5269,plain,
    ! [X2,X3,X0,X1] :
      ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2),X1,X0)
      | c_Groups_Ozero__class_Ozero(X2) = X3
      | ~ sP9(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f3804]) ).

fof(f12310,plain,
    spl50_811,
    inference(avatar_split_clause,[],[f5227,f12308]) ).

fof(f12308,plain,
    ( spl50_811
  <=> ! [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,[spl50_811])]) ).

fof(f5227,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,[],[f3778]) ).

fof(f3778,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,[],[f2054]) ).

fof(f2054,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,[],[f396]) ).

fof(f396,axiom,
    ! [X16,X32,X36] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X36,X32),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X36,X16))
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X32,X16) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel__less) ).

fof(f12306,plain,
    ( spl50_810
    | ~ spl50_190
    | ~ spl50_411 ),
    inference(avatar_split_clause,[],[f8185,f7986,f6996,f12304]) ).

fof(f12304,plain,
    ( spl50_810
  <=> ! [X0] : c_Polynomial_Osmult(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_810])]) ).

fof(f6996,plain,
    ( spl50_190
  <=> class_Rings_Ocomm__semiring__1(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_190])]) ).

fof(f7986,plain,
    ( spl50_411
  <=> ! [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,[spl50_411])]) ).

fof(f8185,plain,
    ( ! [X0] : c_Polynomial_Osmult(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0) = X0
    | ~ spl50_190
    | ~ spl50_411 ),
    inference(resolution,[],[f7987,f6998]) ).

fof(f6998,plain,
    ( class_Rings_Ocomm__semiring__1(tc_Int_Oint)
    | ~ spl50_190 ),
    inference(avatar_component_clause,[],[f6996]) ).

fof(f7987,plain,
    ( ! [X0,X1] :
        ( ~ class_Rings_Ocomm__semiring__1(X1)
        | c_Polynomial_Osmult(X1,c_Groups_Oone__class_Oone(X1),X0) = X0 )
    | ~ spl50_411 ),
    inference(avatar_component_clause,[],[f7986]) ).

fof(f12302,plain,
    spl50_809,
    inference(avatar_split_clause,[],[f5226,f12300]) ).

fof(f12300,plain,
    ( spl50_809
  <=> ! [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,[spl50_809])]) ).

fof(f5226,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,[],[f3778]) ).

fof(f12298,plain,
    spl50_808,
    inference(avatar_split_clause,[],[f5225,f12296]) ).

fof(f12296,plain,
    ( spl50_808
  <=> ! [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,[spl50_808])]) ).

fof(f5225,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,[],[f3777]) ).

fof(f3777,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,[],[f2053]) ).

fof(f2053,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,[],[f411]) ).

fof(f411,axiom,
    ! [X16,X32,X36] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X36,X32),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X36,X16))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X32,X16) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel__le) ).

fof(f12294,plain,
    spl50_807,
    inference(avatar_split_clause,[],[f5224,f12292]) ).

fof(f12292,plain,
    ( spl50_807
  <=> ! [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,[spl50_807])]) ).

fof(f5224,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,[],[f3777]) ).

fof(f12290,plain,
    spl50_806,
    inference(avatar_split_clause,[],[f5219,f12288]) ).

fof(f12288,plain,
    ( spl50_806
  <=> ! [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,[spl50_806])]) ).

fof(f5219,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,[],[f3774]) ).

fof(f3774,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,[],[f2050]) ).

fof(f2050,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,[],[f477]) ).

fof(f477,axiom,
    ! [X36,X55,X56] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X56,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X55,X36))
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X56,X36),X55) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__diff__conv) ).

fof(f12286,plain,
    spl50_805,
    inference(avatar_split_clause,[],[f5218,f12284]) ).

fof(f12284,plain,
    ( spl50_805
  <=> ! [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,[spl50_805])]) ).

fof(f5218,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,[],[f3774]) ).

fof(f12282,plain,
    spl50_804,
    inference(avatar_split_clause,[],[f5217,f12280]) ).

fof(f12280,plain,
    ( spl50_804
  <=> ! [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,[spl50_804])]) ).

fof(f5217,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,[],[f3773]) ).

fof(f3773,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,[],[f2049]) ).

fof(f2049,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,[],[f483]) ).

fof(f483,axiom,
    ! [X56,X36,X55] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X55,X36),X56)
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X55,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X56,X36)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__diff__conv) ).

fof(f12278,plain,
    spl50_803,
    inference(avatar_split_clause,[],[f5216,f12276]) ).

fof(f12276,plain,
    ( spl50_803
  <=> ! [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,[spl50_803])]) ).

fof(f5216,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,[],[f3773]) ).

fof(f12274,plain,
    spl50_802,
    inference(avatar_split_clause,[],[f5178,f12272]) ).

fof(f12272,plain,
    ( spl50_802
  <=> ! [X2,X0,X1] :
        ( X0 = X1
        | c_Polynomial_Opoly(X2,X0) != c_Polynomial_Opoly(X2,X1)
        | ~ class_Rings_Oidom(X2)
        | ~ class_Int_Oring__char__0(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_802])]) ).

fof(f5178,plain,
    ! [X2,X0,X1] :
      ( X0 = X1
      | c_Polynomial_Opoly(X2,X0) != c_Polynomial_Opoly(X2,X1)
      | ~ class_Rings_Oidom(X2)
      | ~ class_Int_Oring__char__0(X2) ),
    inference(cnf_transformation,[],[f3747]) ).

fof(f3747,plain,
    ! [X0,X1,X2] :
      ( ( ( c_Polynomial_Opoly(X2,X0) = c_Polynomial_Opoly(X2,X1)
          | X0 != X1 )
        & ( X0 = X1
          | c_Polynomial_Opoly(X2,X0) != c_Polynomial_Opoly(X2,X1) ) )
      | ~ class_Rings_Oidom(X2)
      | ~ class_Int_Oring__char__0(X2) ),
    inference(nnf_transformation,[],[f3076]) ).

fof(f3076,plain,
    ! [X0,X1,X2] :
      ( ( c_Polynomial_Opoly(X2,X0) = c_Polynomial_Opoly(X2,X1)
      <=> X0 = X1 )
      | ~ class_Rings_Oidom(X2)
      | ~ class_Int_Oring__char__0(X2) ),
    inference(flattening,[],[f3075]) ).

fof(f3075,plain,
    ! [X0,X1,X2] :
      ( ( c_Polynomial_Opoly(X2,X0) = c_Polynomial_Opoly(X2,X1)
      <=> X0 = X1 )
      | ~ class_Rings_Oidom(X2)
      | ~ class_Int_Oring__char__0(X2) ),
    inference(ennf_transformation,[],[f2039]) ).

fof(f2039,plain,
    ! [X0,X1,X2] :
      ( ( class_Rings_Oidom(X2)
        & class_Int_Oring__char__0(X2) )
     => ( c_Polynomial_Opoly(X2,X0) = c_Polynomial_Opoly(X2,X1)
      <=> X0 = X1 ) ),
    inference(rectify,[],[f639]) ).

fof(f639,axiom,
    ! [X66,X64,X5] :
      ( ( class_Rings_Oidom(X5)
        & class_Int_Oring__char__0(X5) )
     => ( c_Polynomial_Opoly(X5,X64) = c_Polynomial_Opoly(X5,X66)
      <=> X64 = X66 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__eq__iff) ).

fof(f12270,plain,
    spl50_801,
    inference(avatar_split_clause,[],[f5139,f12268]) ).

fof(f12268,plain,
    ( spl50_801
  <=> ! [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,[spl50_801])]) ).

fof(f5139,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,[],[f3027]) ).

fof(f3027,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,[],[f2009]) ).

fof(f2009,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,[],[f393]) ).

fof(f393,axiom,
    ! [X38,X39,X18] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X39)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X38),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X39,X38)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__mono1) ).

fof(f12266,plain,
    spl50_800,
    inference(avatar_split_clause,[],[f5132,f12264]) ).

fof(f12264,plain,
    ( spl50_800
  <=> ! [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,[spl50_800])]) ).

fof(f5132,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,[],[f3019]) ).

fof(f3019,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,[],[f2002]) ).

fof(f2002,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,[],[f612]) ).

fof(f612,axiom,
    ! [X38,X39,X18] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X18,X39)
     => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X18,X38),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X39,X38)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__strict__right__mono) ).

fof(f12262,plain,
    ( spl50_799
    | ~ spl50_191
    | ~ spl50_411 ),
    inference(avatar_split_clause,[],[f8183,f7986,f7001,f12260]) ).

fof(f12260,plain,
    ( spl50_799
  <=> ! [X0] : c_Polynomial_Osmult(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_799])]) ).

fof(f7001,plain,
    ( spl50_191
  <=> class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_191])]) ).

fof(f8183,plain,
    ( ! [X0] : c_Polynomial_Osmult(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) = X0
    | ~ spl50_191
    | ~ spl50_411 ),
    inference(resolution,[],[f7987,f7003]) ).

fof(f7003,plain,
    ( class_Rings_Ocomm__semiring__1(tc_Nat_Onat)
    | ~ spl50_191 ),
    inference(avatar_component_clause,[],[f7001]) ).

fof(f12258,plain,
    spl50_798,
    inference(avatar_split_clause,[],[f5112,f12256]) ).

fof(f12256,plain,
    ( spl50_798
  <=> ! [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,[spl50_798])]) ).

fof(f5112,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,[],[f2999]) ).

fof(f2999,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,[],[f1987]) ).

fof(f1987,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,[],[f408]) ).

fof(f408,axiom,
    ! [X38,X39,X18] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X39)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X38),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X39,X38)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__mono1) ).

fof(f12254,plain,
    spl50_797,
    inference(avatar_split_clause,[],[f5111,f12252]) ).

fof(f12252,plain,
    ( spl50_797
  <=> ! [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,[spl50_797])]) ).

fof(f5111,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,[],[f2998]) ).

fof(f2998,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,[],[f1986]) ).

fof(f1986,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,[],[f463]) ).

fof(f463,axiom,
    ! [X51,X3,X17] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X3)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X51),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X51)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__le__mono) ).

fof(f12250,plain,
    spl50_796,
    inference(avatar_split_clause,[],[f5110,f12248]) ).

fof(f12248,plain,
    ( spl50_796
  <=> ! [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,[spl50_796])]) ).

fof(f5110,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,[],[f2997]) ).

fof(f2997,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,[],[f1985]) ).

fof(f1985,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,[],[f464]) ).

fof(f464,axiom,
    ! [X51,X3,X17] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X3)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X51,X3),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X51,X17)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__le__mono2) ).

fof(f12246,plain,
    spl50_795,
    inference(avatar_split_clause,[],[f5109,f12244]) ).

fof(f12244,plain,
    ( spl50_795
  <=> ! [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,[spl50_795])]) ).

fof(f5109,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,[],[f2996]) ).

fof(f2996,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,[],[f1984]) ).

fof(f1984,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,[],[f484]) ).

fof(f484,axiom,
    ! [X17,X3,X38] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X38,X3)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X17),X38)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add__diff) ).

fof(f12242,plain,
    spl50_794,
    inference(avatar_split_clause,[],[f5103,f12240]) ).

fof(f12240,plain,
    ( spl50_794
  <=> ! [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,[spl50_794])]) ).

fof(f5103,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,[],[f2989]) ).

fof(f2989,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,[],[f1978]) ).

fof(f1978,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,[],[f611]) ).

fof(f611,axiom,
    ! [X38,X39,X18] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X18,X39)
     => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X38,X18),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X38,X39)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__left__mono) ).

fof(f12238,plain,
    spl50_793,
    inference(avatar_split_clause,[],[f5101,f12236]) ).

fof(f12236,plain,
    ( spl50_793
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_793])]) ).

fof(f5101,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1) ),
    inference(cnf_transformation,[],[f2986]) ).

fof(f2986,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1) ),
    inference(ennf_transformation,[],[f1976]) ).

fof(f1976,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1)
     => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1)) ),
    inference(rectify,[],[f204]) ).

fof(f204,axiom,
    ! [X14,X7,X9] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X9,X7)
     => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X14,X9),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X14,X7)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__add__left__mono) ).

fof(f12234,plain,
    spl50_792,
    inference(avatar_split_clause,[],[f5064,f12232]) ).

fof(f12232,plain,
    ( spl50_792
  <=> ! [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,[spl50_792])]) ).

fof(f5064,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,[],[f3722]) ).

fof(f3722,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,[],[f3721]) ).

fof(f3721,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,[],[f2943]) ).

fof(f2943,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,[],[f1951]) ).

fof(f1951,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,[],[f765]) ).

fof(f765,axiom,
    ! [X20,X12,X5] :
      ( class_Orderings_Opreorder(X5)
     => ( c_Orderings_Oord__class_Oless(X5,X12,X20)
      <=> ( ~ c_Orderings_Oord__class_Oless__eq(X5,X20,X12)
          & c_Orderings_Oord__class_Oless__eq(X5,X12,X20) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__le__not__le) ).

fof(f12230,plain,
    spl50_791,
    inference(avatar_split_clause,[],[f5041,f12228]) ).

fof(f12228,plain,
    ( spl50_791
  <=> ! [X2,X0,X1] :
        ( c_Groups_Ozero__class_Ozero(X2) = X1
        | c_Polynomial_OpCons(X2,X1,X0) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
        | ~ class_Groups_Ozero(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_791])]) ).

fof(f5041,plain,
    ! [X2,X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X2) = X1
      | c_Polynomial_OpCons(X2,X1,X0) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
      | ~ class_Groups_Ozero(X2) ),
    inference(cnf_transformation,[],[f3720]) ).

fof(f12226,plain,
    spl50_790,
    inference(avatar_split_clause,[],[f5039,f12224]) ).

fof(f12224,plain,
    ( spl50_790
  <=> ! [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,[spl50_790])]) ).

fof(f5039,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,[],[f3718]) ).

fof(f3718,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,[],[f2917]) ).

fof(f2917,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,[],[f1932]) ).

fof(f1932,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,[],[f675]) ).

fof(f675,axiom,
    ! [X16,X24,X5] :
      ( class_Groups_Ozero(X5)
     => ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = c_Polynomial_Omonom(X5,X24,X16)
      <=> c_Groups_Ozero__class_Ozero(X5) = X24 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_monom__eq__0__iff) ).

fof(f12222,plain,
    spl50_789,
    inference(avatar_split_clause,[],[f5013,f12220]) ).

fof(f12220,plain,
    ( spl50_789
  <=> ! [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,[spl50_789])]) ).

fof(f5013,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,[],[f3713]) ).

fof(f3713,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,[],[f2884]) ).

fof(f2884,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,[],[f1911]) ).

fof(f1911,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,[],[f337]) ).

fof(f337,axiom,
    ! [X21,X24,X5] :
      ( class_Groups_Ogroup__add(X5)
     => ( c_Groups_Ouminus__class_Ouminus(X5,X21) = X24
      <=> c_Groups_Ozero__class_Ozero(X5) = c_Groups_Oplus__class_Oplus(X5,X24,X21) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__neg__iff__add__eq__0) ).

fof(f12218,plain,
    ( spl50_788
    | ~ spl50_188
    | ~ spl50_411 ),
    inference(avatar_split_clause,[],[f8182,f7986,f6986,f12216]) ).

fof(f12216,plain,
    ( spl50_788
  <=> ! [X0] : c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_788])]) ).

fof(f8182,plain,
    ( ! [X0] : c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),X0) = X0
    | ~ spl50_188
    | ~ spl50_411 ),
    inference(resolution,[],[f7987,f6988]) ).

fof(f12214,plain,
    spl50_787,
    inference(avatar_split_clause,[],[f5007,f12212]) ).

fof(f12212,plain,
    ( spl50_787
  <=> ! [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,[spl50_787])]) ).

fof(f5007,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,[],[f2881]) ).

fof(f2881,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,[],[f2880]) ).

fof(f2880,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,[],[f1908]) ).

fof(f1908,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,[],[f333]) ).

fof(f333,axiom,
    ! [X13,X4,X5] :
      ( class_Groups_Ogroup__add(X5)
     => ( c_Groups_Ozero__class_Ozero(X5) = c_Groups_Oplus__class_Oplus(X5,X4,X13)
       => c_Groups_Ouminus__class_Ouminus(X5,X4) = X13 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__unique) ).

fof(f12210,plain,
    spl50_786,
    inference(avatar_split_clause,[],[f4900,f12208]) ).

fof(f12208,plain,
    ( spl50_786
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X2),X1,X0)
        | ~ c_Polynomial_Opos__poly(X2,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X2),X0,X1))
        | ~ class_Rings_Olinordered__idom(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_786])]) ).

fof(f4900,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X2),X1,X0)
      | ~ c_Polynomial_Opos__poly(X2,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X2),X0,X1))
      | ~ class_Rings_Olinordered__idom(X2) ),
    inference(cnf_transformation,[],[f3682]) ).

fof(f3682,plain,
    ! [X0,X1,X2] :
      ( ( ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X2),X1,X0)
          | ~ c_Polynomial_Opos__poly(X2,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X2),X0,X1)) )
        & ( c_Polynomial_Opos__poly(X2,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X2),X0,X1))
          | ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X2),X1,X0) ) )
      | ~ class_Rings_Olinordered__idom(X2) ),
    inference(nnf_transformation,[],[f2769]) ).

fof(f2769,plain,
    ! [X0,X1,X2] :
      ( ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X2),X1,X0)
      <=> c_Polynomial_Opos__poly(X2,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X2),X0,X1)) )
      | ~ class_Rings_Olinordered__idom(X2) ),
    inference(ennf_transformation,[],[f1832]) ).

fof(f1832,plain,
    ! [X0,X1,X2] :
      ( class_Rings_Olinordered__idom(X2)
     => ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X2),X1,X0)
      <=> c_Polynomial_Opos__poly(X2,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X2),X0,X1)) ) ),
    inference(rectify,[],[f790]) ).

fof(f790,axiom,
    ! [X20,X12,X5] :
      ( class_Rings_Olinordered__idom(X5)
     => ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X5),X12,X20)
      <=> c_Polynomial_Opos__poly(X5,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X5),X20,X12)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__poly__def) ).

fof(f12206,plain,
    spl50_785,
    inference(avatar_split_clause,[],[f4899,f12204]) ).

fof(f12204,plain,
    ( spl50_785
  <=> ! [X2,X0,X1] :
        ( c_Polynomial_Opos__poly(X2,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X2),X0,X1))
        | ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X2),X1,X0)
        | ~ class_Rings_Olinordered__idom(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_785])]) ).

fof(f4899,plain,
    ! [X2,X0,X1] :
      ( c_Polynomial_Opos__poly(X2,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X2),X0,X1))
      | ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X2),X1,X0)
      | ~ class_Rings_Olinordered__idom(X2) ),
    inference(cnf_transformation,[],[f3682]) ).

fof(f12202,plain,
    spl50_784,
    inference(avatar_split_clause,[],[f4898,f12200]) ).

fof(f12200,plain,
    ( spl50_784
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X2),X1,X0)
        | ~ c_Polynomial_Opos__poly(X2,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X2),X0,X1))
        | ~ class_Rings_Olinordered__idom(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_784])]) ).

fof(f4898,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X2),X1,X0)
      | ~ c_Polynomial_Opos__poly(X2,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X2),X0,X1))
      | ~ class_Rings_Olinordered__idom(X2) ),
    inference(cnf_transformation,[],[f3681]) ).

fof(f12198,plain,
    spl50_783,
    inference(avatar_split_clause,[],[f4889,f12196]) ).

fof(f12196,plain,
    ( spl50_783
  <=> ! [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,[spl50_783])]) ).

fof(f4889,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,[],[f3679]) ).

fof(f3679,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,[],[f2756]) ).

fof(f2756,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,[],[f1824]) ).

fof(f1824,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,[],[f298]) ).

fof(f298,axiom,
    ! [X24,X21,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ouminus__class_Ouminus(X5,X21),c_Groups_Ouminus__class_Ouminus(X5,X24))
      <=> c_Orderings_Oord__class_Oless(X5,X24,X21) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__less__iff__less) ).

fof(f12194,plain,
    spl50_782,
    inference(avatar_split_clause,[],[f4888,f12192]) ).

fof(f12192,plain,
    ( spl50_782
  <=> ! [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,[spl50_782])]) ).

fof(f4888,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,[],[f3679]) ).

fof(f12190,plain,
    spl50_781,
    inference(avatar_split_clause,[],[f4886,f12188]) ).

fof(f12188,plain,
    ( spl50_781
  <=> ! [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,[spl50_781])]) ).

fof(f4886,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,[],[f3678]) ).

fof(f3678,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,[],[f2755]) ).

fof(f2755,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,[],[f1823]) ).

fof(f1823,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,[],[f296]) ).

fof(f296,axiom,
    ! [X24,X21,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ouminus__class_Ouminus(X5,X21),c_Groups_Ouminus__class_Ouminus(X5,X24))
      <=> c_Orderings_Oord__class_Oless__eq(X5,X24,X21) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__le__iff__le) ).

fof(f12186,plain,
    spl50_780,
    inference(avatar_split_clause,[],[f4885,f12184]) ).

fof(f12184,plain,
    ( spl50_780
  <=> ! [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,[spl50_780])]) ).

fof(f4885,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,[],[f3677]) ).

fof(f3677,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,[],[f2754]) ).

fof(f2754,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,[],[f1822]) ).

fof(f1822,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,[],[f299]) ).

fof(f299,axiom,
    ! [X21,X24,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ouminus__class_Ouminus(X5,X24),X21)
      <=> c_Orderings_Oord__class_Oless(X5,c_Groups_Ouminus__class_Ouminus(X5,X21),X24) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__less__iff) ).

fof(f12182,plain,
    spl50_779,
    inference(avatar_split_clause,[],[f4883,f12180]) ).

fof(f12180,plain,
    ( spl50_779
  <=> ! [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,[spl50_779])]) ).

fof(f4883,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,[],[f3676]) ).

fof(f3676,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,[],[f2753]) ).

fof(f2753,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,[],[f1821]) ).

fof(f1821,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,[],[f300]) ).

fof(f300,axiom,
    ! [X21,X24,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => ( c_Orderings_Oord__class_Oless(X5,X24,c_Groups_Ouminus__class_Ouminus(X5,X21))
      <=> c_Orderings_Oord__class_Oless(X5,X21,c_Groups_Ouminus__class_Ouminus(X5,X24)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__minus__iff) ).

fof(f12178,plain,
    spl50_778,
    inference(avatar_split_clause,[],[f4881,f12176]) ).

fof(f12176,plain,
    ( spl50_778
  <=> ! [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,[spl50_778])]) ).

fof(f4881,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,[],[f3675]) ).

fof(f3675,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,[],[f2752]) ).

fof(f2752,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,[],[f1820]) ).

fof(f1820,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,[],[f295]) ).

fof(f295,axiom,
    ! [X21,X24,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ouminus__class_Ouminus(X5,X24),X21)
      <=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ouminus__class_Ouminus(X5,X21),X24) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__le__iff) ).

fof(f12174,plain,
    ( spl50_777
    | ~ spl50_189
    | ~ spl50_411 ),
    inference(avatar_split_clause,[],[f8181,f7986,f6991,f12172]) ).

fof(f12172,plain,
    ( spl50_777
  <=> ! [X0] : c_Polynomial_Osmult(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_777])]) ).

fof(f8181,plain,
    ( ! [X0] : c_Polynomial_Osmult(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X0) = X0
    | ~ spl50_189
    | ~ spl50_411 ),
    inference(resolution,[],[f7987,f6993]) ).

fof(f12170,plain,
    spl50_776,
    inference(avatar_split_clause,[],[f4879,f12168]) ).

fof(f12168,plain,
    ( spl50_776
  <=> ! [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,[spl50_776])]) ).

fof(f4879,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,[],[f3674]) ).

fof(f3674,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,[],[f2751]) ).

fof(f2751,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,[],[f1819]) ).

fof(f1819,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,[],[f294]) ).

fof(f294,axiom,
    ! [X21,X24,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => ( c_Orderings_Oord__class_Oless__eq(X5,X24,c_Groups_Ouminus__class_Ouminus(X5,X21))
      <=> c_Orderings_Oord__class_Oless__eq(X5,X21,c_Groups_Ouminus__class_Ouminus(X5,X24)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__minus__iff) ).

fof(f12166,plain,
    spl50_775,
    inference(avatar_split_clause,[],[f4877,f12164]) ).

fof(f12164,plain,
    ( spl50_775
  <=> ! [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,[spl50_775])]) ).

fof(f4877,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,[],[f3673]) ).

fof(f3673,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,[],[f2750]) ).

fof(f2750,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,[],[f1818]) ).

fof(f1818,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,[],[f324]) ).

fof(f324,axiom,
    ! [X21,X24,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => ( c_Orderings_Oord__class_Oless(X5,X24,X21)
      <=> c_Orderings_Oord__class_Oless(X5,c_Groups_Ominus__class_Ominus(X5,X24,X21),c_Groups_Ozero__class_Ozero(X5)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__iff__diff__less__0) ).

fof(f12162,plain,
    spl50_774,
    inference(avatar_split_clause,[],[f4876,f12160]) ).

fof(f4876,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,[],[f3673]) ).

fof(f12158,plain,
    spl50_773,
    inference(avatar_split_clause,[],[f4875,f12156]) ).

fof(f12156,plain,
    ( spl50_773
  <=> ! [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,[spl50_773])]) ).

fof(f4875,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,[],[f3672]) ).

fof(f3672,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,[],[f2749]) ).

fof(f2749,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,[],[f1817]) ).

fof(f1817,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,[],[f323]) ).

fof(f323,axiom,
    ! [X21,X24,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => ( c_Orderings_Oord__class_Oless__eq(X5,X24,X21)
      <=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ominus__class_Ominus(X5,X24,X21),c_Groups_Ozero__class_Ozero(X5)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__iff__diff__le__0) ).

fof(f12154,plain,
    spl50_772,
    inference(avatar_split_clause,[],[f4874,f12152]) ).

fof(f12152,plain,
    ( spl50_772
  <=> ! [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,[spl50_772])]) ).

fof(f4874,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,[],[f3672]) ).

fof(f12150,plain,
    spl50_771,
    inference(avatar_split_clause,[],[f4873,f12148]) ).

fof(f12148,plain,
    ( spl50_771
  <=> ! [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,[spl50_771])]) ).

fof(f4873,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,[],[f2748]) ).

fof(f2748,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,[],[f2747]) ).

fof(f2747,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,[],[f1816]) ).

fof(f1816,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,[],[f297]) ).

fof(f297,axiom,
    ! [X13,X4,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => ( c_Orderings_Oord__class_Oless__eq(X5,X4,X13)
       => c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ouminus__class_Ouminus(X5,X13),c_Groups_Ouminus__class_Ouminus(X5,X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__neg__le) ).

fof(f12146,plain,
    spl50_770,
    inference(avatar_split_clause,[],[f4862,f12144]) ).

fof(f12144,plain,
    ( spl50_770
  <=> ! [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,[spl50_770])]) ).

fof(f4862,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,[],[f3665]) ).

fof(f3665,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,[],[f3664]) ).

fof(f3664,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,[],[f3663]) ).

fof(f3663,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,[],[f3446]) ).

fof(f3446,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(f12142,plain,
    spl50_769,
    inference(avatar_split_clause,[],[f4861,f12140]) ).

fof(f12140,plain,
    ( spl50_769
  <=> ! [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,[spl50_769])]) ).

fof(f4861,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,[],[f3665]) ).

fof(f12138,plain,
    spl50_768,
    inference(avatar_split_clause,[],[f4860,f12136]) ).

fof(f12136,plain,
    ( spl50_768
  <=> ! [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,[spl50_768])]) ).

fof(f4860,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,[],[f3665]) ).

fof(f12134,plain,
    spl50_767,
    inference(avatar_split_clause,[],[f4859,f12132]) ).

fof(f12132,plain,
    ( spl50_767
  <=> ! [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,[spl50_767])]) ).

fof(f4859,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,[],[f3665]) ).

fof(f12130,plain,
    ( spl50_766
    | ~ spl50_128
    | ~ spl50_408 ),
    inference(avatar_split_clause,[],[f8167,f7974,f6686,f12128]) ).

fof(f12128,plain,
    ( spl50_766
  <=> ! [X0] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_766])]) ).

fof(f6686,plain,
    ( spl50_128
  <=> class_Groups_Omonoid__add(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_128])]) ).

fof(f7974,plain,
    ( spl50_408
  <=> ! [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,[spl50_408])]) ).

fof(f8167,plain,
    ( ! [X0] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X0) = X0
    | ~ spl50_128
    | ~ spl50_408 ),
    inference(resolution,[],[f7975,f6688]) ).

fof(f6688,plain,
    ( class_Groups_Omonoid__add(tc_Complex_Ocomplex)
    | ~ spl50_128 ),
    inference(avatar_component_clause,[],[f6686]) ).

fof(f7975,plain,
    ( ! [X0,X1] :
        ( ~ class_Groups_Omonoid__add(X1)
        | c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X0) = X0 )
    | ~ spl50_408 ),
    inference(avatar_component_clause,[],[f7974]) ).

fof(f12126,plain,
    spl50_765,
    inference(avatar_split_clause,[],[f4858,f12124]) ).

fof(f12124,plain,
    ( spl50_765
  <=> ! [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,[spl50_765])]) ).

fof(f4858,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,[],[f3665]) ).

fof(f12122,plain,
    spl50_764,
    inference(avatar_split_clause,[],[f4857,f12120]) ).

fof(f12120,plain,
    ( spl50_764
  <=> ! [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,[spl50_764])]) ).

fof(f4857,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,[],[f3665]) ).

fof(f12118,plain,
    spl50_763,
    inference(avatar_split_clause,[],[f4853,f12116]) ).

fof(f4853,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,[],[f3660]) ).

fof(f3660,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,[],[f3659]) ).

fof(f3659,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,[],[f3658]) ).

fof(f3658,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,[],[f3443]) ).

fof(f3443,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(f12114,plain,
    spl50_762,
    inference(avatar_split_clause,[],[f4852,f12112]) ).

fof(f12112,plain,
    ( spl50_762
  <=> ! [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,[spl50_762])]) ).

fof(f4852,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,[],[f3660]) ).

fof(f12110,plain,
    spl50_761,
    inference(avatar_split_clause,[],[f4851,f12108]) ).

fof(f12108,plain,
    ( spl50_761
  <=> ! [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,[spl50_761])]) ).

fof(f4851,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,[],[f3660]) ).

fof(f12106,plain,
    spl50_760,
    inference(avatar_split_clause,[],[f4850,f12104]) ).

fof(f12104,plain,
    ( spl50_760
  <=> ! [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,[spl50_760])]) ).

fof(f4850,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,[],[f3660]) ).

fof(f12102,plain,
    spl50_759,
    inference(avatar_split_clause,[],[f4849,f12100]) ).

fof(f12100,plain,
    ( spl50_759
  <=> ! [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,[spl50_759])]) ).

fof(f4849,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,[],[f3660]) ).

fof(f12098,plain,
    spl50_758,
    inference(avatar_split_clause,[],[f4848,f12096]) ).

fof(f12096,plain,
    ( spl50_758
  <=> ! [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,[spl50_758])]) ).

fof(f4848,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,[],[f3660]) ).

fof(f12094,plain,
    spl50_757,
    inference(avatar_split_clause,[],[f4812,f12092]) ).

fof(f12092,plain,
    ( spl50_757
  <=> ! [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,[spl50_757])]) ).

fof(f4812,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,[],[f3654]) ).

fof(f3654,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,[],[f2698]) ).

fof(f2698,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,[],[f1780]) ).

fof(f1780,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,[],[f794]) ).

fof(f794,axiom,
    ! [X20,X12,X5] :
      ( class_Lattices_Oboolean__algebra(X5)
     => ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ouminus__class_Ouminus(X5,X12),c_Groups_Ouminus__class_Ouminus(X5,X20))
      <=> c_Orderings_Oord__class_Oless__eq(X5,X20,X12) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compl__le__compl__iff) ).

fof(f12090,plain,
    spl50_756,
    inference(avatar_split_clause,[],[f4809,f12088]) ).

fof(f12088,plain,
    ( spl50_756
  <=> ! [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,[spl50_756])]) ).

fof(f4809,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,[],[f2696]) ).

fof(f2696,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,[],[f2695]) ).

fof(f2695,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,[],[f1778]) ).

fof(f1778,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,[],[f795]) ).

fof(f795,axiom,
    ! [X7,X9,X5] :
      ( class_Lattices_Oboolean__algebra(X5)
     => ( c_Orderings_Oord__class_Oless__eq(X5,X9,X7)
       => c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ouminus__class_Ouminus(X5,X7),c_Groups_Ouminus__class_Ouminus(X5,X9)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compl__mono) ).

fof(f12086,plain,
    ( spl50_755
    | ~ spl50_129
    | ~ spl50_408 ),
    inference(avatar_split_clause,[],[f8166,f7974,f6691,f12084]) ).

fof(f12084,plain,
    ( spl50_755
  <=> ! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_755])]) ).

fof(f6691,plain,
    ( spl50_129
  <=> class_Groups_Omonoid__add(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_129])]) ).

fof(f8166,plain,
    ( ! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) = X0
    | ~ spl50_129
    | ~ spl50_408 ),
    inference(resolution,[],[f7975,f6693]) ).

fof(f6693,plain,
    ( class_Groups_Omonoid__add(tc_RealDef_Oreal)
    | ~ spl50_129 ),
    inference(avatar_component_clause,[],[f6691]) ).

fof(f12082,plain,
    spl50_754,
    inference(avatar_split_clause,[],[f4732,f12080]) ).

fof(f12080,plain,
    ( spl50_754
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_754])]) ).

fof(f4732,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) ),
    inference(cnf_transformation,[],[f3625]) ).

fof(f3625,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) )
      & ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
    inference(nnf_transformation,[],[f1728]) ).

fof(f1728,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) ),
    inference(rectify,[],[f500]) ).

fof(f500,axiom,
    ! [X20,X12] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X12,X20),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X20,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X12)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__add__less__0__iff) ).

fof(f12078,plain,
    spl50_753,
    inference(avatar_split_clause,[],[f4731,f12076]) ).

fof(f12076,plain,
    ( spl50_753
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_753])]) ).

fof(f4731,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    inference(cnf_transformation,[],[f3625]) ).

fof(f12074,plain,
    spl50_752,
    inference(avatar_split_clause,[],[f4730,f12072]) ).

fof(f12072,plain,
    ( spl50_752
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0))
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_752])]) ).

fof(f4730,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0))
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X0) ),
    inference(cnf_transformation,[],[f3624]) ).

fof(f3624,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0))
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X0) )
      & ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X0)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0)) ) ),
    inference(nnf_transformation,[],[f1727]) ).

fof(f1727,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0))
    <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X0) ),
    inference(rectify,[],[f499]) ).

fof(f499,axiom,
    ! [X20,X12] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X12,X20))
    <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X12),X20) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__0__less__add__iff) ).

fof(f12070,plain,
    spl50_751,
    inference(avatar_split_clause,[],[f4729,f12068]) ).

fof(f12068,plain,
    ( spl50_751
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X0)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_751])]) ).

fof(f4729,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X0)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0)) ),
    inference(cnf_transformation,[],[f3624]) ).

fof(f12066,plain,
    spl50_750,
    inference(avatar_split_clause,[],[f4724,f12064]) ).

fof(f12064,plain,
    ( spl50_750
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_750])]) ).

fof(f4724,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) ),
    inference(cnf_transformation,[],[f3621]) ).

fof(f3621,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
    inference(nnf_transformation,[],[f1724]) ).

fof(f1724,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) ),
    inference(rectify,[],[f497]) ).

fof(f497,axiom,
    ! [X20,X12] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X12,X20),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X20,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X12)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__add__le__0__iff) ).

fof(f12062,plain,
    spl50_749,
    inference(avatar_split_clause,[],[f4723,f12060]) ).

fof(f12060,plain,
    ( spl50_749
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_749])]) ).

fof(f4723,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    inference(cnf_transformation,[],[f3621]) ).

fof(f12058,plain,
    spl50_748,
    inference(avatar_split_clause,[],[f4722,f12056]) ).

fof(f12056,plain,
    ( spl50_748
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_748])]) ).

fof(f4722,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X0) ),
    inference(cnf_transformation,[],[f3620]) ).

fof(f3620,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X0) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X0)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0)) ) ),
    inference(nnf_transformation,[],[f1723]) ).

fof(f1723,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0))
    <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X0) ),
    inference(rectify,[],[f498]) ).

fof(f498,axiom,
    ! [X20,X12] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X12,X20))
    <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X12),X20) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__0__le__add__iff) ).

fof(f12054,plain,
    spl50_747,
    inference(avatar_split_clause,[],[f4721,f12052]) ).

fof(f12052,plain,
    ( spl50_747
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X0)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_747])]) ).

fof(f4721,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0)) ),
    inference(cnf_transformation,[],[f3620]) ).

fof(f12050,plain,
    spl50_746,
    inference(avatar_split_clause,[],[f4630,f12048]) ).

fof(f12048,plain,
    ( spl50_746
  <=> ! [X0,X1] :
        ( X0 = X1
        | hAPP(X1,sK30(X0,X1)) != hAPP(X0,sK30(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_746])]) ).

fof(f4630,plain,
    ! [X0,X1] :
      ( X0 = X1
      | hAPP(X1,sK30(X0,X1)) != hAPP(X0,sK30(X0,X1)) ),
    inference(cnf_transformation,[],[f3559]) ).

fof(f3559,plain,
    ! [X0,X1] :
      ( X0 = X1
      | hAPP(X1,sK30(X0,X1)) != hAPP(X0,sK30(X0,X1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK30])],[f2676,f3558]) ).

fof(f3558,plain,
    ! [X0,X1] :
      ( ? [X2] : hAPP(X1,X2) != hAPP(X0,X2)
     => hAPP(X1,sK30(X0,X1)) != hAPP(X0,sK30(X0,X1)) ),
    introduced(choice_axiom,[]) ).

fof(f2676,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/sandbox/benchmark/theBenchmark.p',fact_ext) ).

fof(f12046,plain,
    spl50_745,
    inference(avatar_split_clause,[],[f4504,f12044]) ).

fof(f12044,plain,
    ( spl50_745
  <=> ! [X0,X1] :
        ( c_Polynomial_Omonom(X1,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
        | ~ class_Groups_Ozero(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_745])]) ).

fof(f4504,plain,
    ! [X0,X1] :
      ( c_Polynomial_Omonom(X1,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
      | ~ class_Groups_Ozero(X1) ),
    inference(cnf_transformation,[],[f2524]) ).

fof(f2524,plain,
    ! [X0,X1] :
      ( c_Polynomial_Omonom(X1,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
      | ~ class_Groups_Ozero(X1) ),
    inference(ennf_transformation,[],[f1582]) ).

fof(f1582,plain,
    ! [X0,X1] :
      ( class_Groups_Ozero(X1)
     => c_Polynomial_Omonom(X1,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) ),
    inference(rectify,[],[f678]) ).

fof(f678,axiom,
    ! [X4,X5] :
      ( class_Groups_Ozero(X5)
     => c_Polynomial_Omonom(X5,X4,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(X5,X4,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_monom__0) ).

fof(f12042,plain,
    ( spl50_744
    | ~ spl50_128
    | ~ spl50_407 ),
    inference(avatar_split_clause,[],[f8162,f7970,f6686,f12040]) ).

fof(f12040,plain,
    ( spl50_744
  <=> ! [X0] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_744])]) ).

fof(f7970,plain,
    ( spl50_407
  <=> ! [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,[spl50_407])]) ).

fof(f8162,plain,
    ( ! [X0] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = X0
    | ~ spl50_128
    | ~ spl50_407 ),
    inference(resolution,[],[f7971,f6688]) ).

fof(f7971,plain,
    ( ! [X0,X1] :
        ( ~ class_Groups_Omonoid__add(X1)
        | c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0 )
    | ~ spl50_407 ),
    inference(avatar_component_clause,[],[f7970]) ).

fof(f12038,plain,
    spl50_743,
    inference(avatar_split_clause,[],[f4474,f12036]) ).

fof(f12036,plain,
    ( spl50_743
  <=> ! [X0,X1] :
        ( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X0) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0)
        | ~ class_Groups_Oab__group__add(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_743])]) ).

fof(f4474,plain,
    ! [X0,X1] :
      ( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X0) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0)
      | ~ class_Groups_Oab__group__add(X1) ),
    inference(cnf_transformation,[],[f2497]) ).

fof(f2497,plain,
    ! [X0,X1] :
      ( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X0) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0)
      | ~ class_Groups_Oab__group__add(X1) ),
    inference(ennf_transformation,[],[f1555]) ).

fof(f1555,plain,
    ! [X0,X1] :
      ( class_Groups_Oab__group__add(X1)
     => c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X0) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0) ),
    inference(rectify,[],[f637]) ).

fof(f637,axiom,
    ! [X53,X5] :
      ( class_Groups_Oab__group__add(X5)
     => c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X5),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X53) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X5),X53) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__poly__code_I1_J) ).

fof(f12034,plain,
    spl50_742,
    inference(avatar_split_clause,[],[f4462,f12032]) ).

fof(f12032,plain,
    ( spl50_742
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(X1,c_Groups_Osgn__class_Osgn(X1,X0),c_Groups_Ozero__class_Ozero(X1))
        | ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
        | ~ class_Rings_Olinordered__idom(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_742])]) ).

fof(f4462,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(X1,c_Groups_Osgn__class_Osgn(X1,X0),c_Groups_Ozero__class_Ozero(X1))
      | ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
      | ~ class_Rings_Olinordered__idom(X1) ),
    inference(cnf_transformation,[],[f3534]) ).

fof(f3534,plain,
    ! [X0,X1] :
      ( ( ( c_Orderings_Oord__class_Oless(X1,c_Groups_Osgn__class_Osgn(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_Ozero__class_Ozero(X1))
          | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Osgn__class_Osgn(X1,X0),c_Groups_Ozero__class_Ozero(X1)) ) )
      | ~ class_Rings_Olinordered__idom(X1) ),
    inference(nnf_transformation,[],[f2489]) ).

fof(f2489,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless(X1,c_Groups_Osgn__class_Osgn(X1,X0),c_Groups_Ozero__class_Ozero(X1))
      <=> c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1)) )
      | ~ class_Rings_Olinordered__idom(X1) ),
    inference(ennf_transformation,[],[f1547]) ).

fof(f1547,plain,
    ! [X0,X1] :
      ( class_Rings_Olinordered__idom(X1)
     => ( c_Orderings_Oord__class_Oless(X1,c_Groups_Osgn__class_Osgn(X1,X0),c_Groups_Ozero__class_Ozero(X1))
      <=> c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ) ),
    inference(rectify,[],[f842]) ).

fof(f842,axiom,
    ! [X24,X5] :
      ( class_Rings_Olinordered__idom(X5)
     => ( c_Orderings_Oord__class_Oless(X5,c_Groups_Osgn__class_Osgn(X5,X24),c_Groups_Ozero__class_Ozero(X5))
      <=> c_Orderings_Oord__class_Oless(X5,X24,c_Groups_Ozero__class_Ozero(X5)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__less) ).

fof(f12030,plain,
    spl50_741,
    inference(avatar_split_clause,[],[f4461,f12028]) ).

fof(f12028,plain,
    ( spl50_741
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
        | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Osgn__class_Osgn(X1,X0),c_Groups_Ozero__class_Ozero(X1))
        | ~ class_Rings_Olinordered__idom(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_741])]) ).

fof(f4461,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
      | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Osgn__class_Osgn(X1,X0),c_Groups_Ozero__class_Ozero(X1))
      | ~ class_Rings_Olinordered__idom(X1) ),
    inference(cnf_transformation,[],[f3534]) ).

fof(f12026,plain,
    spl50_740,
    inference(avatar_split_clause,[],[f4460,f12024]) ).

fof(f12024,plain,
    ( spl50_740
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Osgn__class_Osgn(X1,X0))
        | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
        | ~ class_Rings_Olinordered__idom(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_740])]) ).

fof(f4460,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Osgn__class_Osgn(X1,X0))
      | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
      | ~ class_Rings_Olinordered__idom(X1) ),
    inference(cnf_transformation,[],[f3533]) ).

fof(f3533,plain,
    ! [X0,X1] :
      ( ( ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Osgn__class_Osgn(X1,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_Ozero__class_Ozero(X1),c_Groups_Osgn__class_Osgn(X1,X0)) ) )
      | ~ class_Rings_Olinordered__idom(X1) ),
    inference(nnf_transformation,[],[f2488]) ).

fof(f2488,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Osgn__class_Osgn(X1,X0))
      <=> c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
      | ~ class_Rings_Olinordered__idom(X1) ),
    inference(ennf_transformation,[],[f1546]) ).

fof(f1546,plain,
    ! [X0,X1] :
      ( class_Rings_Olinordered__idom(X1)
     => ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Osgn__class_Osgn(X1,X0))
      <=> c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) ) ),
    inference(rectify,[],[f843]) ).

fof(f843,axiom,
    ! [X24,X5] :
      ( class_Rings_Olinordered__idom(X5)
     => ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),c_Groups_Osgn__class_Osgn(X5,X24))
      <=> c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X24) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__greater) ).

fof(f12022,plain,
    spl50_739,
    inference(avatar_split_clause,[],[f4459,f12020]) ).

fof(f12020,plain,
    ( spl50_739
  <=> ! [X0,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),c_Groups_Osgn__class_Osgn(X1,X0))
        | ~ class_Rings_Olinordered__idom(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_739])]) ).

fof(f4459,plain,
    ! [X0,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),c_Groups_Osgn__class_Osgn(X1,X0))
      | ~ class_Rings_Olinordered__idom(X1) ),
    inference(cnf_transformation,[],[f3533]) ).

fof(f12018,plain,
    spl50_738,
    inference(avatar_split_clause,[],[f4445,f12016]) ).

fof(f12016,plain,
    ( spl50_738
  <=> ! [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,[spl50_738])]) ).

fof(f4445,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,[],[f3529]) ).

fof(f3529,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,[],[f2476]) ).

fof(f2476,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,[],[f1537]) ).

fof(f1537,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,[],[f331]) ).

fof(f331,axiom,
    ! [X24,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ouminus__class_Ouminus(X5,X24),c_Groups_Ozero__class_Ozero(X5))
      <=> c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X24) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__less__0__iff__less) ).

fof(f12014,plain,
    spl50_737,
    inference(avatar_split_clause,[],[f4444,f12012]) ).

fof(f12012,plain,
    ( spl50_737
  <=> ! [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,[spl50_737])]) ).

fof(f4444,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,[],[f3529]) ).

fof(f12010,plain,
    spl50_736,
    inference(avatar_split_clause,[],[f4443,f12008]) ).

fof(f12008,plain,
    ( spl50_736
  <=> ! [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,[spl50_736])]) ).

fof(f4443,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,[],[f3528]) ).

fof(f3528,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,[],[f2475]) ).

fof(f2475,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,[],[f1536]) ).

fof(f1536,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,[],[f332]) ).

fof(f332,axiom,
    ! [X24,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),c_Groups_Ouminus__class_Ouminus(X5,X24))
      <=> c_Orderings_Oord__class_Oless(X5,X24,c_Groups_Ozero__class_Ozero(X5)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__0__less__iff__less) ).

fof(f12006,plain,
    spl50_735,
    inference(avatar_split_clause,[],[f4442,f12004]) ).

fof(f12004,plain,
    ( spl50_735
  <=> ! [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,[spl50_735])]) ).

fof(f4442,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,[],[f3528]) ).

fof(f12002,plain,
    spl50_734,
    inference(avatar_split_clause,[],[f4441,f12000]) ).

fof(f12000,plain,
    ( spl50_734
  <=> ! [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,[spl50_734])]) ).

fof(f4441,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,[],[f3527]) ).

fof(f3527,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,[],[f2474]) ).

fof(f2474,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,[],[f1535]) ).

fof(f1535,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,[],[f327]) ).

fof(f327,axiom,
    ! [X24,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ouminus__class_Ouminus(X5,X24),c_Groups_Ozero__class_Ozero(X5))
      <=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X24) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__le__0__iff__le) ).

fof(f11998,plain,
    ( spl50_733
    | ~ spl50_129
    | ~ spl50_407 ),
    inference(avatar_split_clause,[],[f8161,f7970,f6691,f11996]) ).

fof(f11996,plain,
    ( spl50_733
  <=> ! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_733])]) ).

fof(f8161,plain,
    ( ! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = X0
    | ~ spl50_129
    | ~ spl50_407 ),
    inference(resolution,[],[f7971,f6693]) ).

fof(f11994,plain,
    spl50_732,
    inference(avatar_split_clause,[],[f4440,f11992]) ).

fof(f11992,plain,
    ( spl50_732
  <=> ! [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,[spl50_732])]) ).

fof(f4440,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,[],[f3527]) ).

fof(f11990,plain,
    spl50_731,
    inference(avatar_split_clause,[],[f4439,f11988]) ).

fof(f11988,plain,
    ( spl50_731
  <=> ! [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,[spl50_731])]) ).

fof(f4439,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,[],[f3526]) ).

fof(f3526,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,[],[f2473]) ).

fof(f2473,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,[],[f1534]) ).

fof(f1534,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,[],[f325]) ).

fof(f325,axiom,
    ! [X24,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),c_Groups_Ouminus__class_Ouminus(X5,X24))
      <=> c_Orderings_Oord__class_Oless__eq(X5,X24,c_Groups_Ozero__class_Ozero(X5)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__0__le__iff__le) ).

fof(f11986,plain,
    spl50_730,
    inference(avatar_split_clause,[],[f4438,f11984]) ).

fof(f11984,plain,
    ( spl50_730
  <=> ! [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,[spl50_730])]) ).

fof(f4438,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,[],[f3526]) ).

fof(f11982,plain,
    spl50_729,
    inference(avatar_split_clause,[],[f4394,f11980]) ).

fof(f11980,plain,
    ( spl50_729
  <=> ! [X0,X1] :
        ( c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X1,c_Groups_Osgn__class_Osgn(X1,X0))
        | c_Groups_Ozero__class_Ozero(X1) = X0
        | ~ class_RealVector_Oreal__normed__vector(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_729])]) ).

fof(f4394,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X1,c_Groups_Osgn__class_Osgn(X1,X0))
      | c_Groups_Ozero__class_Ozero(X1) = X0
      | ~ class_RealVector_Oreal__normed__vector(X1) ),
    inference(cnf_transformation,[],[f2448]) ).

fof(f2448,plain,
    ! [X0,X1] :
      ( ( ( c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X1,c_Groups_Osgn__class_Osgn(X1,X0))
          | c_Groups_Ozero__class_Ozero(X1) = X0 )
        & ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X1,c_Groups_Osgn__class_Osgn(X1,X0))
          | c_Groups_Ozero__class_Ozero(X1) != X0 ) )
      | ~ class_RealVector_Oreal__normed__vector(X1) ),
    inference(ennf_transformation,[],[f1509]) ).

fof(f1509,plain,
    ! [X0,X1] :
      ( class_RealVector_Oreal__normed__vector(X1)
     => ( ( c_Groups_Ozero__class_Ozero(X1) != X0
         => c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X1,c_Groups_Osgn__class_Osgn(X1,X0)) )
        & ( c_Groups_Ozero__class_Ozero(X1) = X0
         => c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X1,c_Groups_Osgn__class_Osgn(X1,X0)) ) ) ),
    inference(rectify,[],[f851]) ).

fof(f851,axiom,
    ! [X9,X5] :
      ( class_RealVector_Oreal__normed__vector(X5)
     => ( ( c_Groups_Ozero__class_Ozero(X5) != X9
         => c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X5,c_Groups_Osgn__class_Osgn(X5,X9)) )
        & ( c_Groups_Ozero__class_Ozero(X5) = X9
         => c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X5,c_Groups_Osgn__class_Osgn(X5,X9)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__sgn) ).

fof(f11978,plain,
    spl50_728,
    inference(avatar_split_clause,[],[f4368,f11976]) ).

fof(f11976,plain,
    ( spl50_728
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
        | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
        | ~ class_Fields_Olinordered__field(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_728])]) ).

fof(f4368,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
      | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
      | ~ class_Fields_Olinordered__field(X1) ),
    inference(cnf_transformation,[],[f2413]) ).

fof(f2413,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
      | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
      | ~ class_Fields_Olinordered__field(X1) ),
    inference(flattening,[],[f2412]) ).

fof(f2412,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
      | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
      | ~ class_Fields_Olinordered__field(X1) ),
    inference(ennf_transformation,[],[f1486]) ).

fof(f1486,plain,
    ! [X0,X1] :
      ( class_Fields_Olinordered__field(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),c_Rings_Oinverse__class_Oinverse(X1,X0)) ) ),
    inference(rectify,[],[f160]) ).

fof(f160,axiom,
    ! [X4,X5] :
      ( class_Fields_Olinordered__field(X5)
     => ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X4)
       => c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),c_Rings_Oinverse__class_Oinverse(X5,X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_positive__imp__inverse__positive) ).

fof(f11974,plain,
    spl50_727,
    inference(avatar_split_clause,[],[f4367,f11972]) ).

fof(f11972,plain,
    ( spl50_727
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Ozero__class_Ozero(X1))
        | ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
        | ~ class_Fields_Olinordered__field(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_727])]) ).

fof(f4367,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Ozero__class_Ozero(X1))
      | ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
      | ~ class_Fields_Olinordered__field(X1) ),
    inference(cnf_transformation,[],[f2411]) ).

fof(f2411,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Ozero__class_Ozero(X1))
      | ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
      | ~ class_Fields_Olinordered__field(X1) ),
    inference(flattening,[],[f2410]) ).

fof(f2410,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Ozero__class_Ozero(X1))
      | ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
      | ~ class_Fields_Olinordered__field(X1) ),
    inference(ennf_transformation,[],[f1485]) ).

fof(f1485,plain,
    ! [X0,X1] :
      ( class_Fields_Olinordered__field(X1)
     => ( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
       => c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Ozero__class_Ozero(X1)) ) ),
    inference(rectify,[],[f158]) ).

fof(f158,axiom,
    ! [X4,X5] :
      ( class_Fields_Olinordered__field(X5)
     => ( c_Orderings_Oord__class_Oless(X5,X4,c_Groups_Ozero__class_Ozero(X5))
       => c_Orderings_Oord__class_Oless(X5,c_Rings_Oinverse__class_Oinverse(X5,X4),c_Groups_Ozero__class_Ozero(X5)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negative__imp__inverse__negative) ).

fof(f11970,plain,
    spl50_726,
    inference(avatar_split_clause,[],[f4366,f11968]) ).

fof(f11968,plain,
    ( spl50_726
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Ozero__class_Ozero(X1))
        | ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
        | ~ class_Fields_Olinordered__field__inverse__zero(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_726])]) ).

fof(f4366,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Ozero__class_Ozero(X1))
      | ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
      | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(cnf_transformation,[],[f3504]) ).

fof(f3504,plain,
    ! [X0,X1] :
      ( ( ( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(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_Ozero__class_Ozero(X1))
          | ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Ozero__class_Ozero(X1)) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(nnf_transformation,[],[f2409]) ).

fof(f2409,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Ozero__class_Ozero(X1))
      <=> c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1)) )
      | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(ennf_transformation,[],[f1484]) ).

fof(f1484,plain,
    ! [X0,X1] :
      ( class_Fields_Olinordered__field__inverse__zero(X1)
     => ( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Ozero__class_Ozero(X1))
      <=> c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ) ),
    inference(rectify,[],[f161]) ).

fof(f161,axiom,
    ! [X24,X5] :
      ( class_Fields_Olinordered__field__inverse__zero(X5)
     => ( c_Orderings_Oord__class_Oless(X5,c_Rings_Oinverse__class_Oinverse(X5,X24),c_Groups_Ozero__class_Ozero(X5))
      <=> c_Orderings_Oord__class_Oless(X5,X24,c_Groups_Ozero__class_Ozero(X5)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__negative__iff__negative) ).

fof(f11966,plain,
    spl50_725,
    inference(avatar_split_clause,[],[f4365,f11964]) ).

fof(f11964,plain,
    ( spl50_725
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
        | ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Ozero__class_Ozero(X1))
        | ~ class_Fields_Olinordered__field__inverse__zero(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_725])]) ).

fof(f4365,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
      | ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Ozero__class_Ozero(X1))
      | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(cnf_transformation,[],[f3504]) ).

fof(f11962,plain,
    spl50_724,
    inference(avatar_split_clause,[],[f4364,f11960]) ).

fof(f11960,plain,
    ( spl50_724
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Oone__class_Oone(X1))
        | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X0)
        | ~ class_Fields_Olinordered__field__inverse__zero(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_724])]) ).

fof(f4364,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Oone__class_Oone(X1))
      | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X0)
      | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(cnf_transformation,[],[f3503]) ).

fof(f11958,plain,
    spl50_723,
    inference(avatar_split_clause,[],[f4363,f11956]) ).

fof(f11956,plain,
    ( spl50_723
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Oone__class_Oone(X1))
        | ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
        | ~ class_Fields_Olinordered__field__inverse__zero(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_723])]) ).

fof(f4363,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Oone__class_Oone(X1))
      | ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
      | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(cnf_transformation,[],[f3503]) ).

fof(f11954,plain,
    ( spl50_722
    | ~ spl50_100
    | ~ spl50_406 ),
    inference(avatar_split_clause,[],[f8160,f7966,f6546,f11952]) ).

fof(f11952,plain,
    ( spl50_722
  <=> ! [X0] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_722])]) ).

fof(f6546,plain,
    ( spl50_100
  <=> class_Groups_Ogroup__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_100])]) ).

fof(f7966,plain,
    ( spl50_406
  <=> ! [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,[spl50_406])]) ).

fof(f8160,plain,
    ( ! [X0] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X0
    | ~ spl50_100
    | ~ spl50_406 ),
    inference(resolution,[],[f7967,f6548]) ).

fof(f6548,plain,
    ( class_Groups_Ogroup__add(tc_Int_Oint)
    | ~ spl50_100 ),
    inference(avatar_component_clause,[],[f6546]) ).

fof(f7967,plain,
    ( ! [X0,X1] :
        ( ~ class_Groups_Ogroup__add(X1)
        | c_Groups_Ominus__class_Ominus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0 )
    | ~ spl50_406 ),
    inference(avatar_component_clause,[],[f7966]) ).

fof(f11950,plain,
    spl50_721,
    inference(avatar_split_clause,[],[f4361,f11948]) ).

fof(f4361,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
      | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
      | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(cnf_transformation,[],[f3501]) ).

fof(f3501,plain,
    ! [X0,X1] :
      ( ( ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,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_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X0)) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(nnf_transformation,[],[f2407]) ).

fof(f2407,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
      <=> c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
      | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(ennf_transformation,[],[f1482]) ).

fof(f1482,plain,
    ! [X0,X1] :
      ( class_Fields_Olinordered__field__inverse__zero(X1)
     => ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
      <=> c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) ) ),
    inference(rectify,[],[f162]) ).

fof(f162,axiom,
    ! [X24,X5] :
      ( class_Fields_Olinordered__field__inverse__zero(X5)
     => ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),c_Rings_Oinverse__class_Oinverse(X5,X24))
      <=> c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X24) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__positive__iff__positive) ).

fof(f11946,plain,
    spl50_720,
    inference(avatar_split_clause,[],[f4360,f11944]) ).

fof(f11944,plain,
    ( spl50_720
  <=> ! [X0,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),c_Rings_Oinverse__class_Oinverse(X1,X0))
        | ~ class_Fields_Olinordered__field__inverse__zero(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_720])]) ).

fof(f4360,plain,
    ! [X0,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),c_Rings_Oinverse__class_Oinverse(X1,X0))
      | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(cnf_transformation,[],[f3501]) ).

fof(f11942,plain,
    spl50_719,
    inference(avatar_split_clause,[],[f4358,f11940]) ).

fof(f11940,plain,
    ( spl50_719
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Oone__class_Oone(X1))
        | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
        | ~ class_Fields_Olinordered__field__inverse__zero(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_719])]) ).

fof(f4358,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Oone__class_Oone(X1))
      | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
      | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(cnf_transformation,[],[f3500]) ).

fof(f11938,plain,
    spl50_718,
    inference(avatar_split_clause,[],[f4357,f11936]) ).

fof(f11936,plain,
    ( spl50_718
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
        | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
        | ~ class_Fields_Olinordered__field__inverse__zero(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_718])]) ).

fof(f4357,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
      | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
      | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(cnf_transformation,[],[f3500]) ).

fof(f11934,plain,
    spl50_717,
    inference(avatar_split_clause,[],[f4356,f11932]) ).

fof(f11932,plain,
    ( spl50_717
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Ozero__class_Ozero(X1))
        | ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
        | ~ class_Fields_Olinordered__field__inverse__zero(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_717])]) ).

fof(f4356,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Ozero__class_Ozero(X1))
      | ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
      | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(cnf_transformation,[],[f3498]) ).

fof(f3498,plain,
    ! [X0,X1] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(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_Ozero__class_Ozero(X1))
          | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Ozero__class_Ozero(X1)) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(nnf_transformation,[],[f2405]) ).

fof(f2405,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Ozero__class_Ozero(X1))
      <=> c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1)) )
      | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(ennf_transformation,[],[f1480]) ).

fof(f1480,plain,
    ! [X0,X1] :
      ( class_Fields_Olinordered__field__inverse__zero(X1)
     => ( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Ozero__class_Ozero(X1))
      <=> c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ) ),
    inference(rectify,[],[f51]) ).

fof(f51,axiom,
    ! [X24,X5] :
      ( class_Fields_Olinordered__field__inverse__zero(X5)
     => ( c_Orderings_Oord__class_Oless__eq(X5,c_Rings_Oinverse__class_Oinverse(X5,X24),c_Groups_Ozero__class_Ozero(X5))
      <=> c_Orderings_Oord__class_Oless__eq(X5,X24,c_Groups_Ozero__class_Ozero(X5)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__nonpositive__iff__nonpositive) ).

fof(f11930,plain,
    spl50_716,
    inference(avatar_split_clause,[],[f4355,f11928]) ).

fof(f4355,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_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Ozero__class_Ozero(X1))
      | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(cnf_transformation,[],[f3498]) ).

fof(f11926,plain,
    spl50_715,
    inference(avatar_split_clause,[],[f4354,f11924]) ).

fof(f11924,plain,
    ( spl50_715
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Oone__class_Oone(X1))
        | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),X0)
        | ~ class_Fields_Olinordered__field__inverse__zero(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_715])]) ).

fof(f4354,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Oone__class_Oone(X1))
      | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),X0)
      | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(cnf_transformation,[],[f3497]) ).

fof(f11922,plain,
    spl50_714,
    inference(avatar_split_clause,[],[f4353,f11920]) ).

fof(f11920,plain,
    ( spl50_714
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Oone__class_Oone(X1))
        | ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
        | ~ class_Fields_Olinordered__field__inverse__zero(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_714])]) ).

fof(f4353,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Oone__class_Oone(X1))
      | ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
      | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(cnf_transformation,[],[f3497]) ).

fof(f11918,plain,
    spl50_713,
    inference(avatar_split_clause,[],[f4351,f11916]) ).

fof(f11916,plain,
    ( spl50_713
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
        | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
        | ~ class_Fields_Olinordered__field__inverse__zero(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_713])]) ).

fof(f4351,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
      | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
      | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(cnf_transformation,[],[f3495]) ).

fof(f3495,plain,
    ! [X0,X1] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(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_Ozero__class_Ozero(X1),X0)
          | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X0)) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(nnf_transformation,[],[f2403]) ).

fof(f2403,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
      <=> c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
      | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(ennf_transformation,[],[f1478]) ).

fof(f1478,plain,
    ! [X0,X1] :
      ( class_Fields_Olinordered__field__inverse__zero(X1)
     => ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
      <=> c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0) ) ),
    inference(rectify,[],[f52]) ).

fof(f52,axiom,
    ! [X24,X5] :
      ( class_Fields_Olinordered__field__inverse__zero(X5)
     => ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),c_Rings_Oinverse__class_Oinverse(X5,X24))
      <=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X24) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__nonnegative__iff__nonnegative) ).

fof(f11914,plain,
    spl50_712,
    inference(avatar_split_clause,[],[f4350,f11912]) ).

fof(f11912,plain,
    ( spl50_712
  <=> ! [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),c_Rings_Oinverse__class_Oinverse(X1,X0))
        | ~ class_Fields_Olinordered__field__inverse__zero(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_712])]) ).

fof(f4350,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_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
      | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(cnf_transformation,[],[f3495]) ).

fof(f11910,plain,
    ( spl50_711
    | ~ spl50_98
    | ~ spl50_406 ),
    inference(avatar_split_clause,[],[f8158,f7966,f6536,f11908]) ).

fof(f11908,plain,
    ( spl50_711
  <=> ! [X0] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_711])]) ).

fof(f6536,plain,
    ( spl50_98
  <=> class_Groups_Ogroup__add(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_98])]) ).

fof(f8158,plain,
    ( ! [X0] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = X0
    | ~ spl50_98
    | ~ spl50_406 ),
    inference(resolution,[],[f7967,f6538]) ).

fof(f6538,plain,
    ( class_Groups_Ogroup__add(tc_Complex_Ocomplex)
    | ~ spl50_98 ),
    inference(avatar_component_clause,[],[f6536]) ).

fof(f11906,plain,
    spl50_710,
    inference(avatar_split_clause,[],[f4348,f11904]) ).

fof(f11904,plain,
    ( spl50_710
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Oone__class_Oone(X1))
        | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
        | ~ class_Fields_Olinordered__field__inverse__zero(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_710])]) ).

fof(f4348,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Oone__class_Oone(X1))
      | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
      | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(cnf_transformation,[],[f3494]) ).

fof(f11902,plain,
    spl50_709,
    inference(avatar_split_clause,[],[f4347,f11900]) ).

fof(f11900,plain,
    ( spl50_709
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
        | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
        | ~ class_Fields_Olinordered__field__inverse__zero(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_709])]) ).

fof(f4347,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
      | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
      | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(cnf_transformation,[],[f3494]) ).

fof(f11898,plain,
    spl50_708,
    inference(avatar_split_clause,[],[f4298,f11896]) ).

fof(f11896,plain,
    ( spl50_708
  <=> ! [X0] :
        ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X0
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_708])]) ).

fof(f4298,plain,
    ! [X0] :
      ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X0
      | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),X0)) ),
    inference(cnf_transformation,[],[f3490]) ).

fof(f3490,plain,
    ! [X0] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),X0))
        | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X0 )
      & ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X0
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),X0)) ) ),
    inference(nnf_transformation,[],[f1432]) ).

fof(f1432,plain,
    ! [X0] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),X0))
    <=> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X0 ),
    inference(rectify,[],[f441]) ).

fof(f441,axiom,
    ! [X12] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X12),X12))
    <=> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X12 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__real__square__gt__zero) ).

fof(f11894,plain,
    spl50_707,
    inference(avatar_split_clause,[],[f4180,f11892]) ).

fof(f11892,plain,
    ( spl50_707
  <=> ! [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,[spl50_707])]) ).

fof(f4180,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,[],[f1328]) ).

fof(f1328,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,[],[f421]) ).

fof(f421,axiom,
    ! [X17] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X17))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__cube) ).

fof(f11890,plain,
    spl50_706,
    inference(avatar_split_clause,[],[f4131,f11888]) ).

fof(f11888,plain,
    ( spl50_706
  <=> ! [X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X1)) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,sK19),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_706])]) ).

fof(f4131,plain,
    ! [X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X1)) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,sK19),X1),
    inference(cnf_transformation,[],[f3473]) ).

fof(f11851,plain,
    ( spl50_705
    | ~ spl50_99
    | ~ spl50_406 ),
    inference(avatar_split_clause,[],[f8157,f7966,f6541,f11849]) ).

fof(f11849,plain,
    ( spl50_705
  <=> ! [X0] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_705])]) ).

fof(f6541,plain,
    ( spl50_99
  <=> class_Groups_Ogroup__add(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_99])]) ).

fof(f8157,plain,
    ( ! [X0] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = X0
    | ~ spl50_99
    | ~ spl50_406 ),
    inference(resolution,[],[f7967,f6543]) ).

fof(f6543,plain,
    ( class_Groups_Ogroup__add(tc_RealDef_Oreal)
    | ~ spl50_99 ),
    inference(avatar_component_clause,[],[f6541]) ).

fof(f11401,plain,
    ( spl50_704
    | ~ spl50_98
    | ~ spl50_405 ),
    inference(avatar_split_clause,[],[f8149,f7962,f6536,f11399]) ).

fof(f11399,plain,
    ( spl50_704
  <=> ! [X0] : c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_704])]) ).

fof(f7962,plain,
    ( spl50_405
  <=> ! [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,[spl50_405])]) ).

fof(f8149,plain,
    ( ! [X0] : c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)) = X0
    | ~ spl50_98
    | ~ spl50_405 ),
    inference(resolution,[],[f7963,f6538]) ).

fof(f7963,plain,
    ( ! [X0,X1] :
        ( ~ class_Groups_Ogroup__add(X1)
        | c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0)) = X0 )
    | ~ spl50_405 ),
    inference(avatar_component_clause,[],[f7962]) ).

fof(f11201,plain,
    ( spl50_703
    | ~ spl50_99
    | ~ spl50_405 ),
    inference(avatar_split_clause,[],[f8148,f7962,f6541,f11199]) ).

fof(f11199,plain,
    ( spl50_703
  <=> ! [X0] : c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_703])]) ).

fof(f8148,plain,
    ( ! [X0] : c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0)) = X0
    | ~ spl50_99
    | ~ spl50_405 ),
    inference(resolution,[],[f7963,f6543]) ).

fof(f11059,plain,
    ( spl50_702
    | ~ spl50_100
    | ~ spl50_404 ),
    inference(avatar_split_clause,[],[f8147,f7958,f6546,f11057]) ).

fof(f11057,plain,
    ( spl50_702
  <=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_702])]) ).

fof(f7958,plain,
    ( spl50_404
  <=> ! [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,[spl50_404])]) ).

fof(f8147,plain,
    ( ! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,X0)
    | ~ spl50_100
    | ~ spl50_404 ),
    inference(resolution,[],[f7959,f6548]) ).

fof(f7959,plain,
    ( ! [X0,X1] :
        ( ~ class_Groups_Ogroup__add(X1)
        | c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ominus__class_Ominus(X1,X0,X0) )
    | ~ spl50_404 ),
    inference(avatar_component_clause,[],[f7958]) ).

fof(f10959,plain,
    spl50_701,
    inference(avatar_split_clause,[],[f5719,f10957]) ).

fof(f10957,plain,
    ( spl50_701
  <=> ! [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,[spl50_701])]) ).

fof(f5719,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,[],[f4469]) ).

fof(f4469,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,[],[f3538]) ).

fof(f10955,plain,
    spl50_700,
    inference(avatar_split_clause,[],[f5584,f10953]) ).

fof(f10953,plain,
    ( spl50_700
  <=> ! [X0] :
        ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK24(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,[spl50_700])]) ).

fof(f5584,plain,
    ! [X0] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK24(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,[],[f4292,f4164]) ).

fof(f4292,plain,
    ! [X0] :
      ( c_Nat_OSuc(sK24(X0)) = X0
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
    inference(cnf_transformation,[],[f3487]) ).

fof(f3487,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(sK24(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,[sK24])],[f3485,f3486]) ).

fof(f3486,plain,
    ! [X0] :
      ( ? [X2] : c_Nat_OSuc(X2) = X0
     => c_Nat_OSuc(sK24(X0)) = X0 ),
    introduced(choice_axiom,[]) ).

fof(f3485,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,[],[f3484]) ).

fof(f3484,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,[],[f1429]) ).

fof(f1429,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,[],[f957]) ).

fof(f957,axiom,
    ! [X16] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X16)
    <=> ? [X44] : c_Nat_OSuc(X44) = X16 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr0__conv__Suc) ).

fof(f10951,plain,
    spl50_699,
    inference(avatar_split_clause,[],[f5310,f10949]) ).

fof(f10949,plain,
    ( spl50_699
  <=> ! [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,[spl50_699])]) ).

fof(f5310,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,[],[f3818]) ).

fof(f10947,plain,
    ( spl50_698
    | ~ spl50_98
    | ~ spl50_404 ),
    inference(avatar_split_clause,[],[f8145,f7958,f6536,f10945]) ).

fof(f10945,plain,
    ( spl50_698
  <=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_698])]) ).

fof(f8145,plain,
    ( ! [X0] : c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X0)
    | ~ spl50_98
    | ~ spl50_404 ),
    inference(resolution,[],[f7959,f6538]) ).

fof(f10943,plain,
    spl50_697,
    inference(avatar_split_clause,[],[f5301,f10941]) ).

fof(f10941,plain,
    ( spl50_697
  <=> ! [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,[spl50_697])]) ).

fof(f5301,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,[],[f3813]) ).

fof(f10939,plain,
    spl50_696,
    inference(avatar_split_clause,[],[f5208,f10937]) ).

fof(f10937,plain,
    ( spl50_696
  <=> ! [X2,X0,X1] :
        ( hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
        | ~ sP8(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_696])]) ).

fof(f5208,plain,
    ! [X2,X0,X1] :
      ( hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
      | ~ sP8(X0,X1,X2) ),
    inference(cnf_transformation,[],[f3771]) ).

fof(f10935,plain,
    spl50_695,
    inference(avatar_split_clause,[],[f5200,f10933]) ).

fof(f10933,plain,
    ( spl50_695
  <=> ! [X2,X0,X1] :
        ( hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
        | ~ sP7(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_695])]) ).

fof(f5200,plain,
    ! [X2,X0,X1] :
      ( hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
      | ~ sP7(X0,X1,X2) ),
    inference(cnf_transformation,[],[f3765]) ).

fof(f10931,plain,
    spl50_694,
    inference(avatar_split_clause,[],[f5199,f10929]) ).

fof(f10929,plain,
    ( spl50_694
  <=> ! [X2,X0,X1] :
        ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X2,X1,X0)
        | hAPP(X0,sK38(X0)) != hAPP(X0,sK39(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_694])]) ).

fof(f5199,plain,
    ! [X2,X0,X1] :
      ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X2,X1,X0)
      | hAPP(X0,sK38(X0)) != hAPP(X0,sK39(X0)) ),
    inference(cnf_transformation,[],[f3760]) ).

fof(f3760,plain,
    ! [X0,X1,X2] :
      ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X2,X1,X0)
        | hAPP(X0,sK38(X0)) != hAPP(X0,sK39(X0)) )
      & ( ! [X5,X6] : hAPP(X0,X5) = hAPP(X0,X6)
        | ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X2,X1,X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK38,sK39])],[f3758,f3759]) ).

fof(f3759,plain,
    ! [X0] :
      ( ? [X3,X4] : hAPP(X0,X3) != hAPP(X0,X4)
     => hAPP(X0,sK38(X0)) != hAPP(X0,sK39(X0)) ),
    introduced(choice_axiom,[]) ).

fof(f3758,plain,
    ! [X0,X1,X2] :
      ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X2,X1,X0)
        | ? [X3,X4] : hAPP(X0,X3) != hAPP(X0,X4) )
      & ( ! [X5,X6] : hAPP(X0,X5) = hAPP(X0,X6)
        | ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X2,X1,X0) ) ),
    inference(rectify,[],[f3757]) ).

fof(f3757,plain,
    ! [X0,X1,X2] :
      ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X2,X1,X0)
        | ? [X3,X4] : hAPP(X0,X3) != hAPP(X0,X4) )
      & ( ! [X3,X4] : hAPP(X0,X3) = hAPP(X0,X4)
        | ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X2,X1,X0) ) ),
    inference(nnf_transformation,[],[f2046]) ).

fof(f2046,plain,
    ! [X0,X1,X2] :
      ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X2,X1,X0)
    <=> ! [X3,X4] : hAPP(X0,X3) = hAPP(X0,X4) ),
    inference(rectify,[],[f281]) ).

fof(f281,axiom,
    ! [X1,X46,X5] :
      ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X5,X46,X1)
    <=> ! [X2,X47] : hAPP(X1,X2) = hAPP(X1,X47) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_constant__def) ).

fof(f10927,plain,
    spl50_693,
    inference(avatar_split_clause,[],[f5152,f10925]) ).

fof(f10925,plain,
    ( spl50_693
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK35(X0,X1,X2))
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_693])]) ).

fof(f5152,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK35(X0,X1,X2))
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ),
    inference(cnf_transformation,[],[f3742]) ).

fof(f3742,plain,
    ! [X0,X1,X2] :
      ( ( ! [X4] :
            ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X0),X4),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X0),X1))),X2)
            | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X4,X1)),sK35(X0,X1,X2))
            | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X4,X1))) )
        & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK35(X0,X1,X2)) )
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK35])],[f3044,f3741]) ).

fof(f3741,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ! [X4] :
              ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X0),X4),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X0),X1))),X2)
              | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X4,X1)),X3)
              | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X4,X1))) )
          & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3) )
     => ( ! [X4] :
            ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X0),X4),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X0),X1))),X2)
            | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X4,X1)),sK35(X0,X1,X2))
            | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X4,X1))) )
        & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK35(X0,X1,X2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f3044,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ! [X4] :
              ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X0),X4),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X0),X1))),X2)
              | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X4,X1)),X3)
              | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X4,X1))) )
          & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3) )
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ),
    inference(flattening,[],[f3043]) ).

fof(f3043,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ! [X4] :
              ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X0),X4),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X0),X1))),X2)
              | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X4,X1)),X3)
              | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X4,X1))) )
          & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3) )
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ),
    inference(ennf_transformation,[],[f2019]) ).

fof(f2019,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)
     => ? [X3] :
          ( ! [X4] :
              ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X4,X1)),X3)
                & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X4,X1))) )
             => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X0),X4),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X0),X1))),X2) )
          & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3) ) ),
    inference(rectify,[],[f792]) ).

fof(f792,axiom,
    ! [X54,X14,X27] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X27)
     => ? [X57] :
          ( ! [X43] :
              ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X43,X14)),X57)
                & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X43,X14))) )
             => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X54),X43),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X54),X14))),X27) )
          & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X57) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__cont) ).

fof(f10923,plain,
    spl50_692,
    inference(avatar_split_clause,[],[f5070,f10921]) ).

fof(f10921,plain,
    ( spl50_692
  <=> ! [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,[spl50_692])]) ).

fof(f5070,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,[],[f2955]) ).

fof(f2955,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,[],[f2954]) ).

fof(f2954,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,[],[f1957]) ).

fof(f1957,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,[],[f724]) ).

fof(f724,axiom,
    ! [X9,X7,X5] :
      ( class_Orderings_Oorder(X5)
     => ( c_Orderings_Oord__class_Oless__eq(X5,X7,X9)
       => ( c_Orderings_Oord__class_Oless__eq(X5,X9,X7)
         => X7 = X9 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I5_J) ).

fof(f10919,plain,
    spl50_691,
    inference(avatar_split_clause,[],[f5065,f10917]) ).

fof(f10917,plain,
    ( spl50_691
  <=> ! [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,[spl50_691])]) ).

fof(f5065,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,[],[f2945]) ).

fof(f2945,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,[],[f2944]) ).

fof(f2944,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,[],[f1952]) ).

fof(f1952,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,[],[f760]) ).

fof(f760,axiom,
    ! [X13,X4,X5] :
      ( class_Orderings_Oorder(X5)
     => ( X4 != X13
       => ( c_Orderings_Oord__class_Oless__eq(X5,X4,X13)
         => c_Orderings_Oord__class_Oless(X5,X4,X13) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__neq__le__trans) ).

fof(f10915,plain,
    spl50_690,
    inference(avatar_split_clause,[],[f5005,f10913]) ).

fof(f10913,plain,
    ( spl50_690
  <=> ! [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,[spl50_690])]) ).

fof(f5005,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,[],[f2878]) ).

fof(f2878,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,[],[f1906]) ).

fof(f1906,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,[],[f316]) ).

fof(f316,axiom,
    ! [X13,X4,X5] :
      ( class_Groups_Ogroup__add(X5)
     => c_Groups_Oplus__class_Oplus(X5,c_Groups_Ouminus__class_Ouminus(X5,X4),c_Groups_Oplus__class_Oplus(X5,X4,X13)) = X13 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__add__cancel) ).

fof(f10911,plain,
    spl50_689,
    inference(avatar_split_clause,[],[f5004,f10909]) ).

fof(f10909,plain,
    ( spl50_689
  <=> ! [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,[spl50_689])]) ).

fof(f5004,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,[],[f2877]) ).

fof(f2877,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,[],[f1905]) ).

fof(f1905,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,[],[f317]) ).

fof(f317,axiom,
    ! [X13,X4,X5] :
      ( class_Groups_Ogroup__add(X5)
     => c_Groups_Oplus__class_Oplus(X5,X4,c_Groups_Oplus__class_Oplus(X5,c_Groups_Ouminus__class_Ouminus(X5,X4),X13)) = X13 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__minus__cancel) ).

fof(f10907,plain,
    spl50_688,
    inference(avatar_split_clause,[],[f5003,f10905]) ).

fof(f10905,plain,
    ( spl50_688
  <=> ! [X2,X0,X1] :
        ( c_Groups_Oplus__class_Oplus(X2,X1,X0) = c_Groups_Ominus__class_Ominus(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
        | ~ class_Groups_Ogroup__add(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_688])]) ).

fof(f5003,plain,
    ! [X2,X0,X1] :
      ( c_Groups_Oplus__class_Oplus(X2,X1,X0) = c_Groups_Ominus__class_Ominus(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
      | ~ class_Groups_Ogroup__add(X2) ),
    inference(cnf_transformation,[],[f2876]) ).

fof(f2876,plain,
    ! [X0,X1,X2] :
      ( c_Groups_Oplus__class_Oplus(X2,X1,X0) = c_Groups_Ominus__class_Ominus(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
      | ~ class_Groups_Ogroup__add(X2) ),
    inference(ennf_transformation,[],[f1904]) ).

fof(f1904,plain,
    ! [X0,X1,X2] :
      ( class_Groups_Ogroup__add(X2)
     => c_Groups_Oplus__class_Oplus(X2,X1,X0) = c_Groups_Ominus__class_Ominus(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0)) ),
    inference(rectify,[],[f274]) ).

fof(f274,axiom,
    ! [X13,X4,X5] :
      ( class_Groups_Ogroup__add(X5)
     => c_Groups_Oplus__class_Oplus(X5,X4,X13) = c_Groups_Ominus__class_Ominus(X5,X4,c_Groups_Ouminus__class_Ouminus(X5,X13)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__minus__eq__add) ).

fof(f10903,plain,
    ( spl50_687
    | ~ spl50_99
    | ~ spl50_404 ),
    inference(avatar_split_clause,[],[f8144,f7958,f6541,f10901]) ).

fof(f10901,plain,
    ( spl50_687
  <=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_687])]) ).

fof(f8144,plain,
    ( ! [X0] : c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,X0)
    | ~ spl50_99
    | ~ spl50_404 ),
    inference(resolution,[],[f7959,f6543]) ).

fof(f10899,plain,
    spl50_686,
    inference(avatar_split_clause,[],[f5002,f10897]) ).

fof(f10897,plain,
    ( spl50_686
  <=> ! [X2,X0,X1] :
        ( c_Groups_Ominus__class_Ominus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
        | ~ class_Groups_Ogroup__add(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_686])]) ).

fof(f5002,plain,
    ! [X2,X0,X1] :
      ( c_Groups_Ominus__class_Ominus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
      | ~ class_Groups_Ogroup__add(X2) ),
    inference(cnf_transformation,[],[f2875]) ).

fof(f2875,plain,
    ! [X0,X1,X2] :
      ( c_Groups_Ominus__class_Ominus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
      | ~ class_Groups_Ogroup__add(X2) ),
    inference(ennf_transformation,[],[f1903]) ).

fof(f1903,plain,
    ! [X0,X1,X2] :
      ( class_Groups_Ogroup__add(X2)
     => c_Groups_Ominus__class_Ominus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0)) ),
    inference(rectify,[],[f272]) ).

fof(f272,axiom,
    ! [X13,X4,X5] :
      ( class_Groups_Ogroup__add(X5)
     => c_Groups_Ominus__class_Ominus(X5,X4,X13) = c_Groups_Oplus__class_Oplus(X5,X4,c_Groups_Ouminus__class_Ouminus(X5,X13)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__def) ).

fof(f10895,plain,
    spl50_685,
    inference(avatar_split_clause,[],[f4992,f10893]) ).

fof(f10893,plain,
    ( spl50_685
  <=> ! [X2,X0,X1] :
        ( c_Groups_Ominus__class_Ominus(X2,X0,X1) = c_Groups_Ouminus__class_Ouminus(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0))
        | ~ class_Groups_Oab__group__add(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_685])]) ).

fof(f4992,plain,
    ! [X2,X0,X1] :
      ( c_Groups_Ominus__class_Ominus(X2,X0,X1) = c_Groups_Ouminus__class_Ouminus(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0))
      | ~ class_Groups_Oab__group__add(X2) ),
    inference(cnf_transformation,[],[f2866]) ).

fof(f2866,plain,
    ! [X0,X1,X2] :
      ( c_Groups_Ominus__class_Ominus(X2,X0,X1) = c_Groups_Ouminus__class_Ouminus(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0))
      | ~ class_Groups_Oab__group__add(X2) ),
    inference(ennf_transformation,[],[f1894]) ).

fof(f1894,plain,
    ! [X0,X1,X2] :
      ( class_Groups_Oab__group__add(X2)
     => c_Groups_Ominus__class_Ominus(X2,X0,X1) = c_Groups_Ouminus__class_Ouminus(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0)) ),
    inference(rectify,[],[f279]) ).

fof(f279,axiom,
    ! [X13,X4,X5] :
      ( class_Groups_Oab__group__add(X5)
     => c_Groups_Ouminus__class_Ouminus(X5,c_Groups_Ominus__class_Ominus(X5,X4,X13)) = c_Groups_Ominus__class_Ominus(X5,X13,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__diff__eq) ).

fof(f10891,plain,
    spl50_684,
    inference(avatar_split_clause,[],[f4991,f10889]) ).

fof(f10889,plain,
    ( spl50_684
  <=> ! [X2,X0,X1] :
        ( c_Groups_Ominus__class_Ominus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
        | ~ class_Groups_Oab__group__add(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_684])]) ).

fof(f4991,plain,
    ! [X2,X0,X1] :
      ( c_Groups_Ominus__class_Ominus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
      | ~ class_Groups_Oab__group__add(X2) ),
    inference(cnf_transformation,[],[f2865]) ).

fof(f2865,plain,
    ! [X0,X1,X2] :
      ( c_Groups_Ominus__class_Ominus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
      | ~ class_Groups_Oab__group__add(X2) ),
    inference(ennf_transformation,[],[f1893]) ).

fof(f1893,plain,
    ! [X0,X1,X2] :
      ( class_Groups_Oab__group__add(X2)
     => c_Groups_Ominus__class_Ominus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0)) ),
    inference(rectify,[],[f273]) ).

fof(f273,axiom,
    ! [X13,X4,X5] :
      ( class_Groups_Oab__group__add(X5)
     => c_Groups_Ominus__class_Ominus(X5,X4,X13) = c_Groups_Oplus__class_Oplus(X5,X4,c_Groups_Ouminus__class_Ouminus(X5,X13)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ab__diff__minus) ).

fof(f10887,plain,
    spl50_683,
    inference(avatar_split_clause,[],[f4950,f10885]) ).

fof(f10885,plain,
    ( spl50_683
  <=> ! [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,[spl50_683])]) ).

fof(f4950,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,[],[f3692]) ).

fof(f3692,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,[],[f2833]) ).

fof(f2833,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,[],[f2832]) ).

fof(f2832,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,[],[f1871]) ).

fof(f1871,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,[],[f761]) ).

fof(f761,axiom,
    ! [X20,X12,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ~ c_Orderings_Oord__class_Oless(X5,X12,X20)
       => ( c_Orderings_Oord__class_Oless__eq(X5,X12,X20)
        <=> X12 = X20 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__antisym__conv1) ).

fof(f10883,plain,
    spl50_682,
    inference(avatar_split_clause,[],[f4942,f10881]) ).

fof(f10881,plain,
    ( spl50_682
  <=> ! [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,[spl50_682])]) ).

fof(f4942,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,[],[f2819]) ).

fof(f2819,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,[],[f2818]) ).

fof(f2818,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,[],[f1864]) ).

fof(f1864,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,[],[f745]) ).

fof(f745,axiom,
    ! [X7,X9,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( c_Orderings_Oord__class_Oless(X5,X7,X9)
        | X7 = X9
        | c_Orderings_Oord__class_Oless(X5,X9,X7) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__less__linear) ).

fof(f10879,plain,
    spl50_681,
    inference(avatar_split_clause,[],[f4920,f10877]) ).

fof(f10877,plain,
    ( spl50_681
  <=> ! [X2,X0,X1] :
        ( c_Groups_Ominus__class_Ominus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
        | ~ class_Rings_Ocomm__ring__1(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_681])]) ).

fof(f4920,plain,
    ! [X2,X0,X1] :
      ( c_Groups_Ominus__class_Ominus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
      | ~ class_Rings_Ocomm__ring__1(X2) ),
    inference(cnf_transformation,[],[f2789]) ).

fof(f2789,plain,
    ! [X0,X1,X2] :
      ( c_Groups_Ominus__class_Ominus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
      | ~ class_Rings_Ocomm__ring__1(X2) ),
    inference(ennf_transformation,[],[f1846]) ).

fof(f1846,plain,
    ! [X0,X1,X2] :
      ( class_Rings_Ocomm__ring__1(X2)
     => c_Groups_Ominus__class_Ominus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0)) ),
    inference(rectify,[],[f548]) ).

fof(f548,axiom,
    ! [X7,X9,X5] :
      ( class_Rings_Ocomm__ring__1(X5)
     => c_Groups_Ominus__class_Ominus(X5,X9,X7) = c_Groups_Oplus__class_Oplus(X5,X9,c_Groups_Ouminus__class_Ouminus(X5,X7)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J) ).

fof(f10875,plain,
    spl50_680,
    inference(avatar_split_clause,[],[f4891,f10873]) ).

fof(f10873,plain,
    ( spl50_680
  <=> ! [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,[spl50_680])]) ).

fof(f4891,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,[],[f2759]) ).

fof(f2759,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,[],[f2758]) ).

fof(f2758,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,[],[f1826]) ).

fof(f1826,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,[],[f85]) ).

fof(f85,axiom,
    ! [X7,X9,X5] :
      ( class_Rings_Olinordered__idom(X5)
     => ( X7 != X9
       => ( ~ c_Orderings_Oord__class_Oless(X5,X9,X7)
         => c_Orderings_Oord__class_Oless(X5,X7,X9) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE__linordered__idom) ).

fof(f10871,plain,
    spl50_679,
    inference(avatar_split_clause,[],[f4744,f10869]) ).

fof(f10869,plain,
    ( spl50_679
  <=> ! [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,[spl50_679])]) ).

fof(f4744,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,[],[f3633]) ).

fof(f3633,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,[],[f3632]) ).

fof(f3632,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,[],[f1733]) ).

fof(f1733,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,
    ! [X16,X32] :
      ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X32),X16)
    <=> ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X16
        & c_Groups_Oone__class_Oone(tc_Nat_Onat) = X32 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__eq__1__iff) ).

fof(f10867,plain,
    spl50_678,
    inference(avatar_split_clause,[],[f4743,f10865]) ).

fof(f10865,plain,
    ( spl50_678
  <=> ! [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,[spl50_678])]) ).

fof(f4743,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,[],[f3633]) ).

fof(f10863,plain,
    spl50_677,
    inference(avatar_split_clause,[],[f4597,f10861]) ).

fof(f10861,plain,
    ( spl50_677
  <=> ! [X0,X1] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,X1)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_677])]) ).

fof(f4597,plain,
    ! [X0,X1] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,X1)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(cnf_transformation,[],[f2629]) ).

fof(f2629,plain,
    ! [X0,X1] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,X1)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(flattening,[],[f2628]) ).

fof(f2628,plain,
    ! [X0,X1] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,X1)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(ennf_transformation,[],[f1663]) ).

fof(f1663,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,X1,X0)
       => ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,X1) ) ),
    inference(rectify,[],[f870]) ).

fof(f870,axiom,
    ! [X3,X17] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X17)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X3)
       => ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X17) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__dvd__not__less) ).

fof(f10854,plain,
    spl50_676,
    inference(avatar_split_clause,[],[f4592,f10852]) ).

fof(f10852,plain,
    ( spl50_676
  <=> ! [X0,X1] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,X1)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_676])]) ).

fof(f4592,plain,
    ! [X0,X1] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,X1)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(cnf_transformation,[],[f2624]) ).

fof(f2624,plain,
    ! [X0,X1] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,X1)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(flattening,[],[f2623]) ).

fof(f2623,plain,
    ! [X0,X1] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,X1)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(ennf_transformation,[],[f1660]) ).

fof(f1660,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,X1,X0)
       => ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,X1) ) ),
    inference(rectify,[],[f871]) ).

fof(f871,axiom,
    ! [X3,X17] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X17)
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X17,X3)
       => ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X3,X17) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__not__zless) ).

fof(f10850,plain,
    spl50_675,
    inference(avatar_split_clause,[],[f4568,f10848]) ).

fof(f10848,plain,
    ( spl50_675
  <=> ! [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,[spl50_675])]) ).

fof(f4568,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,[],[f2592]) ).

fof(f2592,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,[],[f1637]) ).

fof(f1637,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,[],[f485]) ).

fof(f485,axiom,
    ! [X17,X3] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X17)
     => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X3)) = X17 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add__diff__inverse) ).

fof(f10846,plain,
    spl50_674,
    inference(avatar_split_clause,[],[f4567,f10844]) ).

fof(f10844,plain,
    ( spl50_674
  <=> ! [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,[spl50_674])]) ).

fof(f4567,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,[],[f2591]) ).

fof(f2591,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,[],[f1636]) ).

fof(f1636,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,[],[f462]) ).

fof(f462,axiom,
    ! [X3,X18] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X3)
     => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X18)) = X18 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__diff__cancel) ).

fof(f10842,plain,
    spl50_673,
    inference(avatar_split_clause,[],[f4558,f10840]) ).

fof(f10840,plain,
    ( spl50_673
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_673])]) ).

fof(f4558,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0) ),
    inference(cnf_transformation,[],[f2581]) ).

fof(f2581,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0) ),
    inference(flattening,[],[f2580]) ).

fof(f2580,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0) ),
    inference(ennf_transformation,[],[f1628]) ).

fof(f1628,plain,
    ! [X0,X1] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
       => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
    inference(rectify,[],[f873]) ).

fof(f873,axiom,
    ! [X3,X38] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X38,X3)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
       => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X38,X3) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__imp__le) ).

fof(f10838,plain,
    spl50_672,
    inference(avatar_split_clause,[],[f4551,f10836]) ).

fof(f10836,plain,
    ( spl50_672
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_672])]) ).

fof(f4551,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X0) ),
    inference(cnf_transformation,[],[f2571]) ).

fof(f2571,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X0) ),
    inference(flattening,[],[f2570]) ).

fof(f2570,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X0) ),
    inference(ennf_transformation,[],[f1623]) ).

fof(f1623,plain,
    ! [X0,X1] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,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,X1,X0) ) ),
    inference(rectify,[],[f872]) ).

fof(f872,axiom,
    ! [X3,X14] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X14,X3)
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
       => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X14,X3) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__imp__le) ).

fof(f10834,plain,
    spl50_671,
    inference(avatar_split_clause,[],[f4547,f10832]) ).

fof(f10832,plain,
    ( spl50_671
  <=> ! [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,[spl50_671])]) ).

fof(f4547,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,[],[f2566]) ).

fof(f2566,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,[],[f1620]) ).

fof(f1620,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,[],[f476]) ).

fof(f476,axiom,
    ! [X3,X17] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X3)
     => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X3)) = X17 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__diff__inverse) ).

fof(f10830,plain,
    spl50_670,
    inference(avatar_split_clause,[],[f4538,f10828]) ).

fof(f10828,plain,
    ( spl50_670
  <=> ! [X0,X1] :
        ( c_SEQ_Odecseq(X1,X0)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK27(X0,X1),sK28(X0,X1))
        | ~ class_Orderings_Oorder(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_670])]) ).

fof(f4538,plain,
    ! [X0,X1] :
      ( c_SEQ_Odecseq(X1,X0)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK27(X0,X1),sK28(X0,X1))
      | ~ class_Orderings_Oorder(X1) ),
    inference(cnf_transformation,[],[f3547]) ).

fof(f10826,plain,
    spl50_669,
    inference(avatar_split_clause,[],[f4507,f10824]) ).

fof(f10824,plain,
    ( spl50_669
  <=> ! [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,[spl50_669])]) ).

fof(f4507,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,[],[f3543]) ).

fof(f3543,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,[],[f2526]) ).

fof(f2526,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,[],[f1584]) ).

fof(f1584,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,[],[f562]) ).

fof(f562,axiom,
    ! [X64,X5] :
      ( class_Groups_Ozero(X5)
     => ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X5,X64)
      <=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = X64 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psize__eq__0__iff) ).

fof(f10822,plain,
    spl50_668,
    inference(avatar_split_clause,[],[f4458,f10820]) ).

fof(f10820,plain,
    ( spl50_668
  <=> ! [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,[spl50_668])]) ).

fof(f4458,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,[],[f3532]) ).

fof(f3532,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,[],[f2487]) ).

fof(f2487,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,[],[f1545]) ).

fof(f1545,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,[],[f329]) ).

fof(f329,axiom,
    ! [X24,X5] :
      ( class_Rings_Olinordered__idom(X5)
     => ( c_Orderings_Oord__class_Oless(X5,X24,c_Groups_Ouminus__class_Ouminus(X5,X24))
      <=> c_Orderings_Oord__class_Oless(X5,X24,c_Groups_Ozero__class_Ozero(X5)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__minus__self__iff) ).

fof(f10818,plain,
    spl50_667,
    inference(avatar_split_clause,[],[f4457,f10816]) ).

fof(f10816,plain,
    ( spl50_667
  <=> ! [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,[spl50_667])]) ).

fof(f4457,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,[],[f3532]) ).

fof(f10814,plain,
    ( spl50_666
    | ~ spl50_472
    | ~ spl50_622 ),
    inference(avatar_split_clause,[],[f10510,f9967,f8684,f10812]) ).

fof(f10812,plain,
    ( spl50_666
  <=> ! [X0] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_666])]) ).

fof(f10510,plain,
    ( ! [X0] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),X0) )
    | ~ spl50_472
    | ~ spl50_622 ),
    inference(resolution,[],[f9968,f8686]) ).

fof(f10810,plain,
    spl50_665,
    inference(avatar_split_clause,[],[f4453,f10808]) ).

fof(f10808,plain,
    ( spl50_665
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
        | c_Groups_Oone__class_Oone(X1) != c_Groups_Osgn__class_Osgn(X1,X0)
        | ~ class_Rings_Olinordered__idom(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_665])]) ).

fof(f4453,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
      | c_Groups_Oone__class_Oone(X1) != c_Groups_Osgn__class_Osgn(X1,X0)
      | ~ class_Rings_Olinordered__idom(X1) ),
    inference(cnf_transformation,[],[f3530]) ).

fof(f3530,plain,
    ! [X0,X1] :
      ( ( ( c_Groups_Oone__class_Oone(X1) = c_Groups_Osgn__class_Osgn(X1,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_Groups_Oone__class_Oone(X1) != c_Groups_Osgn__class_Osgn(X1,X0) ) )
      | ~ class_Rings_Olinordered__idom(X1) ),
    inference(nnf_transformation,[],[f2485]) ).

fof(f2485,plain,
    ! [X0,X1] :
      ( ( c_Groups_Oone__class_Oone(X1) = c_Groups_Osgn__class_Osgn(X1,X0)
      <=> c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
      | ~ class_Rings_Olinordered__idom(X1) ),
    inference(ennf_transformation,[],[f1543]) ).

fof(f1543,plain,
    ! [X0,X1] :
      ( class_Rings_Olinordered__idom(X1)
     => ( c_Groups_Oone__class_Oone(X1) = c_Groups_Osgn__class_Osgn(X1,X0)
      <=> c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) ) ),
    inference(rectify,[],[f845]) ).

fof(f845,axiom,
    ! [X24,X5] :
      ( class_Rings_Olinordered__idom(X5)
     => ( c_Groups_Oone__class_Oone(X5) = c_Groups_Osgn__class_Osgn(X5,X24)
      <=> c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X24) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__1__pos) ).

fof(f10806,plain,
    spl50_664,
    inference(avatar_split_clause,[],[f4452,f10804]) ).

fof(f10804,plain,
    ( spl50_664
  <=> ! [X0,X1] :
        ( c_Groups_Oone__class_Oone(X1) = c_Groups_Osgn__class_Osgn(X1,X0)
        | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
        | ~ class_Rings_Olinordered__idom(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_664])]) ).

fof(f4452,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(X1) = c_Groups_Osgn__class_Osgn(X1,X0)
      | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
      | ~ class_Rings_Olinordered__idom(X1) ),
    inference(cnf_transformation,[],[f2484]) ).

fof(f2484,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(X1) = c_Groups_Osgn__class_Osgn(X1,X0)
      | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
      | ~ class_Rings_Olinordered__idom(X1) ),
    inference(flattening,[],[f2483]) ).

fof(f2483,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(X1) = c_Groups_Osgn__class_Osgn(X1,X0)
      | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
      | ~ class_Rings_Olinordered__idom(X1) ),
    inference(ennf_transformation,[],[f1542]) ).

fof(f1542,plain,
    ! [X0,X1] :
      ( class_Rings_Olinordered__idom(X1)
     => ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
       => c_Groups_Oone__class_Oone(X1) = c_Groups_Osgn__class_Osgn(X1,X0) ) ),
    inference(rectify,[],[f846]) ).

fof(f846,axiom,
    ! [X4,X5] :
      ( class_Rings_Olinordered__idom(X5)
     => ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X4)
       => c_Groups_Oone__class_Oone(X5) = c_Groups_Osgn__class_Osgn(X5,X4) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__pos) ).

fof(f10802,plain,
    spl50_663,
    inference(avatar_split_clause,[],[f4426,f10800]) ).

fof(f10800,plain,
    ( spl50_663
  <=> ! [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,[spl50_663])]) ).

fof(f4426,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,[],[f3520]) ).

fof(f3520,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,[],[f2467]) ).

fof(f2467,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,[],[f1528]) ).

fof(f1528,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,[],[f565]) ).

fof(f565,axiom,
    ! [X24,X5] :
      ( class_Groups_Olinordered__ab__group__add(X5)
     => ( c_Groups_Ozero__class_Ozero(X5) = c_Groups_Oplus__class_Oplus(X5,X24,X24)
      <=> c_Groups_Ozero__class_Ozero(X5) = X24 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__eq__0__iff) ).

fof(f10798,plain,
    spl50_662,
    inference(avatar_split_clause,[],[f4425,f10796]) ).

fof(f10796,plain,
    ( spl50_662
  <=> ! [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,[spl50_662])]) ).

fof(f4425,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,[],[f3519]) ).

fof(f3519,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,[],[f2466]) ).

fof(f2466,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,[],[f1527]) ).

fof(f1527,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,[],[f330]) ).

fof(f330,axiom,
    ! [X24,X5] :
      ( class_Groups_Olinordered__ab__group__add(X5)
     => ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ouminus__class_Ouminus(X5,X24),X24)
      <=> c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X24) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__less__nonneg) ).

fof(f10794,plain,
    spl50_661,
    inference(avatar_split_clause,[],[f4424,f10792]) ).

fof(f10792,plain,
    ( spl50_661
  <=> ! [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,[spl50_661])]) ).

fof(f4424,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,[],[f3519]) ).

fof(f10790,plain,
    spl50_660,
    inference(avatar_split_clause,[],[f4423,f10788]) ).

fof(f10788,plain,
    ( spl50_660
  <=> ! [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,[spl50_660])]) ).

fof(f4423,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,[],[f3518]) ).

fof(f3518,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,[],[f2465]) ).

fof(f2465,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,[],[f1526]) ).

fof(f1526,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,[],[f328]) ).

fof(f328,axiom,
    ! [X24,X5] :
      ( class_Groups_Olinordered__ab__group__add(X5)
     => ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ouminus__class_Ouminus(X5,X24),X24)
      <=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X24) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__le__self__iff) ).

fof(f10786,plain,
    spl50_659,
    inference(avatar_split_clause,[],[f4422,f10784]) ).

fof(f10784,plain,
    ( spl50_659
  <=> ! [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,[spl50_659])]) ).

fof(f4422,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,[],[f3518]) ).

fof(f10782,plain,
    spl50_658,
    inference(avatar_split_clause,[],[f4421,f10780]) ).

fof(f10780,plain,
    ( spl50_658
  <=> ! [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,[spl50_658])]) ).

fof(f4421,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,[],[f3517]) ).

fof(f3517,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,[],[f2464]) ).

fof(f2464,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,[],[f1525]) ).

fof(f1525,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,[],[f326]) ).

fof(f326,axiom,
    ! [X24,X5] :
      ( class_Groups_Olinordered__ab__group__add(X5)
     => ( c_Orderings_Oord__class_Oless__eq(X5,X24,c_Groups_Ouminus__class_Ouminus(X5,X24))
      <=> c_Orderings_Oord__class_Oless__eq(X5,X24,c_Groups_Ozero__class_Ozero(X5)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__minus__self__iff) ).

fof(f10778,plain,
    spl50_657,
    inference(avatar_split_clause,[],[f4420,f10776]) ).

fof(f10776,plain,
    ( spl50_657
  <=> ! [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,[spl50_657])]) ).

fof(f4420,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,[],[f3517]) ).

fof(f10774,plain,
    spl50_656,
    inference(avatar_split_clause,[],[f4402,f10772]) ).

fof(f4402,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X0))
      | c_Groups_Ozero__class_Ozero(X1) = X0
      | ~ class_RealVector_Oreal__normed__vector(X1) ),
    inference(cnf_transformation,[],[f3510]) ).

fof(f3510,plain,
    ! [X0,X1] :
      ( ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X0))
          | c_Groups_Ozero__class_Ozero(X1) = X0 )
        & ( c_Groups_Ozero__class_Ozero(X1) != X0
          | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X0)) ) )
      | ~ class_RealVector_Oreal__normed__vector(X1) ),
    inference(nnf_transformation,[],[f2452]) ).

fof(f2452,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X0))
      <=> c_Groups_Ozero__class_Ozero(X1) != X0 )
      | ~ class_RealVector_Oreal__normed__vector(X1) ),
    inference(ennf_transformation,[],[f1513]) ).

fof(f1513,plain,
    ! [X0,X1] :
      ( class_RealVector_Oreal__normed__vector(X1)
     => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X0))
      <=> c_Groups_Ozero__class_Ozero(X1) != X0 ) ),
    inference(rectify,[],[f11]) ).

fof(f11,axiom,
    ! [X12,X5] :
      ( class_RealVector_Oreal__normed__vector(X5)
     => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5,X12))
      <=> c_Groups_Ozero__class_Ozero(X5) != X12 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__norm__iff) ).

fof(f10770,plain,
    spl50_655,
    inference(avatar_split_clause,[],[f4399,f10768]) ).

fof(f10768,plain,
    ( spl50_655
  <=> ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(X1) = X0
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | ~ class_RealVector_Oreal__normed__vector(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_655])]) ).

fof(f4399,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X1) = X0
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
      | ~ class_RealVector_Oreal__normed__vector(X1) ),
    inference(cnf_transformation,[],[f3509]) ).

fof(f3509,plain,
    ! [X0,X1] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
          | c_Groups_Ozero__class_Ozero(X1) != X0 )
        & ( c_Groups_Ozero__class_Ozero(X1) = X0
          | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) )
      | ~ class_RealVector_Oreal__normed__vector(X1) ),
    inference(nnf_transformation,[],[f2451]) ).

fof(f2451,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
      <=> c_Groups_Ozero__class_Ozero(X1) = X0 )
      | ~ class_RealVector_Oreal__normed__vector(X1) ),
    inference(ennf_transformation,[],[f1512]) ).

fof(f1512,plain,
    ! [X0,X1] :
      ( class_RealVector_Oreal__normed__vector(X1)
     => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
      <=> c_Groups_Ozero__class_Ozero(X1) = X0 ) ),
    inference(rectify,[],[f77]) ).

fof(f77,axiom,
    ! [X12,X5] :
      ( class_RealVector_Oreal__normed__vector(X5)
     => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,X12),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
      <=> c_Groups_Ozero__class_Ozero(X5) = X12 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__le__zero__iff) ).

fof(f10766,plain,
    spl50_654,
    inference(avatar_split_clause,[],[f4392,f10764]) ).

fof(f10764,plain,
    ( spl50_654
  <=> ! [X0,X1] :
        ( c_Groups_Osgn__class_Osgn(X1,c_Groups_Ouminus__class_Ouminus(X1,X0)) = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Osgn__class_Osgn(X1,X0))
        | ~ class_RealVector_Oreal__normed__vector(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_654])]) ).

fof(f4392,plain,
    ! [X0,X1] :
      ( c_Groups_Osgn__class_Osgn(X1,c_Groups_Ouminus__class_Ouminus(X1,X0)) = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Osgn__class_Osgn(X1,X0))
      | ~ class_RealVector_Oreal__normed__vector(X1) ),
    inference(cnf_transformation,[],[f2447]) ).

fof(f2447,plain,
    ! [X0,X1] :
      ( c_Groups_Osgn__class_Osgn(X1,c_Groups_Ouminus__class_Ouminus(X1,X0)) = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Osgn__class_Osgn(X1,X0))
      | ~ class_RealVector_Oreal__normed__vector(X1) ),
    inference(ennf_transformation,[],[f1508]) ).

fof(f1508,plain,
    ! [X0,X1] :
      ( class_RealVector_Oreal__normed__vector(X1)
     => c_Groups_Osgn__class_Osgn(X1,c_Groups_Ouminus__class_Ouminus(X1,X0)) = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Osgn__class_Osgn(X1,X0)) ),
    inference(rectify,[],[f836]) ).

fof(f836,axiom,
    ! [X9,X5] :
      ( class_RealVector_Oreal__normed__vector(X5)
     => c_Groups_Osgn__class_Osgn(X5,c_Groups_Ouminus__class_Ouminus(X5,X9)) = c_Groups_Ouminus__class_Ouminus(X5,c_Groups_Osgn__class_Osgn(X5,X9)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__minus) ).

fof(f10762,plain,
    spl50_653,
    inference(avatar_split_clause,[],[f4384,f10760]) ).

fof(f10760,plain,
    ( spl50_653
  <=> ! [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,[spl50_653])]) ).

fof(f4384,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,[],[f2435]) ).

fof(f2435,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,[],[f2434]) ).

fof(f2434,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,[],[f1500]) ).

fof(f1500,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,[],[f114]) ).

fof(f114,axiom,
    ! [X4,X5] :
      ( class_Rings_Odivision__ring(X5)
     => ( c_Groups_Ozero__class_Ozero(X5) != X4
       => c_Rings_Oinverse__class_Oinverse(X5,c_Rings_Oinverse__class_Oinverse(X5,X4)) = X4 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__inverse__inverse__eq) ).

fof(f10758,plain,
    spl50_652,
    inference(avatar_split_clause,[],[f4380,f10756]) ).

fof(f10756,plain,
    ( spl50_652
  <=> ! [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,[spl50_652])]) ).

fof(f4380,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,[],[f2430]) ).

fof(f2430,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,[],[f1497]) ).

fof(f1497,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,[],[f322]) ).

fof(f322,axiom,
    ! [X4,X5] :
      ( class_Rings_Odivision__ring__inverse__zero(X5)
     => c_Rings_Oinverse__class_Oinverse(X5,c_Groups_Ouminus__class_Ouminus(X5,X4)) = c_Groups_Ouminus__class_Ouminus(X5,c_Rings_Oinverse__class_Oinverse(X5,X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__minus__eq) ).

fof(f10754,plain,
    spl50_651,
    inference(avatar_split_clause,[],[f4328,f10752]) ).

fof(f10752,plain,
    ( spl50_651
  <=> ! [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,[spl50_651])]) ).

fof(f4328,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,[],[f1459]) ).

fof(f1459,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,[],[f371]) ).

fof(f371,axiom,
    ! [X3,X17] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X17),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__commute) ).

fof(f10750,plain,
    spl50_650,
    inference(avatar_split_clause,[],[f4327,f10748]) ).

fof(f10748,plain,
    ( spl50_650
  <=> ! [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,[spl50_650])]) ).

fof(f4327,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,[],[f1458]) ).

fof(f1458,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,[],[f581]) ).

fof(f581,axiom,
    ! [X15,X14] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X14),X15) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X15),X14),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__commute) ).

fof(f10746,plain,
    spl50_649,
    inference(avatar_split_clause,[],[f4326,f10744]) ).

fof(f10744,plain,
    ( spl50_649
  <=> ! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_649])]) ).

fof(f4326,plain,
    ! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),X1),
    inference(cnf_transformation,[],[f1457]) ).

fof(f1457,plain,
    ! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),X1),
    inference(rectify,[],[f208]) ).

fof(f208,axiom,
    ! [X15,X14] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X14),X15) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X15),X14),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__commute) ).

fof(f10742,plain,
    spl50_648,
    inference(avatar_split_clause,[],[f4275,f10740]) ).

fof(f10740,plain,
    ( spl50_648
  <=> ! [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,[spl50_648])]) ).

fof(f4275,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,[],[f2387]) ).

fof(f2387,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,[],[f1416]) ).

fof(f1416,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,[],[f602]) ).

fof(f602,axiom,
    ! [X5] :
      ( class_Rings_Ocomm__semiring__1(X5)
     => c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X5)) = c_Polynomial_OpCons(X5,c_Groups_Oone__class_Oone(X5),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__poly__def) ).

fof(f10738,plain,
    spl50_647,
    inference(avatar_split_clause,[],[f4261,f10736]) ).

fof(f10736,plain,
    ( spl50_647
  <=> ! [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,[spl50_647])]) ).

fof(f4261,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,[],[f2373]) ).

fof(f2373,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,[],[f1402]) ).

fof(f1402,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,[],[f604]) ).

fof(f604,axiom,
    ! [X5] :
      ( class_Groups_Ozero(X5)
     => c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = c_Polynomial_OpCons(X5,c_Groups_Ozero__class_Ozero(X5),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pCons__0__0) ).

fof(f10730,plain,
    ( ~ spl50_646
    | spl50_645
    | ~ spl50_352
    | ~ spl50_618 ),
    inference(avatar_split_clause,[],[f10459,f9951,f7717,f10473,f10727]) ).

fof(f10727,plain,
    ( spl50_646
  <=> class_Groups_Ogroup__add(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_646])]) ).

fof(f10473,plain,
    ( spl50_645
  <=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_645])]) ).

fof(f7717,plain,
    ( spl50_352
  <=> ! [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,[spl50_352])]) ).

fof(f9951,plain,
    ( spl50_618
  <=> ! [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,[spl50_618])]) ).

fof(f10459,plain,
    ( ! [X0] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
        | ~ class_Groups_Ogroup__add(tc_Nat_Onat) )
    | ~ spl50_352
    | ~ spl50_618 ),
    inference(trivial_inequality_removal,[],[f10456]) ).

fof(f10456,plain,
    ( ! [X0] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
        | ~ class_Groups_Ogroup__add(tc_Nat_Onat) )
    | ~ spl50_352
    | ~ spl50_618 ),
    inference(superposition,[],[f9952,f7718]) ).

fof(f7718,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)
    | ~ spl50_352 ),
    inference(avatar_component_clause,[],[f7717]) ).

fof(f9952,plain,
    ( ! [X2,X0,X1] :
        ( c_Groups_Ozero__class_Ozero(X2) != c_Groups_Ominus__class_Ominus(X2,X1,X0)
        | X0 = X1
        | ~ class_Groups_Ogroup__add(X2) )
    | ~ spl50_618 ),
    inference(avatar_component_clause,[],[f9951]) ).

fof(f10475,plain,
    ( ~ spl50_644
    | spl50_645
    | ~ spl50_352
    | ~ spl50_617 ),
    inference(avatar_split_clause,[],[f10451,f9947,f7717,f10473,f10469]) ).

fof(f10469,plain,
    ( spl50_644
  <=> class_Groups_Oab__group__add(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_644])]) ).

fof(f9947,plain,
    ( spl50_617
  <=> ! [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,[spl50_617])]) ).

fof(f10451,plain,
    ( ! [X0] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
        | ~ class_Groups_Oab__group__add(tc_Nat_Onat) )
    | ~ spl50_352
    | ~ spl50_617 ),
    inference(trivial_inequality_removal,[],[f10448]) ).

fof(f10448,plain,
    ( ! [X0] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
        | ~ class_Groups_Oab__group__add(tc_Nat_Onat) )
    | ~ spl50_352
    | ~ spl50_617 ),
    inference(superposition,[],[f9948,f7718]) ).

fof(f9948,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) )
    | ~ spl50_617 ),
    inference(avatar_component_clause,[],[f9947]) ).

fof(f10380,plain,
    ( spl50_643
    | ~ spl50_13
    | ~ spl50_399 ),
    inference(avatar_split_clause,[],[f8141,f7938,f6111,f10378]) ).

fof(f10378,plain,
    ( spl50_643
  <=> ! [X0] : c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X0)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_643])]) ).

fof(f6111,plain,
    ( spl50_13
  <=> class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_13])]) ).

fof(f7938,plain,
    ( spl50_399
  <=> ! [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,[spl50_399])]) ).

fof(f8141,plain,
    ( ! [X0] : c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X0)) = X0
    | ~ spl50_13
    | ~ spl50_399 ),
    inference(resolution,[],[f7939,f6113]) ).

fof(f6113,plain,
    ( class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal)
    | ~ spl50_13 ),
    inference(avatar_component_clause,[],[f6111]) ).

fof(f7939,plain,
    ( ! [X0,X1] :
        ( ~ class_Rings_Odivision__ring__inverse__zero(X1)
        | c_Rings_Oinverse__class_Oinverse(X1,c_Rings_Oinverse__class_Oinverse(X1,X0)) = X0 )
    | ~ spl50_399 ),
    inference(avatar_component_clause,[],[f7938]) ).

fof(f10273,plain,
    ( spl50_642
    | ~ spl50_12
    | ~ spl50_399 ),
    inference(avatar_split_clause,[],[f8140,f7938,f6106,f10271]) ).

fof(f10271,plain,
    ( spl50_642
  <=> ! [X0] : c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,X0)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_642])]) ).

fof(f6106,plain,
    ( spl50_12
  <=> class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_12])]) ).

fof(f8140,plain,
    ( ! [X0] : c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,X0)) = X0
    | ~ spl50_12
    | ~ spl50_399 ),
    inference(resolution,[],[f7939,f6108]) ).

fof(f6108,plain,
    ( class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex)
    | ~ spl50_12 ),
    inference(avatar_component_clause,[],[f6106]) ).

fof(f10141,plain,
    ( spl50_641
    | ~ spl50_100
    | ~ spl50_221
    | ~ spl50_404
    | ~ spl50_566 ),
    inference(avatar_split_clause,[],[f10088,f9739,f7958,f7148,f6546,f10139]) ).

fof(f10139,plain,
    ( spl50_641
  <=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Nat__Transfer_Otsub(X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_641])]) ).

fof(f7148,plain,
    ( spl50_221
  <=> ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_221])]) ).

fof(f9739,plain,
    ( spl50_566
  <=> ! [X0,X1] :
        ( c_Nat__Transfer_Otsub(X0,X1) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,X1)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_566])]) ).

fof(f10088,plain,
    ( ! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Nat__Transfer_Otsub(X0,X0)
    | ~ spl50_100
    | ~ spl50_221
    | ~ spl50_404
    | ~ spl50_566 ),
    inference(forward_demodulation,[],[f10077,f8147]) ).

fof(f10077,plain,
    ( ! [X0] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,X0) = c_Nat__Transfer_Otsub(X0,X0)
    | ~ spl50_221
    | ~ spl50_566 ),
    inference(resolution,[],[f9740,f7149]) ).

fof(f7149,plain,
    ( ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X0)
    | ~ spl50_221 ),
    inference(avatar_component_clause,[],[f7148]) ).

fof(f9740,plain,
    ( ! [X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
        | c_Nat__Transfer_Otsub(X0,X1) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,X1) )
    | ~ spl50_566 ),
    inference(avatar_component_clause,[],[f9739]) ).

fof(f10052,plain,
    spl50_640,
    inference(avatar_split_clause,[],[f5812,f10050]) ).

fof(f10050,plain,
    ( spl50_640
  <=> ! [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,[spl50_640])]) ).

fof(f5812,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,[],[f4982]) ).

fof(f4982,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,[],[f3704]) ).

fof(f10048,plain,
    spl50_639,
    inference(avatar_split_clause,[],[f5811,f10046]) ).

fof(f10046,plain,
    ( spl50_639
  <=> ! [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,[spl50_639])]) ).

fof(f5811,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,[],[f4978]) ).

fof(f4978,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,[],[f3702]) ).

fof(f10044,plain,
    spl50_638,
    inference(avatar_split_clause,[],[f5802,f10042]) ).

fof(f10042,plain,
    ( spl50_638
  <=> ! [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,[spl50_638])]) ).

fof(f5802,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,[],[f4906]) ).

fof(f4906,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,[],[f3686]) ).

fof(f10040,plain,
    spl50_637,
    inference(avatar_split_clause,[],[f5801,f10038]) ).

fof(f10038,plain,
    ( spl50_637
  <=> ! [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,[spl50_637])]) ).

fof(f5801,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,[],[f4907]) ).

fof(f4907,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,[],[f3686]) ).

fof(f10036,plain,
    spl50_636,
    inference(avatar_split_clause,[],[f5716,f10034]) ).

fof(f10034,plain,
    ( spl50_636
  <=> ! [X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
        | ~ class_Rings_Olinordered__idom(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_636])]) ).

fof(f5716,plain,
    ! [X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
      | ~ class_Rings_Olinordered__idom(X1) ),
    inference(equality_resolution,[],[f4447]) ).

fof(f4447,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X1),X0)
      | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) != X0
      | ~ class_Rings_Olinordered__idom(X1) ),
    inference(cnf_transformation,[],[f2478]) ).

fof(f2478,plain,
    ! [X0,X1] :
      ( ( ( ( ( c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X1),X0) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1)))
              | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0) )
            & ( c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X1),X0) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1))
              | ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X1),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_Polynomial_Opoly(X1)) = c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X1),X0)
          | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) != X0 ) )
      | ~ class_Rings_Olinordered__idom(X1) ),
    inference(ennf_transformation,[],[f1539]) ).

fof(f1539,plain,
    ! [X0,X1] :
      ( class_Rings_Olinordered__idom(X1)
     => ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) != X0
         => ( ( ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0)
             => c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X1),X0) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1))) )
            & ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0)
             => c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X1),X0) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1)) ) ) )
        & ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X0
         => c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X1),X0) ) ) ),
    inference(rectify,[],[f803]) ).

fof(f803,axiom,
    ! [X9,X5] :
      ( class_Rings_Olinordered__idom(X5)
     => ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) != X9
         => ( ( ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X5),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X9)
             => c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X5),X9) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X5),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X5))) )
            & ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X5),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X9)
             => c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X5)) = c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X5),X9) ) ) )
        & ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = X9
         => c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X5),X9) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__poly__def) ).

fof(f10032,plain,
    ~ spl50_635,
    inference(avatar_split_clause,[],[f5701,f10029]) ).

fof(f10029,plain,
    ( spl50_635
  <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_635])]) ).

fof(f5701,plain,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),
    inference(equality_resolution,[],[f4299]) ).

fof(f4299,plain,
    ! [X0] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),X0))
      | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X0 ),
    inference(cnf_transformation,[],[f3490]) ).

fof(f10027,plain,
    spl50_634,
    inference(avatar_split_clause,[],[f5638,f10025]) ).

fof(f10025,plain,
    ( spl50_634
  <=> ! [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,[spl50_634])]) ).

fof(f5638,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,[],[f4683,f4164]) ).

fof(f4683,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,[],[f3599]) ).

fof(f3599,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,[],[f1712]) ).

fof(f1712,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,[],[f977]) ).

fof(f977,axiom,
    ! [X16,X32] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X32,c_Nat_OSuc(X16))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X32,X16) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq__le) ).

fof(f10018,plain,
    spl50_633,
    inference(avatar_split_clause,[],[f5625,f10016]) ).

fof(f10016,plain,
    ( spl50_633
  <=> ! [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,[spl50_633])]) ).

fof(f5625,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,[],[f4639,f4164]) ).

fof(f4639,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,[],[f3565]) ).

fof(f3565,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,[],[f1694]) ).

fof(f1694,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,[],[f974]) ).

fof(f974,axiom,
    ! [X16,X32] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X32,X16)
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X16,c_Nat_OSuc(X32)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__eq) ).

fof(f10014,plain,
    spl50_632,
    inference(avatar_split_clause,[],[f5624,f10012]) ).

fof(f10012,plain,
    ( spl50_632
  <=> ! [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,[spl50_632])]) ).

fof(f5624,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,[],[f4640,f4164]) ).

fof(f4640,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,[],[f3565]) ).

fof(f10010,plain,
    spl50_631,
    inference(avatar_split_clause,[],[f5623,f10008]) ).

fof(f10008,plain,
    ( spl50_631
  <=> ! [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,[spl50_631])]) ).

fof(f5623,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,[],[f4637,f4164]) ).

fof(f4637,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,[],[f3564]) ).

fof(f3564,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,[],[f1693]) ).

fof(f1693,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,[],[f954]) ).

fof(f954,axiom,
    ! [X16,X32] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X32,X16)
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X16),X32) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__eq__eq) ).

fof(f10006,plain,
    spl50_630,
    inference(avatar_split_clause,[],[f5622,f10004]) ).

fof(f10004,plain,
    ( spl50_630
  <=> ! [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,[spl50_630])]) ).

fof(f5622,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,[],[f4638,f4164]) ).

fof(f4638,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,[],[f3564]) ).

fof(f10002,plain,
    spl50_629,
    inference(avatar_split_clause,[],[f5615,f10000]) ).

fof(f10000,plain,
    ( spl50_629
  <=> ! [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,[spl50_629])]) ).

fof(f5615,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,[],[f4605,f4164]) ).

fof(f4605,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,[],[f2637]) ).

fof(f2637,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,[],[f1669]) ).

fof(f1669,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,[],[f982]) ).

fof(f982,axiom,
    ! [X3,X17] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X17),X3)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__lessD) ).

fof(f9998,plain,
    spl50_628,
    inference(avatar_split_clause,[],[f5607,f9996]) ).

fof(f9996,plain,
    ( spl50_628
  <=> ! [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,[spl50_628])]) ).

fof(f5607,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,[],[f4581,f4164]) ).

fof(f4581,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,[],[f2606]) ).

fof(f2606,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,[],[f1649]) ).

fof(f1649,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,[],[f980]) ).

fof(f980,axiom,
    ! [X3,X17] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X3)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X17),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__leI) ).

fof(f9994,plain,
    spl50_627,
    inference(avatar_split_clause,[],[f5603,f9992]) ).

fof(f9992,plain,
    ( spl50_627
  <=> ! [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,[spl50_627])]) ).

fof(f5603,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,[],[f4565,f4164]) ).

fof(f4565,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,[],[f2589]) ).

fof(f2589,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,[],[f1634]) ).

fof(f1634,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,[],[f979]) ).

fof(f979,axiom,
    ! [X3,X17] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X3)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,c_Nat_OSuc(X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__less__Suc) ).

fof(f9990,plain,
    spl50_626,
    inference(avatar_split_clause,[],[f5222,f9988]) ).

fof(f9988,plain,
    ( spl50_626
  <=> ! [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,[spl50_626])]) ).

fof(f5222,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,[],[f3776]) ).

fof(f3776,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,[],[f2052]) ).

fof(f2052,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,[],[f360]) ).

fof(f360,axiom,
    ! [X16,X36,X32] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X32,X36) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X16,X36)
    <=> X16 = X32 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__right__cancel) ).

fof(f9986,plain,
    spl50_625,
    inference(avatar_split_clause,[],[f5220,f9984]) ).

fof(f9984,plain,
    ( spl50_625
  <=> ! [X2,X0,X1] :
        ( X0 = X1
        | 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,[spl50_625])]) ).

fof(f5220,plain,
    ! [X2,X0,X1] :
      ( X0 = X1
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0) ),
    inference(cnf_transformation,[],[f3775]) ).

fof(f3775,plain,
    ! [X0,X1,X2] :
      ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)
        | X0 != X1 )
      & ( X0 = X1
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0) ) ),
    inference(nnf_transformation,[],[f2051]) ).

fof(f2051,plain,
    ! [X0,X1,X2] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)
    <=> X0 = X1 ),
    inference(rectify,[],[f361]) ).

fof(f361,axiom,
    ! [X16,X32,X36] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X36,X32) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X36,X16)
    <=> X16 = X32 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel) ).

fof(f9982,plain,
    spl50_624,
    inference(avatar_split_clause,[],[f5120,f9980]) ).

fof(f9980,plain,
    ( spl50_624
  <=> ! [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,[spl50_624])]) ).

fof(f5120,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,[],[f3008]) ).

fof(f3008,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,[],[f3007]) ).

fof(f3007,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,[],[f1995]) ).

fof(f1995,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,[],[f366]) ).

fof(f366,axiom,
    ! [X38,X39,X18] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X39)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X39,X38)
       => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X38) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__trans) ).

fof(f9973,plain,
    spl50_623,
    inference(avatar_split_clause,[],[f5104,f9971]) ).

fof(f9971,plain,
    ( spl50_623
  <=> ! [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,[spl50_623])]) ).

fof(f5104,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,[],[f2991]) ).

fof(f2991,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,[],[f2990]) ).

fof(f2990,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,[],[f1979]) ).

fof(f1979,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,[],[f671]) ).

fof(f671,axiom,
    ! [X38,X39,X18] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X18,X39)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X39,X38)
       => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X18,X38) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__trans) ).

fof(f9969,plain,
    spl50_622,
    inference(avatar_split_clause,[],[f5102,f9967]) ).

fof(f5102,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1) ),
    inference(cnf_transformation,[],[f2988]) ).

fof(f2988,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1) ),
    inference(flattening,[],[f2987]) ).

fof(f2987,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1) ),
    inference(ennf_transformation,[],[f1977]) ).

fof(f1977,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1)
     => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
       => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X0) ) ),
    inference(rectify,[],[f203]) ).

fof(f203,axiom,
    ! [X38,X39,X18] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X18,X39)
     => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X39,X38)
       => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X18,X38) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__trans) ).

fof(f9965,plain,
    spl50_621,
    inference(avatar_split_clause,[],[f5097,f9963]) ).

fof(f9963,plain,
    ( spl50_621
  <=> ! [X2,X0,X1] :
        ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X0)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_621])]) ).

fof(f5097,plain,
    ! [X2,X0,X1] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X0)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
    inference(cnf_transformation,[],[f2981]) ).

fof(f2981,plain,
    ! [X0,X1,X2] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X0)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
    inference(flattening,[],[f2980]) ).

fof(f2980,plain,
    ! [X0,X1,X2] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X0)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
    inference(ennf_transformation,[],[f1973]) ).

fof(f1973,plain,
    ! [X0,X1,X2] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0)
       => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X0) ) ),
    inference(rectify,[],[f904]) ).

fof(f904,axiom,
    ! [X14,X7,X9] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X7)
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X7,X14)
       => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X14) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oorder__trans) ).

fof(f9961,plain,
    spl50_620,
    inference(avatar_split_clause,[],[f5031,f9959]) ).

fof(f9959,plain,
    ( spl50_620
  <=> ! [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,[spl50_620])]) ).

fof(f5031,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,[],[f3717]) ).

fof(f3717,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,[],[f2910]) ).

fof(f2910,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,[],[f1926]) ).

fof(f1926,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,[],[f531]) ).

fof(f531,axiom,
    ! [X24,X21,X5] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5)
     => ( c_Groups_Oplus__class_Oplus(X5,X21,X24) = X21
      <=> c_Groups_Ozero__class_Ozero(X5) = X24 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__iff) ).

fof(f9957,plain,
    spl50_619,
    inference(avatar_split_clause,[],[f5018,f9955]) ).

fof(f9955,plain,
    ( spl50_619
  <=> ! [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,[spl50_619])]) ).

fof(f5018,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,[],[f3716]) ).

fof(f3716,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,[],[f2887]) ).

fof(f2887,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,[],[f1914]) ).

fof(f1914,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,[],[f276]) ).

fof(f276,axiom,
    ! [X21,X24,X5] :
      ( class_Groups_Ogroup__add(X5)
     => ( c_Groups_Ouminus__class_Ouminus(X5,X24) = c_Groups_Ouminus__class_Ouminus(X5,X21)
      <=> X21 = X24 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__equal__iff__equal) ).

fof(f9953,plain,
    spl50_618,
    inference(avatar_split_clause,[],[f5014,f9951]) ).

fof(f5014,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,[],[f3714]) ).

fof(f3714,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,[],[f2885]) ).

fof(f2885,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,[],[f1912]) ).

fof(f1912,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,[],[f283]) ).

fof(f283,axiom,
    ! [X21,X24,X5] :
      ( class_Groups_Ogroup__add(X5)
     => ( c_Groups_Ozero__class_Ozero(X5) = c_Groups_Ominus__class_Ominus(X5,X24,X21)
      <=> X21 = X24 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_right__minus__eq) ).

fof(f9949,plain,
    spl50_617,
    inference(avatar_split_clause,[],[f4999,f9947]) ).

fof(f4999,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,[],[f3710]) ).

fof(f3710,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,[],[f2872]) ).

fof(f2872,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,[],[f1900]) ).

fof(f1900,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,[],[f284]) ).

fof(f284,axiom,
    ! [X21,X24,X5] :
      ( class_Groups_Oab__group__add(X5)
     => ( X21 = X24
      <=> c_Groups_Ozero__class_Ozero(X5) = c_Groups_Ominus__class_Ominus(X5,X24,X21) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__iff__diff__eq__0) ).

fof(f9945,plain,
    spl50_616,
    inference(avatar_split_clause,[],[f4925,f9943]) ).

fof(f9943,plain,
    ( spl50_616
  <=> ! [X2,X0,X1] :
        ( c_Rings_Odvd__class_Odvd(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)
        | ~ c_Rings_Odvd__class_Odvd(X2,X1,X0)
        | ~ class_Rings_Ocomm__ring__1(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_616])]) ).

fof(f4925,plain,
    ! [X2,X0,X1] :
      ( c_Rings_Odvd__class_Odvd(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)
      | ~ c_Rings_Odvd__class_Odvd(X2,X1,X0)
      | ~ class_Rings_Ocomm__ring__1(X2) ),
    inference(cnf_transformation,[],[f3688]) ).

fof(f3688,plain,
    ! [X0,X1,X2] :
      ( ( ( c_Rings_Odvd__class_Odvd(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)
          | ~ c_Rings_Odvd__class_Odvd(X2,X1,X0) )
        & ( c_Rings_Odvd__class_Odvd(X2,X1,X0)
          | ~ c_Rings_Odvd__class_Odvd(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0) ) )
      | ~ class_Rings_Ocomm__ring__1(X2) ),
    inference(nnf_transformation,[],[f2792]) ).

fof(f2792,plain,
    ! [X0,X1,X2] :
      ( ( c_Rings_Odvd__class_Odvd(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)
      <=> c_Rings_Odvd__class_Odvd(X2,X1,X0) )
      | ~ class_Rings_Ocomm__ring__1(X2) ),
    inference(ennf_transformation,[],[f1849]) ).

fof(f1849,plain,
    ! [X0,X1,X2] :
      ( class_Rings_Ocomm__ring__1(X2)
     => ( c_Rings_Odvd__class_Odvd(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)
      <=> c_Rings_Odvd__class_Odvd(X2,X1,X0) ) ),
    inference(rectify,[],[f834]) ).

fof(f834,axiom,
    ! [X20,X12,X5] :
      ( class_Rings_Ocomm__ring__1(X5)
     => ( c_Rings_Odvd__class_Odvd(X5,c_Groups_Ouminus__class_Ouminus(X5,X12),X20)
      <=> c_Rings_Odvd__class_Odvd(X5,X12,X20) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__dvd__iff) ).

fof(f9941,plain,
    spl50_615,
    inference(avatar_split_clause,[],[f4924,f9939]) ).

fof(f9939,plain,
    ( spl50_615
  <=> ! [X2,X0,X1] :
        ( c_Rings_Odvd__class_Odvd(X2,X1,X0)
        | ~ c_Rings_Odvd__class_Odvd(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)
        | ~ class_Rings_Ocomm__ring__1(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_615])]) ).

fof(f4924,plain,
    ! [X2,X0,X1] :
      ( c_Rings_Odvd__class_Odvd(X2,X1,X0)
      | ~ c_Rings_Odvd__class_Odvd(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)
      | ~ class_Rings_Ocomm__ring__1(X2) ),
    inference(cnf_transformation,[],[f3688]) ).

fof(f9937,plain,
    spl50_614,
    inference(avatar_split_clause,[],[f4923,f9935]) ).

fof(f9935,plain,
    ( spl50_614
  <=> ! [X2,X0,X1] :
        ( c_Rings_Odvd__class_Odvd(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
        | ~ c_Rings_Odvd__class_Odvd(X2,X1,X0)
        | ~ class_Rings_Ocomm__ring__1(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_614])]) ).

fof(f4923,plain,
    ! [X2,X0,X1] :
      ( c_Rings_Odvd__class_Odvd(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
      | ~ c_Rings_Odvd__class_Odvd(X2,X1,X0)
      | ~ class_Rings_Ocomm__ring__1(X2) ),
    inference(cnf_transformation,[],[f3687]) ).

fof(f3687,plain,
    ! [X0,X1,X2] :
      ( ( ( c_Rings_Odvd__class_Odvd(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
          | ~ c_Rings_Odvd__class_Odvd(X2,X1,X0) )
        & ( c_Rings_Odvd__class_Odvd(X2,X1,X0)
          | ~ c_Rings_Odvd__class_Odvd(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0)) ) )
      | ~ class_Rings_Ocomm__ring__1(X2) ),
    inference(nnf_transformation,[],[f2791]) ).

fof(f2791,plain,
    ! [X0,X1,X2] :
      ( ( c_Rings_Odvd__class_Odvd(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
      <=> c_Rings_Odvd__class_Odvd(X2,X1,X0) )
      | ~ class_Rings_Ocomm__ring__1(X2) ),
    inference(ennf_transformation,[],[f1848]) ).

fof(f1848,plain,
    ! [X0,X1,X2] :
      ( class_Rings_Ocomm__ring__1(X2)
     => ( c_Rings_Odvd__class_Odvd(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
      <=> c_Rings_Odvd__class_Odvd(X2,X1,X0) ) ),
    inference(rectify,[],[f833]) ).

fof(f833,axiom,
    ! [X20,X12,X5] :
      ( class_Rings_Ocomm__ring__1(X5)
     => ( c_Rings_Odvd__class_Odvd(X5,X12,c_Groups_Ouminus__class_Ouminus(X5,X20))
      <=> c_Rings_Odvd__class_Odvd(X5,X12,X20) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__minus__iff) ).

fof(f9933,plain,
    ( spl50_613
    | ~ spl50_441
    | ~ spl50_570 ),
    inference(avatar_split_clause,[],[f9799,f9755,f8290,f9931]) ).

fof(f9931,plain,
    ( spl50_613
  <=> ! [X0] : c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_613])]) ).

fof(f8290,plain,
    ( spl50_441
  <=> ! [X0,X1] :
        ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X0)
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_441])]) ).

fof(f9755,plain,
    ( spl50_570
  <=> ! [X0] : c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_570])]) ).

fof(f9799,plain,
    ( ! [X0] : c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
    | ~ spl50_441
    | ~ spl50_570 ),
    inference(resolution,[],[f9756,f8291]) ).

fof(f8291,plain,
    ( ! [X0,X1] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X0)
        | c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X0) )
    | ~ spl50_441 ),
    inference(avatar_component_clause,[],[f8290]) ).

fof(f9756,plain,
    ( ! [X0] : c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,X0)
    | ~ spl50_570 ),
    inference(avatar_component_clause,[],[f9755]) ).

fof(f9929,plain,
    spl50_612,
    inference(avatar_split_clause,[],[f4922,f9927]) ).

fof(f9927,plain,
    ( spl50_612
  <=> ! [X2,X0,X1] :
        ( c_Rings_Odvd__class_Odvd(X2,X1,X0)
        | ~ c_Rings_Odvd__class_Odvd(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
        | ~ class_Rings_Ocomm__ring__1(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_612])]) ).

fof(f4922,plain,
    ! [X2,X0,X1] :
      ( c_Rings_Odvd__class_Odvd(X2,X1,X0)
      | ~ c_Rings_Odvd__class_Odvd(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
      | ~ class_Rings_Ocomm__ring__1(X2) ),
    inference(cnf_transformation,[],[f3687]) ).

fof(f9925,plain,
    spl50_611,
    inference(avatar_split_clause,[],[f4820,f9923]) ).

fof(f9923,plain,
    ( spl50_611
  <=> ! [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,[spl50_611])]) ).

fof(f4820,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,[],[f2708]) ).

fof(f2708,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,[],[f2707]) ).

fof(f2707,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,[],[f1787]) ).

fof(f1787,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,[],[f86]) ).

fof(f86,axiom,
    ! [X13,X4,X5] :
      ( class_Rings_Odivision__ring__inverse__zero(X5)
     => ( c_Rings_Oinverse__class_Oinverse(X5,X4) = c_Rings_Oinverse__class_Oinverse(X5,X13)
       => X4 = X13 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__eq__imp__eq) ).

fof(f9921,plain,
    spl50_610,
    inference(avatar_split_clause,[],[f4810,f9919]) ).

fof(f9919,plain,
    ( spl50_610
  <=> ! [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,[spl50_610])]) ).

fof(f4810,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,[],[f3653]) ).

fof(f3653,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,[],[f2697]) ).

fof(f2697,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,[],[f1779]) ).

fof(f1779,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,[],[f802]) ).

fof(f802,axiom,
    ! [X20,X12,X5] :
      ( class_Lattices_Oboolean__algebra(X5)
     => ( c_Groups_Ouminus__class_Ouminus(X5,X12) = c_Groups_Ouminus__class_Ouminus(X5,X20)
      <=> X12 = X20 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compl__eq__compl__iff) ).

fof(f9917,plain,
    spl50_609,
    inference(avatar_split_clause,[],[f4749,f9915]) ).

fof(f9915,plain,
    ( spl50_609
  <=> ! [X0,X1] :
        ( X0 = X1
        | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_609])]) ).

fof(f4749,plain,
    ! [X0,X1] :
      ( X0 = X1
      | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0)) ),
    inference(cnf_transformation,[],[f3636]) ).

fof(f3636,plain,
    ! [X0,X1] :
      ( ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0))
        | X0 != X1 )
      & ( X0 = X1
        | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0)) ) ),
    inference(nnf_transformation,[],[f1735]) ).

fof(f1735,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0))
    <=> X0 = X1 ),
    inference(rectify,[],[f480]) ).

fof(f480,axiom,
    ! [X24,X12] :
      ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X12,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X24))
    <=> X12 = X24 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__add__minus__iff) ).

fof(f9913,plain,
    spl50_608,
    inference(avatar_split_clause,[],[f4739,f9911]) ).

fof(f9911,plain,
    ( spl50_608
  <=> ! [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,[spl50_608])]) ).

fof(f4739,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,[],[f3629]) ).

fof(f3629,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,[],[f1731]) ).

fof(f1731,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,[],[f471]) ).

fof(f471,axiom,
    ! [X32,X16] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X16,X32))
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X32,X16) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__diff) ).

fof(f9909,plain,
    spl50_607,
    inference(avatar_split_clause,[],[f4738,f9907]) ).

fof(f9907,plain,
    ( spl50_607
  <=> ! [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,[spl50_607])]) ).

fof(f4738,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,[],[f3629]) ).

fof(f9905,plain,
    spl50_606,
    inference(avatar_split_clause,[],[f4736,f9903]) ).

fof(f9903,plain,
    ( spl50_606
  <=> ! [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,[spl50_606])]) ).

fof(f4736,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,[],[f3628]) ).

fof(f9901,plain,
    spl50_605,
    inference(avatar_split_clause,[],[f4734,f9899]) ).

fof(f9899,plain,
    ( spl50_605
  <=> ! [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,[spl50_605])]) ).

fof(f4734,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,[],[f3626]) ).

fof(f3626,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,[],[f1729]) ).

fof(f1729,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,[],[f618]) ).

fof(f618,axiom,
    ! [X33,X63] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X63,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X33,c_Groups_Oone__class_Oone(tc_Int_Oint)))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X63,X33) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__add1__eq__le) ).

fof(f9897,plain,
    spl50_604,
    inference(avatar_split_clause,[],[f4733,f9895]) ).

fof(f9895,plain,
    ( spl50_604
  <=> ! [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,[spl50_604])]) ).

fof(f4733,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,[],[f3626]) ).

fof(f9893,plain,
    spl50_603,
    inference(avatar_split_clause,[],[f4727,f9891]) ).

fof(f9891,plain,
    ( spl50_603
  <=> ! [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,[spl50_603])]) ).

fof(f4727,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,[],[f3623]) ).

fof(f3623,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,[],[f1726]) ).

fof(f1726,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,[],[f615]) ).

fof(f615,axiom,
    ! [X33,X63] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X63,c_Groups_Oone__class_Oone(tc_Int_Oint)),X33)
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X63,X33) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add1__zle__eq) ).

fof(f9889,plain,
    ( spl50_602
    | ~ spl50_438
    | ~ spl50_570 ),
    inference(avatar_split_clause,[],[f9798,f9755,f8277,f9887]) ).

fof(f9887,plain,
    ( spl50_602
  <=> ! [X0] : c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_602])]) ).

fof(f8277,plain,
    ( spl50_438
  <=> ! [X0,X1] :
        ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X0)
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_438])]) ).

fof(f9798,plain,
    ( ! [X0] : c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X0)
    | ~ spl50_438
    | ~ spl50_570 ),
    inference(resolution,[],[f9756,f8278]) ).

fof(f8278,plain,
    ( ! [X0,X1] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
        | c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X0) )
    | ~ spl50_438 ),
    inference(avatar_component_clause,[],[f8277]) ).

fof(f9885,plain,
    spl50_601,
    inference(avatar_split_clause,[],[f4726,f9883]) ).

fof(f9883,plain,
    ( spl50_601
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(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,[spl50_601])]) ).

fof(f4726,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(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,[],[f3622]) ).

fof(f3622,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | ~ 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,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(nnf_transformation,[],[f1725]) ).

fof(f1725,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
    inference(rectify,[],[f626]) ).

fof(f626,axiom,
    ! [X33,X63] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X63,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X33,c_Groups_Oone__class_Oone(tc_Int_Oint)))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X63,X33) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__diff1__eq) ).

fof(f9881,plain,
    spl50_600,
    inference(avatar_split_clause,[],[f4725,f9879]) ).

fof(f9879,plain,
    ( spl50_600
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_600])]) ).

fof(f4725,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(cnf_transformation,[],[f3622]) ).

fof(f9877,plain,
    spl50_599,
    inference(avatar_split_clause,[],[f4696,f9875]) ).

fof(f9875,plain,
    ( spl50_599
  <=> ! [X0,X1] :
        ( c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1) = X0
        | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_599])]) ).

fof(f4696,plain,
    ! [X0,X1] :
      ( c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1) = X0
      | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0) ),
    inference(cnf_transformation,[],[f3609]) ).

fof(f3609,plain,
    ! [X0,X1] :
      ( ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0)
        | c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1) != X0 )
      & ( c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1) = X0
        | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0) ) ),
    inference(nnf_transformation,[],[f1717]) ).

fof(f1717,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0)
    <=> c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1) = X0 ),
    inference(rectify,[],[f481]) ).

fof(f481,axiom,
    ! [X20,X12] :
      ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X12,X20)
    <=> c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X12) = X20 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__add__eq__0__iff) ).

fof(f9873,plain,
    spl50_598,
    inference(avatar_split_clause,[],[f4665,f9871]) ).

fof(f9871,plain,
    ( spl50_598
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_598])]) ).

fof(f4665,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(cnf_transformation,[],[f3585]) ).

fof(f3585,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ) ),
    inference(nnf_transformation,[],[f1704]) ).

fof(f1704,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(rectify,[],[f590]) ).

fof(f590,axiom,
    ! [X35,X36] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X36,X35)
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X36,X35),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__bin__lemma) ).

fof(f9869,plain,
    spl50_597,
    inference(avatar_split_clause,[],[f4664,f9867]) ).

fof(f9867,plain,
    ( spl50_597
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_597])]) ).

fof(f4664,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
    inference(cnf_transformation,[],[f3585]) ).

fof(f9865,plain,
    spl50_596,
    inference(avatar_split_clause,[],[f4659,f9863]) ).

fof(f9863,plain,
    ( spl50_596
  <=> ! [X0,X1] :
        ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK32(X0,X1)) = X0
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_596])]) ).

fof(f4659,plain,
    ! [X0,X1] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK32(X0,X1)) = X0
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
    inference(cnf_transformation,[],[f3582]) ).

fof(f3582,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,sK32(X0,X1)) = X0
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK32])],[f3580,f3581]) ).

fof(f3581,plain,
    ! [X0,X1] :
      ( ? [X3] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3) = X0
     => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK32(X0,X1)) = X0 ),
    introduced(choice_axiom,[]) ).

fof(f3580,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,[],[f3579]) ).

fof(f3579,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,[],[f1702]) ).

fof(f1702,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,[],[f192]) ).

fof(f192,axiom,
    ! [X35,X36] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,X35)
    <=> ? [X37] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X36,X37) = X35 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__Suc__ex__iff) ).

fof(f9861,plain,
    spl50_595,
    inference(avatar_split_clause,[],[f4657,f9859]) ).

fof(f9859,plain,
    ( spl50_595
  <=> ! [X0,X1] :
        ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK31(X0,X1)) = X0
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_595])]) ).

fof(f4657,plain,
    ! [X0,X1] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK31(X0,X1)) = X0
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
    inference(cnf_transformation,[],[f3578]) ).

fof(f3578,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,sK31(X0,X1)) = X0
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK31])],[f3576,f3577]) ).

fof(f3577,plain,
    ! [X0,X1] :
      ( ? [X3] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3) = X0
     => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK31(X0,X1)) = X0 ),
    introduced(choice_axiom,[]) ).

fof(f3576,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,[],[f3575]) ).

fof(f3575,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,[],[f1701]) ).

fof(f1701,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,[],[f412]) ).

fof(f412,axiom,
    ! [X16,X32] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X32,X16)
    <=> ? [X52] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X32,X52) = X16 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__iff__add) ).

fof(f9857,plain,
    spl50_594,
    inference(avatar_split_clause,[],[f4650,f9855]) ).

fof(f9855,plain,
    ( spl50_594
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_594])]) ).

fof(f4650,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    inference(cnf_transformation,[],[f3570]) ).

fof(f3570,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ) ),
    inference(nnf_transformation,[],[f1698]) ).

fof(f1698,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
    <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    inference(rectify,[],[f469]) ).

fof(f469,axiom,
    ! [X20,X12] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X12,X20)
    <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X12,X20),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__eq__diff) ).

fof(f9853,plain,
    spl50_593,
    inference(avatar_split_clause,[],[f4649,f9851]) ).

fof(f9851,plain,
    ( spl50_593
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_593])]) ).

fof(f4649,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ),
    inference(cnf_transformation,[],[f3570]) ).

fof(f9849,plain,
    spl50_592,
    inference(avatar_split_clause,[],[f4575,f9847]) ).

fof(f9847,plain,
    ( spl50_592
  <=> ! [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,[spl50_592])]) ).

fof(f4575,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,[],[f2600]) ).

fof(f2600,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,[],[f1643]) ).

fof(f1643,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,[],[f613]) ).

fof(f613,axiom,
    ! [X14,X15] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X15,X14)
     => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X15,c_Groups_Oone__class_Oone(tc_Int_Oint)),X14) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__imp__add1__zle) ).

fof(f9845,plain,
    ( spl50_591
    | ~ spl50_361
    | ~ spl50_562 ),
    inference(avatar_split_clause,[],[f9710,f9640,f7753,f9842]) ).

fof(f9842,plain,
    ( spl50_591
  <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_k____,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK19)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_591])]) ).

fof(f7753,plain,
    ( spl50_361
  <=> ! [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,[spl50_361])]) ).

fof(f9640,plain,
    ( spl50_562
  <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_k____,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK19)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_562])]) ).

fof(f9710,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_k____,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK19))
    | ~ spl50_361
    | ~ spl50_562 ),
    inference(resolution,[],[f9642,f7754]) ).

fof(f7754,plain,
    ( ! [X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
    | ~ spl50_361 ),
    inference(avatar_component_clause,[],[f7753]) ).

fof(f9642,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_k____,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK19))
    | ~ spl50_562 ),
    inference(avatar_component_clause,[],[f9640]) ).

fof(f9840,plain,
    spl50_590,
    inference(avatar_split_clause,[],[f4528,f9838]) ).

fof(f9838,plain,
    ( spl50_590
  <=> ! [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,[spl50_590])]) ).

fof(f4528,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,[],[f2546]) ).

fof(f2546,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,[],[f1604]) ).

fof(f1604,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,[],[f527]) ).

fof(f527,axiom,
    ! [X4,X5] :
      ( class_Rings_Ocomm__semiring__1(X5)
     => c_Groups_Ozero__class_Ozero(X5) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ozero__class_Ozero(X5)),X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).

fof(f9836,plain,
    spl50_589,
    inference(avatar_split_clause,[],[f4527,f9834]) ).

fof(f9834,plain,
    ( spl50_589
  <=> ! [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,[spl50_589])]) ).

fof(f4527,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,[],[f2545]) ).

fof(f2545,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,[],[f1603]) ).

fof(f1603,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,[],[f528]) ).

fof(f528,axiom,
    ! [X4,X5] :
      ( class_Rings_Ocomm__semiring__1(X5)
     => c_Groups_Ozero__class_Ozero(X5) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),c_Groups_Ozero__class_Ozero(X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).

fof(f9832,plain,
    spl50_588,
    inference(avatar_split_clause,[],[f4526,f9830]) ).

fof(f9830,plain,
    ( spl50_588
  <=> ! [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,[spl50_588])]) ).

fof(f4526,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,[],[f2544]) ).

fof(f2544,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,[],[f1602]) ).

fof(f1602,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,[],[f647]) ).

fof(f647,axiom,
    ! [X9,X5] :
      ( class_Rings_Ocomm__semiring__1(X5)
     => c_Groups_Oone__class_Oone(X5) = hAPP(c_Polynomial_Opoly(X5,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X5))),X9) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__1) ).

fof(f9828,plain,
    spl50_587,
    inference(avatar_split_clause,[],[f4525,f9826]) ).

fof(f9826,plain,
    ( spl50_587
  <=> ! [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,[spl50_587])]) ).

fof(f4525,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,[],[f2543]) ).

fof(f2543,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,[],[f1601]) ).

fof(f1601,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,[],[f549]) ).

fof(f549,axiom,
    ! [X9,X5] :
      ( class_Rings_Ocomm__semiring__1(X5)
     => c_Groups_Oone__class_Oone(X5) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),X9),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).

fof(f9824,plain,
    spl50_586,
    inference(avatar_split_clause,[],[f4513,f9822]) ).

fof(f9822,plain,
    ( spl50_586
  <=> ! [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,[spl50_586])]) ).

fof(f4513,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,[],[f2531]) ).

fof(f2531,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,[],[f1589]) ).

fof(f1589,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,[],[f657]) ).

fof(f657,axiom,
    ! [X4,X5] :
      ( class_Rings_Ocomm__semiring__0(X5)
     => c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = c_Polynomial_Osmult(X5,X4,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__0__right) ).

fof(f9820,plain,
    spl50_585,
    inference(avatar_split_clause,[],[f4512,f9818]) ).

fof(f9818,plain,
    ( spl50_585
  <=> ! [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,[spl50_585])]) ).

fof(f4512,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,[],[f2530]) ).

fof(f2530,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,[],[f1588]) ).

fof(f1588,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,[],[f690]) ).

fof(f690,axiom,
    ! [X23,X5] :
      ( class_Rings_Ocomm__semiring__0(X5)
     => c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = c_Polynomial_Osynthetic__div(X5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X23) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_synthetic__div__0) ).

fof(f9816,plain,
    spl50_584,
    inference(avatar_split_clause,[],[f4511,f9814]) ).

fof(f9814,plain,
    ( spl50_584
  <=> ! [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,[spl50_584])]) ).

fof(f4511,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,[],[f2529]) ).

fof(f2529,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,[],[f1587]) ).

fof(f1587,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,[],[f703]) ).

fof(f703,axiom,
    ! [X53,X5] :
      ( class_Rings_Ocomm__semiring__0(X5)
     => c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = c_Polynomial_Opcompose(X5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X53) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pcompose__0) ).

fof(f9812,plain,
    spl50_583,
    inference(avatar_split_clause,[],[f4510,f9810]) ).

fof(f9810,plain,
    ( spl50_583
  <=> ! [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,[spl50_583])]) ).

fof(f4510,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,[],[f2528]) ).

fof(f2528,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,[],[f1586]) ).

fof(f1586,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,[],[f658]) ).

fof(f658,axiom,
    ! [X9,X5] :
      ( class_Rings_Ocomm__semiring__0(X5)
     => c_Groups_Ozero__class_Ozero(X5) = hAPP(c_Polynomial_Opoly(X5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))),X9) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__0) ).

fof(f9808,plain,
    spl50_582,
    inference(avatar_split_clause,[],[f4502,f9806]) ).

fof(f9806,plain,
    ( spl50_582
  <=> ! [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,[spl50_582])]) ).

fof(f4502,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,[],[f2522]) ).

fof(f2522,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,[],[f1580]) ).

fof(f1580,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,[],[f111]) ).

fof(f111,axiom,
    ! [X3,X5] :
      ( class_Groups_Omonoid__mult(X5)
     => c_Groups_Oone__class_Oone(X5) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),c_Groups_Oone__class_Oone(X5)),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__one) ).

fof(f9804,plain,
    spl50_581,
    inference(avatar_split_clause,[],[f4494,f9802]) ).

fof(f9802,plain,
    ( spl50_581
  <=> ! [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,[spl50_581])]) ).

fof(f4494,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,[],[f2514]) ).

fof(f2514,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,[],[f1572]) ).

fof(f1572,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,[],[f55]) ).

fof(f55,axiom,
    ! [X4,X5] :
      ( class_Power_Opower(X5)
     => c_Groups_Oone__class_Oone(X5) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__0) ).

fof(f9797,plain,
    spl50_580,
    inference(avatar_split_clause,[],[f4493,f9795]) ).

fof(f9795,plain,
    ( spl50_580
  <=> ! [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,[spl50_580])]) ).

fof(f4493,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,[],[f2513]) ).

fof(f2513,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,[],[f1571]) ).

fof(f1571,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,[],[f98]) ).

fof(f98,axiom,
    ! [X4,X5] :
      ( class_Rings_Omult__zero(X5)
     => c_Groups_Ozero__class_Ozero(X5) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ozero__class_Ozero(X5)),X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__zero__left) ).

fof(f9793,plain,
    spl50_579,
    inference(avatar_split_clause,[],[f4492,f9791]) ).

fof(f9791,plain,
    ( spl50_579
  <=> ! [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,[spl50_579])]) ).

fof(f4492,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,[],[f2512]) ).

fof(f2512,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,[],[f1570]) ).

fof(f1570,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,[],[f95]) ).

fof(f95,axiom,
    ! [X4,X5] :
      ( class_Rings_Omult__zero(X5)
     => c_Groups_Ozero__class_Ozero(X5) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),c_Groups_Ozero__class_Ozero(X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__zero__right) ).

fof(f9789,plain,
    spl50_578,
    inference(avatar_split_clause,[],[f4481,f9787]) ).

fof(f9787,plain,
    ( spl50_578
  <=> ! [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,[spl50_578])]) ).

fof(f4481,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,[],[f3539]) ).

fof(f3539,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,[],[f2504]) ).

fof(f2504,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,[],[f1562]) ).

fof(f1562,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,[],[f291]) ).

fof(f291,axiom,
    ! [X24,X5] :
      ( class_Groups_Ogroup__add(X5)
     => ( c_Groups_Ozero__class_Ozero(X5) = c_Groups_Ouminus__class_Ouminus(X5,X24)
      <=> c_Groups_Ozero__class_Ozero(X5) = X24 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__0__equal__iff__equal) ).

fof(f9785,plain,
    spl50_577,
    inference(avatar_split_clause,[],[f4455,f9783]) ).

fof(f9783,plain,
    ( spl50_577
  <=> ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(X1) = X0
        | c_Groups_Ozero__class_Ozero(X1) != c_Groups_Osgn__class_Osgn(X1,X0)
        | ~ class_Rings_Olinordered__idom(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_577])]) ).

fof(f4455,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X1) = X0
      | c_Groups_Ozero__class_Ozero(X1) != c_Groups_Osgn__class_Osgn(X1,X0)
      | ~ class_Rings_Olinordered__idom(X1) ),
    inference(cnf_transformation,[],[f3531]) ).

fof(f3531,plain,
    ! [X0,X1] :
      ( ( ( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Osgn__class_Osgn(X1,X0)
          | c_Groups_Ozero__class_Ozero(X1) != X0 )
        & ( c_Groups_Ozero__class_Ozero(X1) = X0
          | c_Groups_Ozero__class_Ozero(X1) != c_Groups_Osgn__class_Osgn(X1,X0) ) )
      | ~ class_Rings_Olinordered__idom(X1) ),
    inference(nnf_transformation,[],[f2486]) ).

fof(f2486,plain,
    ! [X0,X1] :
      ( ( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Osgn__class_Osgn(X1,X0)
      <=> c_Groups_Ozero__class_Ozero(X1) = X0 )
      | ~ class_Rings_Olinordered__idom(X1) ),
    inference(ennf_transformation,[],[f1544]) ).

fof(f1544,plain,
    ! [X0,X1] :
      ( class_Rings_Olinordered__idom(X1)
     => ( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Osgn__class_Osgn(X1,X0)
      <=> c_Groups_Ozero__class_Ozero(X1) = X0 ) ),
    inference(rectify,[],[f807]) ).

fof(f807,axiom,
    ! [X24,X5] :
      ( class_Rings_Olinordered__idom(X5)
     => ( c_Groups_Ozero__class_Ozero(X5) = c_Groups_Osgn__class_Osgn(X5,X24)
      <=> c_Groups_Ozero__class_Ozero(X5) = X24 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__0__0) ).

fof(f9781,plain,
    spl50_576,
    inference(avatar_split_clause,[],[f4415,f9779]) ).

fof(f9779,plain,
    ( spl50_576
  <=> ! [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,[spl50_576])]) ).

fof(f4415,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,[],[f2461]) ).

fof(f2461,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,[],[f1522]) ).

fof(f1522,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,[],[f45]) ).

fof(f45,axiom,
    ! [X4,X5] :
      ( class_Rings_Olinordered__ring(X5)
     => c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__square) ).

fof(f9777,plain,
    spl50_575,
    inference(avatar_split_clause,[],[f4414,f9775]) ).

fof(f9775,plain,
    ( spl50_575
  <=> ! [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,[spl50_575])]) ).

fof(f4414,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,[],[f2460]) ).

fof(f2460,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,[],[f1521]) ).

fof(f1521,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,[],[f141]) ).

fof(f141,axiom,
    ! [X4,X5] :
      ( class_Rings_Olinordered__ring(X5)
     => ~ c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X4),c_Groups_Ozero__class_Ozero(X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__square__less__zero) ).

fof(f9773,plain,
    spl50_574,
    inference(avatar_split_clause,[],[f4405,f9771]) ).

fof(f9771,plain,
    ( spl50_574
  <=> ! [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,[spl50_574])]) ).

fof(f4405,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,[],[f2455]) ).

fof(f2455,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,[],[f1516]) ).

fof(f1516,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,[],[f96]) ).

fof(f96,axiom,
    ! [X7,X5] :
      ( class_RealVector_Oreal__normed__algebra(X5)
     => c_Groups_Ozero__class_Ozero(X5) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ozero__class_Ozero(X5)),X7) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left_Ozero) ).

fof(f9769,plain,
    spl50_573,
    inference(avatar_split_clause,[],[f4403,f9767]) ).

fof(f9767,plain,
    ( spl50_573
  <=> ! [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,[spl50_573])]) ).

fof(f4403,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,[],[f2453]) ).

fof(f2453,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,[],[f1514]) ).

fof(f1514,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,[],[f93]) ).

fof(f93,axiom,
    ! [X9,X5] :
      ( class_RealVector_Oreal__normed__algebra(X5)
     => c_Groups_Ozero__class_Ozero(X5) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X9),c_Groups_Ozero__class_Ozero(X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right_Ozero) ).

fof(f9765,plain,
    spl50_572,
    inference(avatar_split_clause,[],[f4397,f9763]) ).

fof(f9763,plain,
    ( spl50_572
  <=> ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(X1) = X0
        | c_Groups_Ozero__class_Ozero(X1) != c_Groups_Osgn__class_Osgn(X1,X0)
        | ~ class_RealVector_Oreal__normed__vector(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_572])]) ).

fof(f4397,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X1) = X0
      | c_Groups_Ozero__class_Ozero(X1) != c_Groups_Osgn__class_Osgn(X1,X0)
      | ~ class_RealVector_Oreal__normed__vector(X1) ),
    inference(cnf_transformation,[],[f3508]) ).

fof(f3508,plain,
    ! [X0,X1] :
      ( ( ( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Osgn__class_Osgn(X1,X0)
          | c_Groups_Ozero__class_Ozero(X1) != X0 )
        & ( c_Groups_Ozero__class_Ozero(X1) = X0
          | c_Groups_Ozero__class_Ozero(X1) != c_Groups_Osgn__class_Osgn(X1,X0) ) )
      | ~ class_RealVector_Oreal__normed__vector(X1) ),
    inference(nnf_transformation,[],[f2450]) ).

fof(f2450,plain,
    ! [X0,X1] :
      ( ( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Osgn__class_Osgn(X1,X0)
      <=> c_Groups_Ozero__class_Ozero(X1) = X0 )
      | ~ class_RealVector_Oreal__normed__vector(X1) ),
    inference(ennf_transformation,[],[f1511]) ).

fof(f1511,plain,
    ! [X0,X1] :
      ( class_RealVector_Oreal__normed__vector(X1)
     => ( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Osgn__class_Osgn(X1,X0)
      <=> c_Groups_Ozero__class_Ozero(X1) = X0 ) ),
    inference(rectify,[],[f806]) ).

fof(f806,axiom,
    ! [X12,X5] :
      ( class_RealVector_Oreal__normed__vector(X5)
     => ( c_Groups_Ozero__class_Ozero(X5) = c_Groups_Osgn__class_Osgn(X5,X12)
      <=> c_Groups_Ozero__class_Ozero(X5) = X12 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__zero__iff) ).

fof(f9761,plain,
    spl50_571,
    inference(avatar_split_clause,[],[f4395,f9759]) ).

fof(f9759,plain,
    ( spl50_571
  <=> ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(X1) = X0
        | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_RealVector_Onorm__class_Onorm(X1,X0)
        | ~ class_RealVector_Oreal__normed__vector(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_571])]) ).

fof(f4395,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X1) = X0
      | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_RealVector_Onorm__class_Onorm(X1,X0)
      | ~ class_RealVector_Oreal__normed__vector(X1) ),
    inference(cnf_transformation,[],[f3507]) ).

fof(f3507,plain,
    ! [X0,X1] :
      ( ( ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X1,X0)
          | c_Groups_Ozero__class_Ozero(X1) != X0 )
        & ( c_Groups_Ozero__class_Ozero(X1) = X0
          | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_RealVector_Onorm__class_Onorm(X1,X0) ) )
      | ~ class_RealVector_Oreal__normed__vector(X1) ),
    inference(nnf_transformation,[],[f2449]) ).

fof(f2449,plain,
    ! [X0,X1] :
      ( ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X1,X0)
      <=> c_Groups_Ozero__class_Ozero(X1) = X0 )
      | ~ class_RealVector_Oreal__normed__vector(X1) ),
    inference(ennf_transformation,[],[f1510]) ).

fof(f1510,plain,
    ! [X0,X1] :
      ( class_RealVector_Oreal__normed__vector(X1)
     => ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X1,X0)
      <=> c_Groups_Ozero__class_Ozero(X1) = X0 ) ),
    inference(rectify,[],[f164]) ).

fof(f164,axiom,
    ! [X12,X5] :
      ( class_RealVector_Oreal__normed__vector(X5)
     => ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X5,X12)
      <=> c_Groups_Ozero__class_Ozero(X5) = X12 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__eq__zero) ).

fof(f9757,plain,
    ( ~ spl50_162
    | spl50_570
    | ~ spl50_374
    | ~ spl50_544 ),
    inference(avatar_split_clause,[],[f9653,f8980,f7836,f9755,f6856]) ).

fof(f7836,plain,
    ( spl50_374
  <=> ! [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,[spl50_374])]) ).

fof(f9653,plain,
    ( ! [X0] :
        ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,X0)
        | ~ class_Rings_Odvd(tc_Int_Oint) )
    | ~ spl50_374
    | ~ spl50_544 ),
    inference(superposition,[],[f8981,f7837]) ).

fof(f7837,plain,
    ( ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X0
    | ~ spl50_374 ),
    inference(avatar_component_clause,[],[f7836]) ).

fof(f9753,plain,
    spl50_569,
    inference(avatar_split_clause,[],[f4383,f9751]) ).

fof(f9751,plain,
    ( spl50_569
  <=> ! [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,[spl50_569])]) ).

fof(f4383,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,[],[f2433]) ).

fof(f2433,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,[],[f2432]) ).

fof(f2432,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,[],[f1499]) ).

fof(f1499,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,[],[f115]) ).

fof(f115,axiom,
    ! [X4,X5] :
      ( class_Rings_Odivision__ring(X5)
     => ( c_Groups_Ozero__class_Ozero(X5) != X4
       => c_Groups_Ozero__class_Ozero(X5) != c_Rings_Oinverse__class_Oinverse(X5,X4) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__imp__inverse__nonzero) ).

fof(f9749,plain,
    spl50_568,
    inference(avatar_split_clause,[],[f4381,f9747]) ).

fof(f9747,plain,
    ( spl50_568
  <=> ! [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,[spl50_568])]) ).

fof(f4381,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,[],[f3506]) ).

fof(f3506,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,[],[f2431]) ).

fof(f2431,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,[],[f1498]) ).

fof(f1498,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,[],[f116]) ).

fof(f116,axiom,
    ! [X24,X5] :
      ( class_Rings_Odivision__ring__inverse__zero(X5)
     => ( c_Groups_Ozero__class_Ozero(X5) = c_Rings_Oinverse__class_Oinverse(X5,X24)
      <=> c_Groups_Ozero__class_Ozero(X5) = X24 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__nonzero__iff__nonzero) ).

fof(f9745,plain,
    spl50_567,
    inference(avatar_split_clause,[],[f4373,f9743]) ).

fof(f9743,plain,
    ( spl50_567
  <=> ! [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,[spl50_567])]) ).

fof(f4373,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,[],[f3505]) ).

fof(f3505,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,[],[f2422]) ).

fof(f2422,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,[],[f1491]) ).

fof(f1491,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,[],[f121]) ).

fof(f121,axiom,
    ! [X12,X5] :
      ( class_Fields_Ofield__inverse__zero(X5)
     => ( c_Groups_Oone__class_Oone(X5) = c_Rings_Oinverse__class_Oinverse(X5,X12)
      <=> c_Groups_Oone__class_Oone(X5) = X12 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__eq__1__iff) ).

fof(f9741,plain,
    spl50_566,
    inference(avatar_split_clause,[],[f4341,f9739]) ).

fof(f4341,plain,
    ! [X0,X1] :
      ( c_Nat__Transfer_Otsub(X0,X1) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,X1)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ),
    inference(cnf_transformation,[],[f2401]) ).

fof(f2401,plain,
    ! [X0,X1] :
      ( ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Nat__Transfer_Otsub(X0,X1)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) )
      & ( c_Nat__Transfer_Otsub(X0,X1) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,X1)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ) ),
    inference(ennf_transformation,[],[f1470]) ).

fof(f1470,plain,
    ! [X0,X1] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
       => c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Nat__Transfer_Otsub(X0,X1) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
       => c_Nat__Transfer_Otsub(X0,X1) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,X1) ) ),
    inference(rectify,[],[f776]) ).

fof(f776,axiom,
    ! [X9,X7] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X7,X9)
       => c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Nat__Transfer_Otsub(X9,X7) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X7,X9)
       => c_Nat__Transfer_Otsub(X9,X7) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X9,X7) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tsub__def) ).

fof(f9737,plain,
    spl50_565,
    inference(avatar_split_clause,[],[f4250,f9735]) ).

fof(f9735,plain,
    ( spl50_565
  <=> ! [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,[spl50_565])]) ).

fof(f4250,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,[],[f2362]) ).

fof(f2362,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,[],[f1391]) ).

fof(f1391,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,[],[f174]) ).

fof(f174,axiom,
    ! [X5] :
      ( class_Rings_Olinordered__semidom(X5)
     => c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),c_Groups_Oplus__class_Oplus(X5,c_Groups_Oone__class_Oone(X5),c_Groups_Oone__class_Oone(X5))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__two) ).

fof(f9733,plain,
    spl50_564,
    inference(avatar_split_clause,[],[f4244,f9731]) ).

fof(f9731,plain,
    ( spl50_564
  <=> ! [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,[spl50_564])]) ).

fof(f4244,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,[],[f2356]) ).

fof(f2356,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,[],[f1385]) ).

fof(f1385,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,[],[f636]) ).

fof(f636,axiom,
    ! [X5] :
      ( class_Groups_Oab__group__add(X5)
     => c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X5),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__poly__code_I1_J) ).

fof(f9729,plain,
    spl50_563,
    inference(avatar_split_clause,[],[f4114,f9726]) ).

fof(f9726,plain,
    ( spl50_563
  <=> hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_563])]) ).

fof(f9643,plain,
    ( spl50_562
    | ~ spl50_463
    | ~ spl50_529 ),
    inference(avatar_split_clause,[],[f9536,f8919,f8380,f9640]) ).

fof(f8380,plain,
    ( spl50_463
  <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK19)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_463])]) ).

fof(f8919,plain,
    ( spl50_529
  <=> ! [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,[spl50_529])]) ).

fof(f9536,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_k____,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK19))
    | ~ spl50_463
    | ~ spl50_529 ),
    inference(resolution,[],[f8920,f8382]) ).

fof(f8382,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK19))
    | ~ spl50_463 ),
    inference(avatar_component_clause,[],[f8380]) ).

fof(f8920,plain,
    ( ! [X2,X0,X1] :
        ( ~ 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) )
    | ~ spl50_529 ),
    inference(avatar_component_clause,[],[f8919]) ).

fof(f9254,plain,
    ( spl50_561
    | ~ spl50_291
    | ~ spl50_469 ),
    inference(avatar_split_clause,[],[f9060,f8672,f7434,f9251]) ).

fof(f9251,plain,
    ( spl50_561
  <=> c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,sK45) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_561])]) ).

fof(f8672,plain,
    ( spl50_469
  <=> ! [X0] :
        ( c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X0)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_469])]) ).

fof(f9060,plain,
    ( c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,sK45)
    | ~ spl50_291
    | ~ spl50_469 ),
    inference(resolution,[],[f8673,f7436]) ).

fof(f8673,plain,
    ( ! [X0] :
        ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
        | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X0) )
    | ~ spl50_469 ),
    inference(avatar_component_clause,[],[f8672]) ).

fof(f9172,plain,
    ( spl50_560
    | ~ spl50_230
    | ~ spl50_469 ),
    inference(avatar_split_clause,[],[f9056,f8672,f7189,f9169]) ).

fof(f9169,plain,
    ( spl50_560
  <=> c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,sK18) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_560])]) ).

fof(f9056,plain,
    ( c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,sK18)
    | ~ spl50_230
    | ~ spl50_469 ),
    inference(resolution,[],[f8673,f7191]) ).

fof(f9122,plain,
    ( spl50_559
    | ~ spl50_229
    | ~ spl50_469 ),
    inference(avatar_split_clause,[],[f9055,f8672,f7184,f9119]) ).

fof(f9119,plain,
    ( spl50_559
  <=> c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_m____) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_559])]) ).

fof(f9055,plain,
    ( c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_m____)
    | ~ spl50_229
    | ~ spl50_469 ),
    inference(resolution,[],[f8673,f7186]) ).

fof(f9041,plain,
    ( spl50_558
    | ~ spl50_7
    | ~ spl50_398 ),
    inference(avatar_split_clause,[],[f8138,f7934,f6081,f9039]) ).

fof(f9039,plain,
    ( spl50_558
  <=> ! [X0] : c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool,c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool,X0)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_558])]) ).

fof(f6081,plain,
    ( spl50_7
  <=> class_Lattices_Oboolean__algebra(tc_HOL_Obool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_7])]) ).

fof(f7934,plain,
    ( spl50_398
  <=> ! [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,[spl50_398])]) ).

fof(f8138,plain,
    ( ! [X0] : c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool,c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool,X0)) = X0
    | ~ spl50_7
    | ~ spl50_398 ),
    inference(resolution,[],[f7935,f6083]) ).

fof(f6083,plain,
    ( class_Lattices_Oboolean__algebra(tc_HOL_Obool)
    | ~ spl50_7 ),
    inference(avatar_component_clause,[],[f6081]) ).

fof(f7935,plain,
    ( ! [X0,X1] :
        ( ~ class_Lattices_Oboolean__algebra(X1)
        | c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0)) = X0 )
    | ~ spl50_398 ),
    inference(avatar_component_clause,[],[f7934]) ).

fof(f9035,plain,
    spl50_557,
    inference(avatar_split_clause,[],[f6040,f9033]) ).

fof(f9033,plain,
    ( spl50_557
  <=> ! [X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,sK19),X1) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,sK46),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_557])]) ).

fof(f6040,plain,
    ! [X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,sK19),X1) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,sK46),X1),
    inference(forward_demodulation,[],[f5561,f4131]) ).

fof(f5561,plain,
    ! [X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X1)) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,sK46),X1),
    inference(cnf_transformation,[],[f3871]) ).

fof(f3871,plain,
    ( ! [X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X1)) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,sK46),X1)
    & c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK46) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK46])],[f2294,f3870]) ).

fof(f3870,plain,
    ( ? [X0] :
        ( ! [X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X1)) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X0),X1)
        & c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,X0) )
   => ( ! [X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X1)) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,sK46),X1)
      & c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK46) ) ),
    introduced(choice_axiom,[]) ).

fof(f2294,plain,
    ? [X0] :
      ( ! [X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X1)) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X0),X1)
      & c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,X0) ),
    inference(rectify,[],[f567]) ).

fof(f567,axiom,
    ? [X65] :
      ( ! [X2] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X2)) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X65),X2)
      & c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,X65) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096EX_Aq_O_Apsize_Aq_A_061_Apsize_Ap_A_G_A_IALL_Ax_O_Apoly_Aq_Ax_A_061_Apoly_Ap_A_Ic_A_L_Ax_J_J_096) ).

fof(f9031,plain,
    spl50_556,
    inference(avatar_split_clause,[],[f5995,f9029]) ).

fof(f9029,plain,
    ( spl50_556
  <=> ! [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,[spl50_556])]) ).

fof(f5995,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,[],[f5994,f4161]) ).

fof(f5994,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,[],[f5661,f4313]) ).

fof(f5661,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,[],[f4713,f4164]) ).

fof(f4713,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,[],[f3618]) ).

fof(f3618,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,[],[f3617]) ).

fof(f3617,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,[],[f3441]) ).

fof(f3441,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(f9027,plain,
    spl50_555,
    inference(avatar_split_clause,[],[f5993,f9025]) ).

fof(f9025,plain,
    ( spl50_555
  <=> ! [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,[spl50_555])]) ).

fof(f5993,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,[],[f5992,f4161]) ).

fof(f5992,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,[],[f5991,f4313]) ).

fof(f5991,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,[],[f5990,f4161]) ).

fof(f5990,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,[],[f5660,f4313]) ).

fof(f5660,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,[],[f4715,f4164,f4164]) ).

fof(f4715,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,[],[f3618]) ).

fof(f9023,plain,
    spl50_554,
    inference(avatar_split_clause,[],[f5989,f9021]) ).

fof(f9021,plain,
    ( spl50_554
  <=> ! [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,[spl50_554])]) ).

fof(f5989,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,[],[f5988,f4161]) ).

fof(f5988,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,[],[f5659,f4313]) ).

fof(f5659,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,[],[f4716,f4164]) ).

fof(f4716,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,[],[f3618]) ).

fof(f9019,plain,
    spl50_553,
    inference(avatar_split_clause,[],[f5979,f9017]) ).

fof(f9017,plain,
    ( spl50_553
  <=> ! [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,[spl50_553])]) ).

fof(f5979,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,[],[f5978,f4161]) ).

fof(f5978,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,[],[f5654,f4313]) ).

fof(f5654,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,[],[f4705,f4164]) ).

fof(f4705,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,[],[f3615]) ).

fof(f3615,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,[],[f3614]) ).

fof(f3614,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,[],[f3439]) ).

fof(f3439,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(f9015,plain,
    spl50_552,
    inference(avatar_split_clause,[],[f5977,f9013]) ).

fof(f9013,plain,
    ( spl50_552
  <=> ! [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,[spl50_552])]) ).

fof(f5977,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,[],[f5976,f4161]) ).

fof(f5976,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,[],[f5975,f4313]) ).

fof(f5975,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,[],[f5974,f4161]) ).

fof(f5974,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,[],[f5653,f4313]) ).

fof(f5653,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,[],[f4707,f4164,f4164]) ).

fof(f4707,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,[],[f3615]) ).

fof(f9011,plain,
    spl50_551,
    inference(avatar_split_clause,[],[f5973,f9009]) ).

fof(f9009,plain,
    ( spl50_551
  <=> ! [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,[spl50_551])]) ).

fof(f5973,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,[],[f5972,f4161]) ).

fof(f5972,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,[],[f5652,f4313]) ).

fof(f5652,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,[],[f4708,f4164]) ).

fof(f4708,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,[],[f3615]) ).

fof(f9007,plain,
    spl50_550,
    inference(avatar_split_clause,[],[f5964,f9005]) ).

fof(f9005,plain,
    ( spl50_550
  <=> ! [X2,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_550])]) ).

fof(f5964,plain,
    ! [X2,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
    inference(forward_demodulation,[],[f5757,f5594]) ).

fof(f5757,plain,
    ! [X2,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,X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
    inference(equality_resolution,[],[f5628]) ).

fof(f5628,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X0 ),
    inference(definition_unfolding,[],[f4675,f4164]) ).

fof(f4675,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
      | c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) != X0 ),
    inference(cnf_transformation,[],[f3594]) ).

fof(f9003,plain,
    spl50_549,
    inference(avatar_split_clause,[],[f5944,f9001]) ).

fof(f9001,plain,
    ( spl50_549
  <=> ! [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,[spl50_549])]) ).

fof(f5944,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,[],[f5590,f5579]) ).

fof(f5590,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,[],[f4310,f4164]) ).

fof(f4310,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,[],[f1441]) ).

fof(f1441,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,[],[f961]) ).

fof(f961,axiom,
    ! [X17,X18] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X17))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__Suc1) ).

fof(f8999,plain,
    ( spl50_548
    | ~ spl50_344
    | ~ spl50_395 ),
    inference(avatar_split_clause,[],[f8110,f7922,f7667,f8997]) ).

fof(f8997,plain,
    ( spl50_548
  <=> ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) != X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_548])]) ).

fof(f7667,plain,
    ( spl50_344
  <=> ! [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,[spl50_344])]) ).

fof(f8110,plain,
    ( ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) != X0
    | ~ spl50_344
    | ~ spl50_395 ),
    inference(superposition,[],[f7668,f7923]) ).

fof(f7668,plain,
    ( ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X0
    | ~ spl50_344 ),
    inference(avatar_component_clause,[],[f7667]) ).

fof(f8995,plain,
    spl50_547,
    inference(avatar_split_clause,[],[f5943,f8993]) ).

fof(f8993,plain,
    ( spl50_547
  <=> ! [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,[spl50_547])]) ).

fof(f5943,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,[],[f5589,f5579]) ).

fof(f5589,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,[],[f4309,f4164]) ).

fof(f4309,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,[],[f1440]) ).

fof(f1440,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,[],[f962]) ).

fof(f962,axiom,
    ! [X17,X18] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X18))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__Suc2) ).

fof(f8991,plain,
    spl50_546,
    inference(avatar_split_clause,[],[f5919,f8989]) ).

fof(f8989,plain,
    ( spl50_546
  <=> ! [X0] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),X0) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,sK19),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_546])]) ).

fof(f5919,plain,
    ! [X0] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),X0) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,sK19),X0),
    inference(forward_demodulation,[],[f4179,f4131]) ).

fof(f4179,plain,
    ! [X0] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),X0) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X0)),
    inference(cnf_transformation,[],[f1327]) ).

fof(f1327,plain,
    ! [X0] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),X0) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X0)),
    inference(rectify,[],[f556]) ).

fof(f556,axiom,
    ! [X2] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),X2) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_q_I2_J) ).

fof(f8987,plain,
    spl50_545,
    inference(avatar_split_clause,[],[f5908,f8984]) ).

fof(f8984,plain,
    ( spl50_545
  <=> c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_545])]) ).

fof(f5908,plain,
    c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),
    inference(forward_demodulation,[],[f4119,f4116]) ).

fof(f4119,plain,
    c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____)),
    inference(cnf_transformation,[],[f19]) ).

fof(f19,axiom,
    c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_w) ).

fof(f8982,plain,
    spl50_544,
    inference(avatar_split_clause,[],[f5877,f8980]) ).

fof(f5877,plain,
    ! [X3,X0,X1] :
      ( c_Rings_Odvd__class_Odvd(X3,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0))
      | ~ class_Rings_Odvd(X3) ),
    inference(equality_resolution,[],[f5382]) ).

fof(f5382,plain,
    ! [X2,X3,X0,X1] :
      ( c_Rings_Odvd__class_Odvd(X3,X1,X2)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0) != X2
      | ~ class_Rings_Odvd(X3) ),
    inference(cnf_transformation,[],[f3228]) ).

fof(f3228,plain,
    ! [X0,X1,X2,X3] :
      ( c_Rings_Odvd__class_Odvd(X3,X1,X2)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0) != X2
      | ~ class_Rings_Odvd(X3) ),
    inference(flattening,[],[f3227]) ).

fof(f3227,plain,
    ! [X0,X1,X2,X3] :
      ( c_Rings_Odvd__class_Odvd(X3,X1,X2)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0) != X2
      | ~ class_Rings_Odvd(X3) ),
    inference(ennf_transformation,[],[f2149]) ).

fof(f2149,plain,
    ! [X0,X1,X2,X3] :
      ( class_Rings_Odvd(X3)
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0) = X2
       => c_Rings_Odvd__class_Odvd(X3,X1,X2) ) ),
    inference(rectify,[],[f826]) ).

fof(f826,axiom,
    ! [X38,X13,X4,X5] :
      ( class_Rings_Odvd(X5)
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),X38) = X4
       => c_Rings_Odvd__class_Odvd(X5,X13,X4) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvdI) ).

fof(f8978,plain,
    spl50_543,
    inference(avatar_split_clause,[],[f5873,f8976]) ).

fof(f8976,plain,
    ( spl50_543
  <=> ! [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,[spl50_543])]) ).

fof(f5873,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,[],[f5268]) ).

fof(f5268,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,[],[f3804]) ).

fof(f8974,plain,
    spl50_542,
    inference(avatar_split_clause,[],[f5858,f8972]) ).

fof(f8972,plain,
    ( spl50_542
  <=> ! [X4,X0,X2] :
        ( hBOOL(hAPP(X0,X4))
        | ~ sP8(X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X4),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_542])]) ).

fof(f5858,plain,
    ! [X2,X0,X4] :
      ( hBOOL(hAPP(X0,X4))
      | ~ sP8(X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X4),X2) ),
    inference(equality_resolution,[],[f5209]) ).

fof(f5209,plain,
    ! [X2,X0,X1,X4] :
      ( hBOOL(hAPP(X0,X4))
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X4) != X1
      | ~ sP8(X0,X1,X2) ),
    inference(cnf_transformation,[],[f3771]) ).

fof(f8970,plain,
    spl50_541,
    inference(avatar_split_clause,[],[f5857,f8968]) ).

fof(f8968,plain,
    ( spl50_541
  <=> ! [X4,X0,X2] :
        ( hBOOL(hAPP(X0,X4))
        | ~ sP7(X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X4),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_541])]) ).

fof(f5857,plain,
    ! [X2,X0,X4] :
      ( hBOOL(hAPP(X0,X4))
      | ~ sP7(X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X4),X2) ),
    inference(equality_resolution,[],[f5201]) ).

fof(f5201,plain,
    ! [X2,X0,X1,X4] :
      ( hBOOL(hAPP(X0,X4))
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X4) != X1
      | ~ sP7(X0,X1,X2) ),
    inference(cnf_transformation,[],[f3765]) ).

fof(f8966,plain,
    spl50_540,
    inference(avatar_split_clause,[],[f5813,f8964]) ).

fof(f8964,plain,
    ( spl50_540
  <=> ! [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,[spl50_540])]) ).

fof(f5813,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,[],[f4981]) ).

fof(f4981,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,[],[f3704]) ).

fof(f8962,plain,
    spl50_539,
    inference(avatar_split_clause,[],[f5714,f8960]) ).

fof(f8960,plain,
    ( spl50_539
  <=> ! [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,[spl50_539])]) ).

fof(f5714,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,[],[f4427]) ).

fof(f4427,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,[],[f3520]) ).

fof(f8958,plain,
    spl50_538,
    inference(avatar_split_clause,[],[f5706,f8956]) ).

fof(f8956,plain,
    ( spl50_538
  <=> ! [X1] :
        ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X1,c_Groups_Osgn__class_Osgn(X1,c_Groups_Ozero__class_Ozero(X1)))
        | ~ class_RealVector_Oreal__normed__vector(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_538])]) ).

fof(f5706,plain,
    ! [X1] :
      ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X1,c_Groups_Osgn__class_Osgn(X1,c_Groups_Ozero__class_Ozero(X1)))
      | ~ class_RealVector_Oreal__normed__vector(X1) ),
    inference(equality_resolution,[],[f4393]) ).

fof(f4393,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X1,c_Groups_Osgn__class_Osgn(X1,X0))
      | c_Groups_Ozero__class_Ozero(X1) != X0
      | ~ class_RealVector_Oreal__normed__vector(X1) ),
    inference(cnf_transformation,[],[f2448]) ).

fof(f8954,plain,
    ( spl50_537
    | ~ spl50_98
    | ~ spl50_389 ),
    inference(avatar_split_clause,[],[f8064,f7897,f6536,f8951]) ).

fof(f8951,plain,
    ( spl50_537
  <=> c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_537])]) ).

fof(f7897,plain,
    ( spl50_389
  <=> ! [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,[spl50_389])]) ).

fof(f8064,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))
    | ~ spl50_98
    | ~ spl50_389 ),
    inference(resolution,[],[f7898,f6538]) ).

fof(f7898,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)) )
    | ~ spl50_389 ),
    inference(avatar_component_clause,[],[f7897]) ).

fof(f8949,plain,
    spl50_536,
    inference(avatar_split_clause,[],[f5591,f8947]) ).

fof(f8947,plain,
    ( spl50_536
  <=> ! [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,[spl50_536])]) ).

fof(f5591,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,[],[f4311,f4164]) ).

fof(f4311,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,[],[f1442]) ).

fof(f1442,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,[],[f983]) ).

fof(f983,axiom,
    ! [X3,X17] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X3),c_Nat_OSuc(X17)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__less__Suc) ).

fof(f8945,plain,
    spl50_535,
    inference(avatar_split_clause,[],[f5260,f8943]) ).

fof(f8943,plain,
    ( spl50_535
  <=> ! [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,[spl50_535])]) ).

fof(f5260,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,[],[f2067]) ).

fof(f2067,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,[],[f711]) ).

fof(f711,axiom,
    ! [X24,X72,X73,X5] : hAPP(hAPP(c_Power_Opower_Opower(X5,X73,X72),X24),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X73,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power_Opower_Opower__0) ).

fof(f8941,plain,
    spl50_534,
    inference(avatar_split_clause,[],[f5215,f8939]) ).

fof(f8939,plain,
    ( spl50_534
  <=> ! [X2,X0,X1] :
        ( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
        | ~ sP8(X2,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_534])]) ).

fof(f5215,plain,
    ! [X2,X0,X1] :
      ( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
      | ~ sP8(X2,X1,X0) ),
    inference(cnf_transformation,[],[f3772]) ).

fof(f3772,plain,
    ! [X0,X1,X2] :
      ( ( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
        | ~ sP8(X2,X1,X0) )
      & ( sP8(X2,X1,X0)
        | ~ hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ) ),
    inference(nnf_transformation,[],[f3454]) ).

fof(f3454,plain,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
    <=> sP8(X2,X1,X0) ),
    inference(definition_folding,[],[f3090,f3453]) ).

fof(f3090,plain,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
    <=> ( ! [X3] :
            ( hBOOL(hAPP(X2,X3))
            | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3) != X1 )
        & ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ) ),
    inference(ennf_transformation,[],[f2048]) ).

fof(f2048,plain,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
    <=> ~ ( ? [X3] :
              ( ~ hBOOL(hAPP(X2,X3))
              & c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3) = X1 )
          | ( ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            & c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ) ),
    inference(rectify,[],[f496]) ).

fof(f496,axiom,
    ! [X21,X24,X49] :
      ( hBOOL(hAPP(X49,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X24,X21)))
    <=> ~ ( ? [X57] :
              ( ~ hBOOL(hAPP(X49,X57))
              & c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X57) = X24 )
          | ( ~ hBOOL(hAPP(X49,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            & c_Orderings_Oord__class_Oless(tc_Nat_Onat,X24,X21) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__diff__split__asm) ).

fof(f8937,plain,
    spl50_533,
    inference(avatar_split_clause,[],[f5214,f8935]) ).

fof(f8935,plain,
    ( spl50_533
  <=> ! [X2,X0,X1] :
        ( sP8(X2,X1,X0)
        | ~ hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_533])]) ).

fof(f5214,plain,
    ! [X2,X0,X1] :
      ( sP8(X2,X1,X0)
      | ~ hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ),
    inference(cnf_transformation,[],[f3772]) ).

fof(f8933,plain,
    spl50_532,
    inference(avatar_split_clause,[],[f5207,f8931]) ).

fof(f8931,plain,
    ( spl50_532
  <=> ! [X2,X0,X1] :
        ( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
        | ~ sP7(X2,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_532])]) ).

fof(f5207,plain,
    ! [X2,X0,X1] :
      ( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
      | ~ sP7(X2,X1,X0) ),
    inference(cnf_transformation,[],[f3766]) ).

fof(f3766,plain,
    ! [X0,X1,X2] :
      ( ( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
        | ~ sP7(X2,X1,X0) )
      & ( sP7(X2,X1,X0)
        | ~ hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ) ),
    inference(nnf_transformation,[],[f3452]) ).

fof(f3452,plain,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
    <=> sP7(X2,X1,X0) ),
    inference(definition_folding,[],[f3089,f3451]) ).

fof(f3089,plain,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
    <=> ( ! [X3] :
            ( hBOOL(hAPP(X2,X3))
            | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3) != X1 )
        & ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ) ),
    inference(ennf_transformation,[],[f2047]) ).

fof(f2047,plain,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
    <=> ( ! [X3] :
            ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3) = X1
           => hBOOL(hAPP(X2,X3)) )
        & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
         => hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
    inference(rectify,[],[f495]) ).

fof(f495,axiom,
    ! [X21,X24,X49] :
      ( hBOOL(hAPP(X49,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X24,X21)))
    <=> ( ! [X57] :
            ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X57) = X24
           => hBOOL(hAPP(X49,X57)) )
        & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X24,X21)
         => hBOOL(hAPP(X49,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__diff__split) ).

fof(f8929,plain,
    spl50_531,
    inference(avatar_split_clause,[],[f5206,f8927]) ).

fof(f8927,plain,
    ( spl50_531
  <=> ! [X2,X0,X1] :
        ( sP7(X2,X1,X0)
        | ~ hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_531])]) ).

fof(f5206,plain,
    ! [X2,X0,X1] :
      ( sP7(X2,X1,X0)
      | ~ hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ),
    inference(cnf_transformation,[],[f3766]) ).

fof(f8925,plain,
    spl50_530,
    inference(avatar_split_clause,[],[f5198,f8923]) ).

fof(f8923,plain,
    ( spl50_530
  <=> ! [X5,X2,X0,X6,X1] :
        ( hAPP(X0,X5) = hAPP(X0,X6)
        | ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X2,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_530])]) ).

fof(f5198,plain,
    ! [X2,X0,X1,X6,X5] :
      ( hAPP(X0,X5) = hAPP(X0,X6)
      | ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X2,X1,X0) ),
    inference(cnf_transformation,[],[f3760]) ).

fof(f8921,plain,
    spl50_529,
    inference(avatar_split_clause,[],[f5172,f8919]) ).

fof(f5172,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,[],[f3064]) ).

fof(f3064,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,[],[f2033]) ).

fof(f2033,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,[],[f390]) ).

fof(f390,axiom,
    ! [X38,X39,X18] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X39),X38)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X38) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__lessD1) ).

fof(f8917,plain,
    spl50_528,
    inference(avatar_split_clause,[],[f5169,f8915]) ).

fof(f8915,plain,
    ( spl50_528
  <=> ! [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,[spl50_528])]) ).

fof(f5169,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,[],[f3062]) ).

fof(f3062,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,[],[f2031]) ).

fof(f2031,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,[],[f405]) ).

fof(f405,axiom,
    ! [X3,X38,X17] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X38),X3)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leD1) ).

fof(f8913,plain,
    spl50_527,
    inference(avatar_split_clause,[],[f5168,f8911]) ).

fof(f8911,plain,
    ( spl50_527
  <=> ! [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,[spl50_527])]) ).

fof(f5168,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,[],[f3061]) ).

fof(f3061,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,[],[f2030]) ).

fof(f2030,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,[],[f406]) ).

fof(f406,axiom,
    ! [X3,X38,X17] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X38),X3)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X38,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leD2) ).

fof(f8909,plain,
    ( spl50_526
    | ~ spl50_99
    | ~ spl50_389 ),
    inference(avatar_split_clause,[],[f8063,f7897,f6541,f8906]) ).

fof(f8906,plain,
    ( spl50_526
  <=> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_526])]) ).

fof(f8063,plain,
    ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    | ~ spl50_99
    | ~ spl50_389 ),
    inference(resolution,[],[f7898,f6543]) ).

fof(f8904,plain,
    spl50_525,
    inference(avatar_split_clause,[],[f5138,f8902]) ).

fof(f5138,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,[],[f3026]) ).

fof(f3026,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,[],[f2008]) ).

fof(f2008,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,[],[f453]) ).

fof(f453,axiom,
    ! [X3,X38,X39] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X39,X38)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X39,X3),X38) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__diff__less) ).

fof(f8900,plain,
    spl50_524,
    inference(avatar_split_clause,[],[f5135,f8898]) ).

fof(f8898,plain,
    ( spl50_524
  <=> ! [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,[spl50_524])]) ).

fof(f5135,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,[],[f3023]) ).

fof(f3023,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,[],[f2005]) ).

fof(f2005,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,[],[f394]) ).

fof(f394,axiom,
    ! [X17,X39,X18] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X39)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X39)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__less__add2) ).

fof(f8896,plain,
    spl50_523,
    inference(avatar_split_clause,[],[f5134,f8894]) ).

fof(f8894,plain,
    ( spl50_523
  <=> ! [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,[spl50_523])]) ).

fof(f5134,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,[],[f3022]) ).

fof(f3022,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,[],[f2004]) ).

fof(f2004,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,[],[f395]) ).

fof(f395,axiom,
    ! [X17,X39,X18] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X39)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X39,X17)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__less__add1) ).

fof(f8892,plain,
    spl50_522,
    inference(avatar_split_clause,[],[f5107,f8890]) ).

fof(f8890,plain,
    ( spl50_522
  <=> ! [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,[spl50_522])]) ).

fof(f5107,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,[],[f2994]) ).

fof(f2994,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,[],[f1982]) ).

fof(f1982,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,[],[f410]) ).

fof(f410,axiom,
    ! [X17,X39,X18] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X39)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X39,X17)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__le__add1) ).

fof(f8888,plain,
    spl50_521,
    inference(avatar_split_clause,[],[f5105,f8886]) ).

fof(f8886,plain,
    ( spl50_521
  <=> ! [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,[spl50_521])]) ).

fof(f5105,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,[],[f2992]) ).

fof(f2992,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,[],[f1980]) ).

fof(f1980,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,[],[f777]) ).

fof(f777,axiom,
    ! [X7,X14,X9] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X9,X14)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X9,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,X14)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I4_J) ).

fof(f8884,plain,
    spl50_520,
    inference(avatar_split_clause,[],[f5047,f8882]) ).

fof(f8882,plain,
    ( spl50_520
  <=> ! [X2,X0,X1] :
        ( 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,[spl50_520])]) ).

fof(f5047,plain,
    ! [X2,X0,X1] :
      ( 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,[],[f2922]) ).

fof(f2922,plain,
    ! [X0,X1,X2] :
      ( 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,[],[f1937]) ).

fof(f1937,plain,
    ! [X0,X1,X2] :
      ( class_Rings_Ocomm__semiring__1(X2)
     => c_Rings_Odvd__class_Odvd(X2,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) ),
    inference(rectify,[],[f831]) ).

fof(f831,axiom,
    ! [X13,X4,X5] :
      ( class_Rings_Ocomm__semiring__1(X5)
     => c_Rings_Odvd__class_Odvd(X5,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X13)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__triv__left) ).

fof(f8880,plain,
    spl50_519,
    inference(avatar_split_clause,[],[f5046,f8878]) ).

fof(f8878,plain,
    ( spl50_519
  <=> ! [X2,X0,X1] :
        ( 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,[spl50_519])]) ).

fof(f5046,plain,
    ! [X2,X0,X1] :
      ( 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,[],[f2921]) ).

fof(f2921,plain,
    ! [X0,X1,X2] :
      ( 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,[],[f1936]) ).

fof(f1936,plain,
    ! [X0,X1,X2] :
      ( class_Rings_Ocomm__semiring__1(X2)
     => c_Rings_Odvd__class_Odvd(X2,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1)) ),
    inference(rectify,[],[f830]) ).

fof(f830,axiom,
    ! [X13,X4,X5] :
      ( class_Rings_Ocomm__semiring__1(X5)
     => c_Rings_Odvd__class_Odvd(X5,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__triv__right) ).

fof(f8876,plain,
    spl50_518,
    inference(avatar_split_clause,[],[f5045,f8874]) ).

fof(f5045,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,[],[f2920]) ).

fof(f2920,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,[],[f1935]) ).

fof(f1935,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,[],[f515]) ).

fof(f515,axiom,
    ! [X23,X4,X5] :
      ( class_Rings_Ocomm__semiring__1(X5)
     => c_Groups_Oplus__class_Oplus(X5,X4,X23) = c_Groups_Oplus__class_Oplus(X5,X23,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).

fof(f8872,plain,
    spl50_517,
    inference(avatar_split_clause,[],[f5001,f8870]) ).

fof(f8870,plain,
    ( spl50_517
  <=> ! [X2,X0,X1] :
        ( c_Groups_Oplus__class_Oplus(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),X0) = X1
        | ~ class_Groups_Ogroup__add(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_517])]) ).

fof(f5001,plain,
    ! [X2,X0,X1] :
      ( c_Groups_Oplus__class_Oplus(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),X0) = X1
      | ~ class_Groups_Ogroup__add(X2) ),
    inference(cnf_transformation,[],[f2874]) ).

fof(f2874,plain,
    ! [X0,X1,X2] :
      ( c_Groups_Oplus__class_Oplus(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),X0) = X1
      | ~ class_Groups_Ogroup__add(X2) ),
    inference(ennf_transformation,[],[f1902]) ).

fof(f1902,plain,
    ! [X0,X1,X2] :
      ( class_Groups_Ogroup__add(X2)
     => c_Groups_Oplus__class_Oplus(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),X0) = X1 ),
    inference(rectify,[],[f306]) ).

fof(f306,axiom,
    ! [X13,X4,X5] :
      ( class_Groups_Ogroup__add(X5)
     => c_Groups_Oplus__class_Oplus(X5,c_Groups_Ominus__class_Ominus(X5,X4,X13),X13) = X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__cancel) ).

fof(f8868,plain,
    spl50_516,
    inference(avatar_split_clause,[],[f5000,f8866]) ).

fof(f8866,plain,
    ( spl50_516
  <=> ! [X2,X0,X1] :
        ( c_Groups_Ominus__class_Ominus(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),X0) = X1
        | ~ class_Groups_Ogroup__add(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_516])]) ).

fof(f5000,plain,
    ! [X2,X0,X1] :
      ( c_Groups_Ominus__class_Ominus(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),X0) = X1
      | ~ class_Groups_Ogroup__add(X2) ),
    inference(cnf_transformation,[],[f2873]) ).

fof(f2873,plain,
    ! [X0,X1,X2] :
      ( c_Groups_Ominus__class_Ominus(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),X0) = X1
      | ~ class_Groups_Ogroup__add(X2) ),
    inference(ennf_transformation,[],[f1901]) ).

fof(f1901,plain,
    ! [X0,X1,X2] :
      ( class_Groups_Ogroup__add(X2)
     => c_Groups_Ominus__class_Ominus(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),X0) = X1 ),
    inference(rectify,[],[f305]) ).

fof(f305,axiom,
    ! [X13,X4,X5] :
      ( class_Groups_Ogroup__add(X5)
     => c_Groups_Ominus__class_Ominus(X5,c_Groups_Oplus__class_Oplus(X5,X4,X13),X13) = X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__diff__cancel) ).

fof(f8864,plain,
    ( spl50_515
    | ~ spl50_16
    | ~ spl50_387 ),
    inference(avatar_split_clause,[],[f8058,f7889,f6126,f8861]) ).

fof(f8861,plain,
    ( spl50_515
  <=> c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_515])]) ).

fof(f7889,plain,
    ( spl50_387
  <=> ! [X0] :
        ( c_Groups_Ozero__class_Ozero(X0) = c_Groups_Osgn__class_Osgn(X0,c_Groups_Ozero__class_Ozero(X0))
        | ~ class_RealVector_Oreal__normed__vector(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_387])]) ).

fof(f8058,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))
    | ~ spl50_16
    | ~ spl50_387 ),
    inference(resolution,[],[f7890,f6128]) ).

fof(f6128,plain,
    ( class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
    | ~ spl50_16 ),
    inference(avatar_component_clause,[],[f6126]) ).

fof(f7890,plain,
    ( ! [X0] :
        ( ~ class_RealVector_Oreal__normed__vector(X0)
        | c_Groups_Ozero__class_Ozero(X0) = c_Groups_Osgn__class_Osgn(X0,c_Groups_Ozero__class_Ozero(X0)) )
    | ~ spl50_387 ),
    inference(avatar_component_clause,[],[f7889]) ).

fof(f8859,plain,
    spl50_514,
    inference(avatar_split_clause,[],[f4903,f8857]) ).

fof(f8857,plain,
    ( spl50_514
  <=> ! [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,[spl50_514])]) ).

fof(f4903,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,[],[f3684]) ).

fof(f8855,plain,
    spl50_513,
    inference(avatar_split_clause,[],[f4714,f8853]) ).

fof(f8853,plain,
    ( spl50_513
  <=> ! [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,[spl50_513])]) ).

fof(f4714,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,[],[f3618]) ).

fof(f8851,plain,
    spl50_512,
    inference(avatar_split_clause,[],[f4706,f8849]) ).

fof(f8849,plain,
    ( spl50_512
  <=> ! [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,[spl50_512])]) ).

fof(f4706,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,[],[f3615]) ).

fof(f8847,plain,
    spl50_511,
    inference(avatar_split_clause,[],[f4704,f8845]) ).

fof(f8845,plain,
    ( spl50_511
  <=> ! [X0,X1] :
        ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_511])]) ).

fof(f4704,plain,
    ! [X0,X1] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0) ),
    inference(cnf_transformation,[],[f3613]) ).

fof(f3613,plain,
    ! [X0,X1] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0) )
      & ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ) ),
    inference(nnf_transformation,[],[f1720]) ).

fof(f1720,plain,
    ! [X0,X1] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
    <=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0) ),
    inference(rectify,[],[f865]) ).

fof(f865,axiom,
    ! [X16,X36] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X36,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X16,X36))
    <=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X36,X16) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__reduce) ).

fof(f8843,plain,
    spl50_510,
    inference(avatar_split_clause,[],[f4703,f8841]) ).

fof(f8841,plain,
    ( spl50_510
  <=> ! [X0,X1] :
        ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_510])]) ).

fof(f4703,plain,
    ! [X0,X1] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
    inference(cnf_transformation,[],[f3613]) ).

fof(f8839,plain,
    spl50_509,
    inference(avatar_split_clause,[],[f4701,f8837]) ).

fof(f8837,plain,
    ( spl50_509
  <=> ! [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,[spl50_509])]) ).

fof(f4701,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,[],[f3612]) ).

fof(f3612,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,[],[f3611]) ).

fof(f3611,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,[],[f1719]) ).

fof(f1719,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,[],[f379]) ).

fof(f379,axiom,
    ! [X16,X32] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X32,X16)
    <=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X16
        & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X32 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__is__0) ).

fof(f8835,plain,
    spl50_508,
    inference(avatar_split_clause,[],[f4700,f8833]) ).

fof(f8833,plain,
    ( spl50_508
  <=> ! [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,[spl50_508])]) ).

fof(f4700,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,[],[f3612]) ).

fof(f8831,plain,
    spl50_507,
    inference(avatar_split_clause,[],[f4698,f8829]) ).

fof(f8829,plain,
    ( spl50_507
  <=> ! [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,[spl50_507])]) ).

fof(f4698,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,[],[f3610]) ).

fof(f3610,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,[],[f1718]) ).

fof(f1718,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,[],[f474]) ).

fof(f474,axiom,
    ! [X16,X32] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X32,X16)
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X32,X16) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__is__0__eq) ).

fof(f8827,plain,
    spl50_506,
    inference(avatar_split_clause,[],[f4668,f8825]) ).

fof(f8825,plain,
    ( spl50_506
  <=> ! [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,[spl50_506])]) ).

fof(f4668,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,[],[f3587]) ).

fof(f3587,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,[],[f3586]) ).

fof(f3586,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,[],[f1705]) ).

fof(f1705,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,[],[f620]) ).

fof(f620,axiom,
    ! [X63,X33] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X33,X63)
    <=> ( X33 != X63
        & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X33,X63) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__le) ).

fof(f8823,plain,
    spl50_505,
    inference(avatar_split_clause,[],[f4651,f8821]) ).

fof(f8821,plain,
    ( spl50_505
  <=> ! [X0,X1] :
        ( X0 = X1
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_505])]) ).

fof(f4651,plain,
    ! [X0,X1] :
      ( X0 = X1
      | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ),
    inference(cnf_transformation,[],[f3572]) ).

fof(f3572,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
        | ( X0 != X1
          & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) ) )
      & ( X0 = X1
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ) ),
    inference(flattening,[],[f3571]) ).

fof(f3571,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
        | ( X0 != X1
          & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) ) )
      & ( X0 = X1
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ) ),
    inference(nnf_transformation,[],[f1699]) ).

fof(f1699,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
    <=> ( X0 = X1
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) ) ),
    inference(rectify,[],[f236]) ).

fof(f236,axiom,
    ! [X20,X12] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X12,X20)
    <=> ( X12 = X20
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X12,X20) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__real__def) ).

fof(f8819,plain,
    ( spl50_504
    | ~ spl50_17
    | ~ spl50_386 ),
    inference(avatar_split_clause,[],[f8057,f7885,f6131,f8816]) ).

fof(f8816,plain,
    ( spl50_504
  <=> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_504])]) ).

fof(f6131,plain,
    ( spl50_17
  <=> class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_17])]) ).

fof(f7885,plain,
    ( spl50_386
  <=> ! [X0] :
        ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X0,c_Groups_Ozero__class_Ozero(X0))
        | ~ class_RealVector_Oreal__normed__vector(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_386])]) ).

fof(f8057,plain,
    ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    | ~ spl50_17
    | ~ spl50_386 ),
    inference(resolution,[],[f7886,f6133]) ).

fof(f6133,plain,
    ( class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal)
    | ~ spl50_17 ),
    inference(avatar_component_clause,[],[f6131]) ).

fof(f7886,plain,
    ( ! [X0] :
        ( ~ class_RealVector_Oreal__normed__vector(X0)
        | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X0,c_Groups_Ozero__class_Ozero(X0)) )
    | ~ spl50_386 ),
    inference(avatar_component_clause,[],[f7885]) ).

fof(f8814,plain,
    spl50_503,
    inference(avatar_split_clause,[],[f4572,f8812]) ).

fof(f8812,plain,
    ( spl50_503
  <=> ! [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,[spl50_503])]) ).

fof(f4572,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,[],[f2598]) ).

fof(f2598,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,[],[f2597]) ).

fof(f2597,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,[],[f1641]) ).

fof(f1641,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,[],[f365]) ).

fof(f365,axiom,
    ! [X3,X17] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X3)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X17)
       => X3 = X17 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__antisym) ).

fof(f8810,plain,
    spl50_502,
    inference(avatar_split_clause,[],[f4571,f8808]) ).

fof(f8808,plain,
    ( spl50_502
  <=> ! [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,[spl50_502])]) ).

fof(f4571,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,[],[f2596]) ).

fof(f2596,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,[],[f2595]) ).

fof(f2595,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,[],[f1640]) ).

fof(f1640,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,[],[f400]) ).

fof(f400,axiom,
    ! [X3,X17] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X3)
     => ( X3 != X17
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X3) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__neq__implies__less) ).

fof(f8806,plain,
    spl50_501,
    inference(avatar_split_clause,[],[f4566,f8804]) ).

fof(f8804,plain,
    ( spl50_501
  <=> ! [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,[spl50_501])]) ).

fof(f4566,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,[],[f2590]) ).

fof(f2590,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,[],[f1635]) ).

fof(f1635,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,[],[f475]) ).

fof(f475,axiom,
    ! [X3,X17] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X3)
     => c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__is__0__eq_H) ).

fof(f8802,plain,
    spl50_500,
    inference(avatar_split_clause,[],[f4563,f8800]) ).

fof(f8800,plain,
    ( spl50_500
  <=> ! [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,[spl50_500])]) ).

fof(f4563,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,[],[f2587]) ).

fof(f2587,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,[],[f2586]) ).

fof(f2586,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,[],[f1632]) ).

fof(f1632,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,[],[f672]) ).

fof(f672,axiom,
    ! [X15,X14] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X14,X15)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X15,X14)
       => X14 = X15 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__antisym) ).

fof(f8798,plain,
    spl50_499,
    inference(avatar_split_clause,[],[f4561,f8796]) ).

fof(f8796,plain,
    ( spl50_499
  <=> ! [X0,X1] :
        ( X0 = X1
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_499])]) ).

fof(f4561,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ),
    inference(cnf_transformation,[],[f2584]) ).

fof(f2584,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ),
    inference(flattening,[],[f2583]) ).

fof(f2583,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ),
    inference(ennf_transformation,[],[f1630]) ).

fof(f1630,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
     => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
       => X0 = X1 ) ),
    inference(rectify,[],[f202]) ).

fof(f202,axiom,
    ! [X15,X14] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X14,X15)
     => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X15,X14)
       => X14 = X15 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__antisym) ).

fof(f8794,plain,
    spl50_498,
    inference(avatar_split_clause,[],[f4543,f8792]) ).

fof(f8792,plain,
    ( spl50_498
  <=> ! [X0,X1] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,X1)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0)
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_498])]) ).

fof(f4543,plain,
    ! [X0,X1] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,X1)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0)
      | X0 = X1 ),
    inference(cnf_transformation,[],[f2561]) ).

fof(f2561,plain,
    ! [X0,X1] :
      ( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,X1)
        & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0) )
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0)
      | X0 = X1 ),
    inference(flattening,[],[f2560]) ).

fof(f2560,plain,
    ! [X0,X1] :
      ( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,X1)
        & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0) )
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0)
      | X0 = X1 ),
    inference(ennf_transformation,[],[f1616]) ).

fof(f1616,plain,
    ! [X0,X1] :
      ( X0 != X1
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0)
       => ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,X1)
          & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0) ) ) ),
    inference(rectify,[],[f895]) ).

fof(f895,axiom,
    ! [X13,X4] :
      ( X4 != X13
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X4,X13)
       => ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X13,X4)
          & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X4,X13) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oneq__le__trans) ).

fof(f8790,plain,
    spl50_497,
    inference(avatar_split_clause,[],[f4541,f8788]) ).

fof(f8788,plain,
    ( spl50_497
  <=> ! [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,[spl50_497])]) ).

fof(f4541,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,[],[f2559]) ).

fof(f2559,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,[],[f2558]) ).

fof(f2558,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,[],[f1615]) ).

fof(f1615,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,[],[f357]) ).

fof(f357,axiom,
    ! [X7,X9] :
      ( X7 != X9
     => ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X9,X7)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,X9) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE__nat) ).

fof(f8786,plain,
    spl50_496,
    inference(avatar_split_clause,[],[f4530,f8784]) ).

fof(f8784,plain,
    ( spl50_496
  <=> ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(X1) = X0
        | ~ 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,[spl50_496])]) ).

fof(f4530,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X1) = X0
      | ~ c_Rings_Odvd__class_Odvd(X1,c_Groups_Ozero__class_Ozero(X1),X0)
      | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(cnf_transformation,[],[f2549]) ).

fof(f2549,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X1) = X0
      | ~ c_Rings_Odvd__class_Odvd(X1,c_Groups_Ozero__class_Ozero(X1),X0)
      | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(flattening,[],[f2548]) ).

fof(f2548,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X1) = X0
      | ~ c_Rings_Odvd__class_Odvd(X1,c_Groups_Ozero__class_Ozero(X1),X0)
      | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(ennf_transformation,[],[f1606]) ).

fof(f1606,plain,
    ! [X0,X1] :
      ( class_Rings_Ocomm__semiring__1(X1)
     => ( c_Rings_Odvd__class_Odvd(X1,c_Groups_Ozero__class_Ozero(X1),X0)
       => c_Groups_Ozero__class_Ozero(X1) = X0 ) ),
    inference(rectify,[],[f812]) ).

fof(f812,axiom,
    ! [X4,X5] :
      ( class_Rings_Ocomm__semiring__1(X5)
     => ( c_Rings_Odvd__class_Odvd(X5,c_Groups_Ozero__class_Ozero(X5),X4)
       => c_Groups_Ozero__class_Ozero(X5) = X4 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__0__left) ).

fof(f8782,plain,
    spl50_495,
    inference(avatar_split_clause,[],[f4524,f8780]) ).

fof(f8780,plain,
    ( spl50_495
  <=> ! [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,[spl50_495])]) ).

fof(f4524,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,[],[f2542]) ).

fof(f2542,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,[],[f1600]) ).

fof(f1600,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,[],[f537]) ).

fof(f537,axiom,
    ! [X4,X5] :
      ( class_Rings_Ocomm__semiring__1(X5)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Oone__class_Oone(X5)),X4) = X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).

fof(f8778,plain,
    spl50_494,
    inference(avatar_split_clause,[],[f4523,f8776]) ).

fof(f8776,plain,
    ( spl50_494
  <=> ! [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,[spl50_494])]) ).

fof(f4523,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,[],[f2541]) ).

fof(f2541,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,[],[f1599]) ).

fof(f1599,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,[],[f538]) ).

fof(f538,axiom,
    ! [X4,X5] :
      ( class_Rings_Ocomm__semiring__1(X5)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),c_Groups_Oone__class_Oone(X5)) = X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).

fof(f8774,plain,
    ( spl50_493
    | ~ spl50_16
    | ~ spl50_386 ),
    inference(avatar_split_clause,[],[f8056,f7885,f6126,f8771]) ).

fof(f8771,plain,
    ( spl50_493
  <=> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_493])]) ).

fof(f8056,plain,
    ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))
    | ~ spl50_16
    | ~ spl50_386 ),
    inference(resolution,[],[f7886,f6128]) ).

fof(f8769,plain,
    spl50_492,
    inference(avatar_split_clause,[],[f4522,f8767]) ).

fof(f8767,plain,
    ( spl50_492
  <=> ! [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,[spl50_492])]) ).

fof(f4522,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,[],[f2540]) ).

fof(f2540,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,[],[f1598]) ).

fof(f1598,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,[],[f542]) ).

fof(f542,axiom,
    ! [X9,X5] :
      ( class_Rings_Ocomm__semiring__1(X5)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X5),X9),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X9 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).

fof(f8765,plain,
    spl50_491,
    inference(avatar_split_clause,[],[f4509,f8763]) ).

fof(f8763,plain,
    ( spl50_491
  <=> ! [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,[spl50_491])]) ).

fof(f4509,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,[],[f2527]) ).

fof(f2527,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,[],[f1585]) ).

fof(f1585,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,[],[f659]) ).

fof(f659,axiom,
    ! [X54,X5] :
      ( class_Rings_Ocomm__semiring__0(X5)
     => c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = c_Polynomial_Osmult(X5,c_Groups_Ozero__class_Ozero(X5),X54) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__0__left) ).

fof(f8761,plain,
    spl50_490,
    inference(avatar_split_clause,[],[f4503,f8759]) ).

fof(f8759,plain,
    ( spl50_490
  <=> ! [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,[spl50_490])]) ).

fof(f4503,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,[],[f2523]) ).

fof(f2523,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,[],[f1581]) ).

fof(f1581,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,[],[f674]) ).

fof(f674,axiom,
    ! [X3,X5] :
      ( class_Groups_Ozero(X5)
     => c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = c_Polynomial_Omonom(X5,c_Groups_Ozero__class_Ozero(X5),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_monom__eq__0) ).

fof(f8757,plain,
    spl50_489,
    inference(avatar_split_clause,[],[f4501,f8755]) ).

fof(f8755,plain,
    ( spl50_489
  <=> ! [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,[spl50_489])]) ).

fof(f4501,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,[],[f2521]) ).

fof(f2521,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,[],[f1579]) ).

fof(f1579,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,[],[f633]) ).

fof(f633,axiom,
    ! [X53,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X5),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X53) = X53 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__poly__code_I1_J) ).

fof(f8753,plain,
    spl50_488,
    inference(avatar_split_clause,[],[f4500,f8751]) ).

fof(f8751,plain,
    ( spl50_488
  <=> ! [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,[spl50_488])]) ).

fof(f4500,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,[],[f2520]) ).

fof(f2520,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,[],[f1578]) ).

fof(f1578,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,[],[f635]) ).

fof(f635,axiom,
    ! [X54,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X5),X54,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))) = X54 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__poly__code_I2_J) ).

fof(f8749,plain,
    spl50_487,
    inference(avatar_split_clause,[],[f4499,f8747]) ).

fof(f8747,plain,
    ( spl50_487
  <=> ! [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,[spl50_487])]) ).

fof(f4499,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,[],[f2519]) ).

fof(f2519,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,[],[f1577]) ).

fof(f1577,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,[],[f231]) ).

fof(f231,axiom,
    ! [X4,X5] :
      ( class_Groups_Omonoid__mult(X5)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Oone__class_Oone(X5)),X4) = X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__1__left) ).

fof(f8745,plain,
    spl50_486,
    inference(avatar_split_clause,[],[f4498,f8743]) ).

fof(f8743,plain,
    ( spl50_486
  <=> ! [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,[spl50_486])]) ).

fof(f4498,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,[],[f2518]) ).

fof(f2518,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,[],[f1576]) ).

fof(f1576,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,[],[f233]) ).

fof(f233,axiom,
    ! [X4,X5] :
      ( class_Groups_Omonoid__mult(X5)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),c_Groups_Oone__class_Oone(X5)) = X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__1__right) ).

fof(f8741,plain,
    spl50_485,
    inference(avatar_split_clause,[],[f4497,f8739]) ).

fof(f8739,plain,
    ( spl50_485
  <=> ! [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,[spl50_485])]) ).

fof(f4497,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,[],[f2517]) ).

fof(f2517,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,[],[f1575]) ).

fof(f1575,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,[],[f124]) ).

fof(f124,axiom,
    ! [X4,X5] :
      ( class_Groups_Omonoid__mult(X5)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__one__right) ).

fof(f8737,plain,
    spl50_484,
    inference(avatar_split_clause,[],[f4491,f8735]) ).

fof(f8735,plain,
    ( spl50_484
  <=> ! [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,[spl50_484])]) ).

fof(f4491,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,[],[f2511]) ).

fof(f2511,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,[],[f1569]) ).

fof(f1569,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,[],[f232]) ).

fof(f232,axiom,
    ! [X4,X5] :
      ( class_Groups_Ocomm__monoid__mult(X5)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Oone__class_Oone(X5)),X4) = X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__1) ).

fof(f8733,plain,
    spl50_483,
    inference(avatar_split_clause,[],[f4490,f8731]) ).

fof(f8731,plain,
    ( spl50_483
  <=> ! [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,[spl50_483])]) ).

fof(f4490,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,[],[f2510]) ).

fof(f2510,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,[],[f1568]) ).

fof(f1568,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,[],[f234]) ).

fof(f234,axiom,
    ! [X4,X5] :
      ( class_Groups_Ocomm__monoid__mult(X5)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),c_Groups_Oone__class_Oone(X5)) = X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Ocomm__neutral) ).

fof(f8727,plain,
    spl50_482,
    inference(avatar_split_clause,[],[f4480,f8725]) ).

fof(f8725,plain,
    ( spl50_482
  <=> ! [X0,X1] :
        ( c_Groups_Ouminus__class_Ouminus(X1,X0) = c_Groups_Ominus__class_Ominus(X1,c_Groups_Ozero__class_Ozero(X1),X0)
        | ~ class_Groups_Ogroup__add(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_482])]) ).

fof(f4480,plain,
    ! [X0,X1] :
      ( c_Groups_Ouminus__class_Ouminus(X1,X0) = c_Groups_Ominus__class_Ominus(X1,c_Groups_Ozero__class_Ozero(X1),X0)
      | ~ class_Groups_Ogroup__add(X1) ),
    inference(cnf_transformation,[],[f2503]) ).

fof(f2503,plain,
    ! [X0,X1] :
      ( c_Groups_Ouminus__class_Ouminus(X1,X0) = c_Groups_Ominus__class_Ominus(X1,c_Groups_Ozero__class_Ozero(X1),X0)
      | ~ class_Groups_Ogroup__add(X1) ),
    inference(ennf_transformation,[],[f1561]) ).

fof(f1561,plain,
    ! [X0,X1] :
      ( class_Groups_Ogroup__add(X1)
     => c_Groups_Ouminus__class_Ouminus(X1,X0) = c_Groups_Ominus__class_Ominus(X1,c_Groups_Ozero__class_Ozero(X1),X0) ),
    inference(rectify,[],[f271]) ).

fof(f271,axiom,
    ! [X4,X5] :
      ( class_Groups_Ogroup__add(X5)
     => c_Groups_Ominus__class_Ominus(X5,c_Groups_Ozero__class_Ozero(X5),X4) = c_Groups_Ouminus__class_Ouminus(X5,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__0) ).

fof(f8723,plain,
    spl50_481,
    inference(avatar_split_clause,[],[f4479,f8721]) ).

fof(f8721,plain,
    ( spl50_481
  <=> ! [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,[spl50_481])]) ).

fof(f4479,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,[],[f2502]) ).

fof(f2502,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,[],[f1560]) ).

fof(f1560,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,[],[f336]) ).

fof(f336,axiom,
    ! [X4,X5] :
      ( class_Groups_Ogroup__add(X5)
     => c_Groups_Ozero__class_Ozero(X5) = c_Groups_Oplus__class_Oplus(X5,c_Groups_Ouminus__class_Ouminus(X5,X4),X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_left__minus) ).

fof(f8719,plain,
    spl50_480,
    inference(avatar_split_clause,[],[f4478,f8717]) ).

fof(f8717,plain,
    ( spl50_480
  <=> ! [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,[spl50_480])]) ).

fof(f4478,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,[],[f2501]) ).

fof(f2501,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,[],[f1559]) ).

fof(f1559,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,[],[f338]) ).

fof(f338,axiom,
    ! [X4,X5] :
      ( class_Groups_Ogroup__add(X5)
     => c_Groups_Ozero__class_Ozero(X5) = c_Groups_Oplus__class_Oplus(X5,X4,c_Groups_Ouminus__class_Ouminus(X5,X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_right__minus) ).

fof(f8715,plain,
    spl50_479,
    inference(avatar_split_clause,[],[f4473,f8713]) ).

fof(f8713,plain,
    ( spl50_479
  <=> ! [X0,X1] :
        ( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = X0
        | ~ class_Groups_Oab__group__add(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_479])]) ).

fof(f4473,plain,
    ! [X0,X1] :
      ( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = X0
      | ~ class_Groups_Oab__group__add(X1) ),
    inference(cnf_transformation,[],[f2496]) ).

fof(f2496,plain,
    ! [X0,X1] :
      ( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = X0
      | ~ class_Groups_Oab__group__add(X1) ),
    inference(ennf_transformation,[],[f1554]) ).

fof(f1554,plain,
    ! [X0,X1] :
      ( class_Groups_Oab__group__add(X1)
     => c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = X0 ),
    inference(rectify,[],[f638]) ).

fof(f638,axiom,
    ! [X54,X5] :
      ( class_Groups_Oab__group__add(X5)
     => c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X5),X54,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))) = X54 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__poly__code_I2_J) ).

fof(f8711,plain,
    spl50_478,
    inference(avatar_split_clause,[],[f4472,f8709]) ).

fof(f8709,plain,
    ( spl50_478
  <=> ! [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,[spl50_478])]) ).

fof(f4472,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,[],[f2495]) ).

fof(f2495,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,[],[f1553]) ).

fof(f1553,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,[],[f335]) ).

fof(f335,axiom,
    ! [X4,X5] :
      ( class_Groups_Oab__group__add(X5)
     => c_Groups_Ozero__class_Ozero(X5) = c_Groups_Oplus__class_Oplus(X5,c_Groups_Ouminus__class_Ouminus(X5,X4),X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ab__left__minus) ).

fof(f8707,plain,
    spl50_477,
    inference(avatar_split_clause,[],[f4446,f8705]) ).

fof(f8705,plain,
    ( spl50_477
  <=> ! [X0,X1] :
        ( c_Groups_Osgn__class_Osgn(X1,X0) = c_Groups_Osgn__class_Osgn(X1,c_Groups_Osgn__class_Osgn(X1,X0))
        | ~ class_Rings_Olinordered__idom(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_477])]) ).

fof(f4446,plain,
    ! [X0,X1] :
      ( c_Groups_Osgn__class_Osgn(X1,X0) = c_Groups_Osgn__class_Osgn(X1,c_Groups_Osgn__class_Osgn(X1,X0))
      | ~ class_Rings_Olinordered__idom(X1) ),
    inference(cnf_transformation,[],[f2477]) ).

fof(f2477,plain,
    ! [X0,X1] :
      ( c_Groups_Osgn__class_Osgn(X1,X0) = c_Groups_Osgn__class_Osgn(X1,c_Groups_Osgn__class_Osgn(X1,X0))
      | ~ class_Rings_Olinordered__idom(X1) ),
    inference(ennf_transformation,[],[f1538]) ).

fof(f1538,plain,
    ! [X0,X1] :
      ( class_Rings_Olinordered__idom(X1)
     => c_Groups_Osgn__class_Osgn(X1,X0) = c_Groups_Osgn__class_Osgn(X1,c_Groups_Osgn__class_Osgn(X1,X0)) ),
    inference(rectify,[],[f814]) ).

fof(f814,axiom,
    ! [X4,X5] :
      ( class_Rings_Olinordered__idom(X5)
     => c_Groups_Osgn__class_Osgn(X5,X4) = c_Groups_Osgn__class_Osgn(X5,c_Groups_Osgn__class_Osgn(X5,X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__sgn) ).

fof(f8703,plain,
    spl50_476,
    inference(avatar_split_clause,[],[f4416,f8701]) ).

fof(f8701,plain,
    ( spl50_476
  <=> ! [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,[spl50_476])]) ).

fof(f4416,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,[],[f3515]) ).

fof(f3515,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,[],[f2462]) ).

fof(f2462,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,[],[f1523]) ).

fof(f1523,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,[],[f288]) ).

fof(f288,axiom,
    ! [X24,X5] :
      ( class_Groups_Olinordered__ab__group__add(X5)
     => ( c_Groups_Ouminus__class_Ouminus(X5,X24) = X24
      <=> c_Groups_Ozero__class_Ozero(X5) = X24 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__equal__zero) ).

fof(f8699,plain,
    spl50_475,
    inference(avatar_split_clause,[],[f4391,f8697]) ).

fof(f8697,plain,
    ( spl50_475
  <=> ! [X0,X1] :
        ( c_RealVector_Onorm__class_Onorm(X1,X0) = c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ouminus__class_Ouminus(X1,X0))
        | ~ class_RealVector_Oreal__normed__vector(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_475])]) ).

fof(f4391,plain,
    ! [X0,X1] :
      ( c_RealVector_Onorm__class_Onorm(X1,X0) = c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ouminus__class_Ouminus(X1,X0))
      | ~ class_RealVector_Oreal__normed__vector(X1) ),
    inference(cnf_transformation,[],[f2446]) ).

fof(f2446,plain,
    ! [X0,X1] :
      ( c_RealVector_Onorm__class_Onorm(X1,X0) = c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ouminus__class_Ouminus(X1,X0))
      | ~ class_RealVector_Oreal__normed__vector(X1) ),
    inference(ennf_transformation,[],[f1507]) ).

fof(f1507,plain,
    ! [X0,X1] :
      ( class_RealVector_Oreal__normed__vector(X1)
     => c_RealVector_Onorm__class_Onorm(X1,X0) = c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ouminus__class_Ouminus(X1,X0)) ),
    inference(rectify,[],[f321]) ).

fof(f321,axiom,
    ! [X9,X5] :
      ( class_RealVector_Oreal__normed__vector(X5)
     => c_RealVector_Onorm__class_Onorm(X5,X9) = c_RealVector_Onorm__class_Onorm(X5,c_Groups_Ouminus__class_Ouminus(X5,X9)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__minus__cancel) ).

fof(f8695,plain,
    spl50_474,
    inference(avatar_split_clause,[],[f4346,f8693]) ).

fof(f8693,plain,
    ( spl50_474
  <=> ! [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,[spl50_474])]) ).

fof(f4346,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,[],[f1474]) ).

fof(f1474,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,[],[f619]) ).

fof(f619,axiom,
    ! [X7,X9] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X7,X9)
      | X7 = X9
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,X9,X7) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__linear) ).

fof(f8691,plain,
    spl50_473,
    inference(avatar_split_clause,[],[f4324,f8689]) ).

fof(f8689,plain,
    ( spl50_473
  <=> ! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_473])]) ).

fof(f4324,plain,
    ! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0),
    inference(cnf_transformation,[],[f1455]) ).

fof(f1455,plain,
    ! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0),
    inference(rectify,[],[f628]) ).

fof(f628,axiom,
    ! [X15,X14] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X14,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X15)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X14,X15),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__int__def) ).

fof(f8687,plain,
    ( ~ spl50_86
    | spl50_472
    | spl50_298
    | ~ spl50_443 ),
    inference(avatar_split_clause,[],[f8463,f8298,f7469,f8684,f6476]) ).

fof(f8463,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    | ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
    | spl50_298
    | ~ spl50_443 ),
    inference(resolution,[],[f8299,f7471]) ).

fof(f8682,plain,
    spl50_471,
    inference(avatar_split_clause,[],[f4318,f8680]) ).

fof(f8680,plain,
    ( spl50_471
  <=> ! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X0) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_471])]) ).

fof(f4318,plain,
    ! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X0) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0)),
    inference(cnf_transformation,[],[f1449]) ).

fof(f1449,plain,
    ! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X0) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0)),
    inference(rectify,[],[f446]) ).

fof(f446,axiom,
    ! [X10,X11] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X11,X10) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X11,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X10)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__diff__def) ).

fof(f8678,plain,
    spl50_470,
    inference(avatar_split_clause,[],[f4317,f8676]) ).

fof(f8676,plain,
    ( spl50_470
  <=> ! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_470])]) ).

fof(f4317,plain,
    ! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)),
    inference(cnf_transformation,[],[f1448]) ).

fof(f1448,plain,
    ! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)),
    inference(rectify,[],[f438]) ).

fof(f438,axiom,
    ! [X7,X9] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X9,X7) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X9,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X7)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__diff__def) ).

fof(f8674,plain,
    spl50_469,
    inference(avatar_split_clause,[],[f4279,f8672]) ).

fof(f4279,plain,
    ! [X0] :
      ( c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X0)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ),
    inference(cnf_transformation,[],[f2391]) ).

fof(f2391,plain,
    ! [X0] :
      ( c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X0)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ),
    inference(ennf_transformation,[],[f1420]) ).

fof(f1420,plain,
    ! [X0] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
     => c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X0) ),
    inference(rectify,[],[f876]) ).

fof(f876,axiom,
    ! [X9] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X9)
     => c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X9) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__sgn__pos) ).

fof(f8670,plain,
    spl50_468,
    inference(avatar_split_clause,[],[f4256,f8668]) ).

fof(f8668,plain,
    ( spl50_468
  <=> ! [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,[spl50_468])]) ).

fof(f4256,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,[],[f2368]) ).

fof(f2368,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,[],[f1397]) ).

fof(f1397,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,[],[f710]) ).

fof(f710,axiom,
    ! [X5] :
      ( class_Power_Opower(X5)
     => c_Power_Opower__class_Opower(X5) = c_Power_Opower_Opower(X5,c_Groups_Oone__class_Oone(X5),c_Groups_Otimes__class_Otimes(X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__power__power) ).

fof(f8666,plain,
    spl50_467,
    inference(avatar_split_clause,[],[f4177,f8664]) ).

fof(f8664,plain,
    ( spl50_467
  <=> ! [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,[spl50_467])]) ).

fof(f4177,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,[],[f1325]) ).

fof(f1325,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,[],[f594]) ).

fof(f594,axiom,
    ! [X14] : 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),X14),X14),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_odd__nonzero) ).

fof(f8662,plain,
    spl50_466,
    inference(avatar_split_clause,[],[f4113,f8659]) ).

fof(f8659,plain,
    ( spl50_466
  <=> c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),c_Complex_Oii) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_466])]) ).

fof(f4113,plain,
    c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),c_Complex_Oii),
    inference(cnf_transformation,[],[f707]) ).

fof(f707,axiom,
    c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),c_Complex_Oii),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_i__mult__eq2) ).

fof(f8549,plain,
    ( spl50_465
    | ~ spl50_442 ),
    inference(avatar_split_clause,[],[f8451,f8294,f8547]) ).

fof(f8547,plain,
    ( spl50_465
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X0,X1,X1)
        | ~ class_Orderings_Olinorder(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_465])]) ).

fof(f8294,plain,
    ( spl50_442
  <=> ! [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,[spl50_442])]) ).

fof(f8451,plain,
    ( ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X0,X1,X1)
        | ~ class_Orderings_Olinorder(X0) )
    | ~ spl50_442 ),
    inference(factoring,[],[f8295]) ).

fof(f8295,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) )
    | ~ spl50_442 ),
    inference(avatar_component_clause,[],[f8294]) ).

fof(f8424,plain,
    ( spl50_464
    | ~ spl50_15
    | ~ spl50_385 ),
    inference(avatar_split_clause,[],[f8055,f7881,f6121,f8421]) ).

fof(f8421,plain,
    ( spl50_464
  <=> c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_464])]) ).

fof(f6121,plain,
    ( spl50_15
  <=> class_Rings_Odivision__ring(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_15])]) ).

fof(f7881,plain,
    ( spl50_385
  <=> ! [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,[spl50_385])]) ).

fof(f8055,plain,
    ( c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
    | ~ spl50_15
    | ~ spl50_385 ),
    inference(resolution,[],[f7882,f6123]) ).

fof(f6123,plain,
    ( class_Rings_Odivision__ring(tc_RealDef_Oreal)
    | ~ spl50_15 ),
    inference(avatar_component_clause,[],[f6121]) ).

fof(f7882,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)) )
    | ~ spl50_385 ),
    inference(avatar_component_clause,[],[f7881]) ).

fof(f8383,plain,
    ( spl50_463
    | ~ spl50_324
    | ~ spl50_426 ),
    inference(avatar_split_clause,[],[f8230,f8226,f7586,f8380]) ).

fof(f8226,plain,
    ( spl50_426
  <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_426])]) ).

fof(f8230,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK19))
    | ~ spl50_324
    | ~ spl50_426 ),
    inference(forward_demodulation,[],[f8228,f7588]) ).

fof(f8228,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____))
    | ~ spl50_426 ),
    inference(avatar_component_clause,[],[f8226]) ).

fof(f8378,plain,
    ( spl50_462
    | ~ spl50_14
    | ~ spl50_385 ),
    inference(avatar_split_clause,[],[f8054,f7881,f6116,f8375]) ).

fof(f8375,plain,
    ( spl50_462
  <=> c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_462])]) ).

fof(f6116,plain,
    ( spl50_14
  <=> class_Rings_Odivision__ring(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_14])]) ).

fof(f8054,plain,
    ( c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))
    | ~ spl50_14
    | ~ spl50_385 ),
    inference(resolution,[],[f7882,f6118]) ).

fof(f6118,plain,
    ( class_Rings_Odivision__ring(tc_Complex_Ocomplex)
    | ~ spl50_14 ),
    inference(avatar_component_clause,[],[f6116]) ).

fof(f8373,plain,
    spl50_461,
    inference(avatar_split_clause,[],[f5999,f8371]) ).

fof(f8371,plain,
    ( spl50_461
  <=> ! [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,[spl50_461])]) ).

fof(f5999,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,[],[f5998,f4161]) ).

fof(f5998,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,[],[f5663,f4313]) ).

fof(f5663,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,[],[f4719,f4164]) ).

fof(f4719,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,[],[f3619]) ).

fof(f3619,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,[],[f3442]) ).

fof(f3442,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,[],[f1722,f3441]) ).

fof(f1722,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,[],[f926]) ).

fof(f926,axiom,
    ! [X16,X32] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X32,X16) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    <=> ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X16
          & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X32 )
        | ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X16
          & c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X32 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__is__1) ).

fof(f8369,plain,
    spl50_460,
    inference(avatar_split_clause,[],[f5997,f8367]) ).

fof(f8367,plain,
    ( spl50_460
  <=> ! [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,[spl50_460])]) ).

fof(f5997,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,[],[f5996,f4161]) ).

fof(f5996,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,[],[f5662,f4313]) ).

fof(f5662,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,[],[f4720,f4164]) ).

fof(f4720,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,[],[f3619]) ).

fof(f8365,plain,
    spl50_459,
    inference(avatar_split_clause,[],[f5983,f8363]) ).

fof(f8363,plain,
    ( spl50_459
  <=> ! [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,[spl50_459])]) ).

fof(f5983,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,[],[f5982,f4161]) ).

fof(f5982,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,[],[f5656,f4313]) ).

fof(f5656,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,[],[f4711,f4164]) ).

fof(f4711,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,[],[f3616]) ).

fof(f3616,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,[],[f3440]) ).

fof(f3440,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,[],[f1721,f3439]) ).

fof(f1721,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,[],[f925]) ).

fof(f925,axiom,
    ! [X16,X32] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X32,X16) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    <=> ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X16
          & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X32 )
        | ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X16
          & c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X32 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__is__add) ).

fof(f8361,plain,
    spl50_458,
    inference(avatar_split_clause,[],[f5981,f8359]) ).

fof(f8359,plain,
    ( spl50_458
  <=> ! [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,[spl50_458])]) ).

fof(f5981,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,[],[f5980,f4161]) ).

fof(f5980,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,[],[f5655,f4313]) ).

fof(f5655,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,[],[f4712,f4164]) ).

fof(f4712,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,[],[f3616]) ).

fof(f8357,plain,
    spl50_457,
    inference(avatar_split_clause,[],[f5918,f8355]) ).

fof(f8355,plain,
    ( spl50_457
  <=> ! [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,[spl50_457])]) ).

fof(f5918,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,[],[f5917,f4161]) ).

fof(f5917,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,[],[f5581,f5579]) ).

fof(f5581,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,[],[f4178,f4164,f4164]) ).

fof(f4178,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,[],[f1326]) ).

fof(f1326,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,[],[f947]) ).

fof(f947,axiom,
    ! [X3] : 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))),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__Suc__0) ).

fof(f8353,plain,
    spl50_456,
    inference(avatar_split_clause,[],[f5726,f8351]) ).

fof(f8351,plain,
    ( spl50_456
  <=> ! [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,[spl50_456])]) ).

fof(f5726,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,[],[f4508]) ).

fof(f4508,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,[],[f3543]) ).

fof(f8349,plain,
    spl50_455,
    inference(avatar_split_clause,[],[f5710,f8347]) ).

fof(f8347,plain,
    ( spl50_455
  <=> ! [X1] :
        ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ozero__class_Ozero(X1)))
        | ~ class_RealVector_Oreal__normed__vector(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_455])]) ).

fof(f5710,plain,
    ! [X1] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ozero__class_Ozero(X1)))
      | ~ class_RealVector_Oreal__normed__vector(X1) ),
    inference(equality_resolution,[],[f4401]) ).

fof(f4401,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X1) != X0
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X0))
      | ~ class_RealVector_Oreal__normed__vector(X1) ),
    inference(cnf_transformation,[],[f3510]) ).

fof(f8345,plain,
    spl50_454,
    inference(avatar_split_clause,[],[f5709,f8343]) ).

fof(f8343,plain,
    ( spl50_454
  <=> ! [X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | ~ class_RealVector_Oreal__normed__vector(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_454])]) ).

fof(f5709,plain,
    ! [X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
      | ~ class_RealVector_Oreal__normed__vector(X1) ),
    inference(equality_resolution,[],[f4400]) ).

fof(f4400,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
      | c_Groups_Ozero__class_Ozero(X1) != X0
      | ~ class_RealVector_Oreal__normed__vector(X1) ),
    inference(cnf_transformation,[],[f3509]) ).

fof(f8341,plain,
    spl50_453,
    inference(avatar_split_clause,[],[f5702,f8339]) ).

fof(f8339,plain,
    ( spl50_453
  <=> ! [X0] : c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_453])]) ).

fof(f5702,plain,
    ! [X0] : c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(equality_resolution,[],[f4337]) ).

fof(f4337,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1)
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
    inference(cnf_transformation,[],[f2399]) ).

fof(f2399,plain,
    ! [X0,X1] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,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) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1)
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ) ),
    inference(ennf_transformation,[],[f1468]) ).

fof(f1468,plain,
    ! [X0,X1] :
      ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,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) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1) ) ),
    inference(rectify,[],[f524]) ).

fof(f524,axiom,
    ! [X54,X17] :
      ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X17
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X54),X17) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X54),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X54),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
      & ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X17
       => c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X54),X17) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__eq__if) ).

fof(f8337,plain,
    spl50_452,
    inference(avatar_split_clause,[],[f5193,f8335]) ).

fof(f8335,plain,
    ( spl50_452
  <=> ! [X2,X0,X1] :
        ( ~ hBOOL(hAPP(hAPP(X2,X1),X0))
        | ~ sP6(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_452])]) ).

fof(f5193,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP(hAPP(X2,X1),X0))
      | ~ sP6(X0,X1,X2) ),
    inference(cnf_transformation,[],[f3756]) ).

fof(f3756,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,[],[f3755]) ).

fof(f3755,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,[],[f3449]) ).

fof(f8333,plain,
    ( spl50_451
    | ~ spl50_6
    | ~ spl50_382 ),
    inference(avatar_split_clause,[],[f8046,f7868,f6076,f8330]) ).

fof(f8330,plain,
    ( spl50_451
  <=> c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_451])]) ).

fof(f6076,plain,
    ( spl50_6
  <=> class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_6])]) ).

fof(f7868,plain,
    ( spl50_382
  <=> ! [X0] :
        ( c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X0,c_Groups_Oone__class_Oone(X0))
        | ~ class_RealVector_Oreal__normed__algebra__1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_382])]) ).

fof(f8046,plain,
    ( c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
    | ~ spl50_6
    | ~ spl50_382 ),
    inference(resolution,[],[f7869,f6078]) ).

fof(f6078,plain,
    ( class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal)
    | ~ spl50_6 ),
    inference(avatar_component_clause,[],[f6076]) ).

fof(f7869,plain,
    ( ! [X0] :
        ( ~ class_RealVector_Oreal__normed__algebra__1(X0)
        | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X0,c_Groups_Oone__class_Oone(X0)) )
    | ~ spl50_382 ),
    inference(avatar_component_clause,[],[f7868]) ).

fof(f8328,plain,
    spl50_450,
    inference(avatar_split_clause,[],[f5082,f8326]) ).

fof(f8326,plain,
    ( spl50_450
  <=> ! [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,[spl50_450])]) ).

fof(f5082,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,[],[f3727]) ).

fof(f3727,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,[],[f3726]) ).

fof(f3726,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,[],[f2969]) ).

fof(f2969,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,[],[f1965]) ).

fof(f1965,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,[],[f764]) ).

fof(f764,axiom,
    ! [X20,X12,X5] :
      ( class_Orderings_Oorder(X5)
     => ( c_Orderings_Oord__class_Oless__eq(X5,X12,X20)
      <=> ( X12 = X20
          | c_Orderings_Oord__class_Oless(X5,X12,X20) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__less) ).

fof(f8324,plain,
    spl50_449,
    inference(avatar_split_clause,[],[f5077,f8322]) ).

fof(f8322,plain,
    ( spl50_449
  <=> ! [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,[spl50_449])]) ).

fof(f5077,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,[],[f2967]) ).

fof(f2967,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,[],[f2966]) ).

fof(f2966,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,[],[f1963]) ).

fof(f1963,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,[],[f736]) ).

fof(f736,axiom,
    ! [X4,X13,X5] :
      ( class_Orderings_Oorder(X5)
     => ( c_Orderings_Oord__class_Oless(X5,X13,X4)
       => ~ c_Orderings_Oord__class_Oless(X5,X4,X13) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I9_J) ).

fof(f8320,plain,
    spl50_448,
    inference(avatar_split_clause,[],[f5063,f8318]) ).

fof(f5063,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,[],[f3722]) ).

fof(f8316,plain,
    spl50_447,
    inference(avatar_split_clause,[],[f5061,f8314]) ).

fof(f8314,plain,
    ( spl50_447
  <=> ! [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,[spl50_447])]) ).

fof(f5061,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,[],[f2942]) ).

fof(f2942,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,[],[f2941]) ).

fof(f2941,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,[],[f1950]) ).

fof(f1950,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,[],[f757]) ).

fof(f757,axiom,
    ! [X7,X9,X5] :
      ( class_Orderings_Opreorder(X5)
     => ( c_Orderings_Oord__class_Oless(X5,X9,X7)
       => c_Orderings_Oord__class_Oless__eq(X5,X9,X7) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__le) ).

fof(f8312,plain,
    spl50_446,
    inference(avatar_split_clause,[],[f5057,f8310]) ).

fof(f5057,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,[],[f2934]) ).

fof(f2934,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,[],[f2933]) ).

fof(f2933,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,[],[f1946]) ).

fof(f1946,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,[],[f729]) ).

fof(f729,axiom,
    ! [X7,X9,X5] :
      ( class_Orderings_Opreorder(X5)
     => ( c_Orderings_Oord__class_Oless(X5,X9,X7)
       => ~ c_Orderings_Oord__class_Oless(X5,X7,X9) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__asym) ).

fof(f8308,plain,
    spl50_445,
    inference(avatar_split_clause,[],[f4969,f8306]) ).

fof(f4969,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,[],[f3699]) ).

fof(f3699,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,[],[f3698]) ).

fof(f3698,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,[],[f2853]) ).

fof(f2853,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,[],[f1883]) ).

fof(f1883,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,[],[f746]) ).

fof(f746,axiom,
    ! [X20,X12,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ~ c_Orderings_Oord__class_Oless(X5,X12,X20)
      <=> ( X12 = X20
          | c_Orderings_Oord__class_Oless(X5,X20,X12) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__iff__gr__or__eq) ).

fof(f8304,plain,
    spl50_444,
    inference(avatar_split_clause,[],[f4952,f8302]) ).

fof(f4952,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,[],[f2835]) ).

fof(f2835,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,[],[f2834]) ).

fof(f2834,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,[],[f1872]) ).

fof(f1872,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,[],[f758]) ).

fof(f758,axiom,
    ! [X9,X7,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( c_Orderings_Oord__class_Oless__eq(X5,X7,X9)
       => ~ c_Orderings_Oord__class_Oless(X5,X9,X7) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_leD) ).

fof(f8300,plain,
    spl50_443,
    inference(avatar_split_clause,[],[f4941,f8298]) ).

fof(f4941,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,[],[f2817]) ).

fof(f2817,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,[],[f2816]) ).

fof(f2816,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,[],[f1863]) ).

fof(f1863,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,[],[f767]) ).

fof(f767,axiom,
    ! [X7,X9,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( c_Orderings_Oord__class_Oless(X5,X7,X9)
        | c_Orderings_Oord__class_Oless__eq(X5,X9,X7) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__le__less__linear) ).

fof(f8296,plain,
    spl50_442,
    inference(avatar_split_clause,[],[f4940,f8294]) ).

fof(f4940,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,[],[f2815]) ).

fof(f2815,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,[],[f2814]) ).

fof(f2814,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,[],[f1862]) ).

fof(f1862,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,[],[f713]) ).

fof(f713,axiom,
    ! [X7,X9,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( c_Orderings_Oord__class_Oless__eq(X5,X7,X9)
        | c_Orderings_Oord__class_Oless__eq(X5,X9,X7) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__linear) ).

fof(f8292,plain,
    spl50_441,
    inference(avatar_split_clause,[],[f4644,f8290]) ).

fof(f4644,plain,
    ! [X0,X1] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X0)
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X0) ),
    inference(cnf_transformation,[],[f3567]) ).

fof(f3567,plain,
    ! [X0,X1] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X0)
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X0) )
      & ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X0)
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X0) ) ),
    inference(nnf_transformation,[],[f1696]) ).

fof(f1696,plain,
    ! [X0,X1] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X0)
    <=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X0) ),
    inference(rectify,[],[f863]) ).

fof(f863,axiom,
    ! [X80,X45] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X45,X80)
    <=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X45),X80) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_uminus__dvd__conv_I1_J) ).

fof(f8288,plain,
    ( spl50_440
    | ~ spl50_4
    | ~ spl50_382 ),
    inference(avatar_split_clause,[],[f8045,f7868,f6066,f8285]) ).

fof(f8285,plain,
    ( spl50_440
  <=> c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_440])]) ).

fof(f6066,plain,
    ( spl50_4
  <=> class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_4])]) ).

fof(f8045,plain,
    ( c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))
    | ~ spl50_4
    | ~ spl50_382 ),
    inference(resolution,[],[f7869,f6068]) ).

fof(f6068,plain,
    ( class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex)
    | ~ spl50_4 ),
    inference(avatar_component_clause,[],[f6066]) ).

fof(f8283,plain,
    spl50_439,
    inference(avatar_split_clause,[],[f4643,f8281]) ).

fof(f8281,plain,
    ( spl50_439
  <=> ! [X0,X1] :
        ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X0)
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_439])]) ).

fof(f4643,plain,
    ! [X0,X1] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X0)
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X0) ),
    inference(cnf_transformation,[],[f3567]) ).

fof(f8279,plain,
    spl50_438,
    inference(avatar_split_clause,[],[f4642,f8277]) ).

fof(f4642,plain,
    ! [X0,X1] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X0)
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) ),
    inference(cnf_transformation,[],[f3566]) ).

fof(f3566,plain,
    ! [X0,X1] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X0)
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) )
      & ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X0) ) ),
    inference(nnf_transformation,[],[f1695]) ).

fof(f1695,plain,
    ! [X0,X1] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X0)
    <=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) ),
    inference(rectify,[],[f862]) ).

fof(f862,axiom,
    ! [X80,X45] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X45,X80)
    <=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,X45,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X80)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_uminus__dvd__conv_I2_J) ).

fof(f8275,plain,
    spl50_437,
    inference(avatar_split_clause,[],[f4641,f8273]) ).

fof(f8273,plain,
    ( spl50_437
  <=> ! [X0,X1] :
        ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_437])]) ).

fof(f4641,plain,
    ! [X0,X1] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X0) ),
    inference(cnf_transformation,[],[f3566]) ).

fof(f8271,plain,
    spl50_436,
    inference(avatar_split_clause,[],[f4607,f8269]) ).

fof(f8269,plain,
    ( spl50_436
  <=> ! [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,[spl50_436])]) ).

fof(f4607,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,[],[f2639]) ).

fof(f2639,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,[],[f1671]) ).

fof(f1671,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,[],[f378]) ).

fof(f378,axiom,
    ! [X3,X17] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X3) = X17
     => c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X3 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__eq__self__zero) ).

fof(f8267,plain,
    spl50_435,
    inference(avatar_split_clause,[],[f4485,f8265]) ).

fof(f8265,plain,
    ( spl50_435
  <=> ! [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,[spl50_435])]) ).

fof(f4485,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,[],[f2506]) ).

fof(f2506,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,[],[f1564]) ).

fof(f1564,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,[],[f147]) ).

fof(f147,axiom,
    ! [X4,X5] :
      ( class_Rings_Olinordered__semidom(X5)
     => c_Orderings_Oord__class_Oless(X5,X4,c_Groups_Oplus__class_Oplus(X5,X4,c_Groups_Oone__class_Oone(X5))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__one) ).

fof(f8263,plain,
    spl50_434,
    inference(avatar_split_clause,[],[f4342,f8261]) ).

fof(f8261,plain,
    ( spl50_434
  <=> ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Nat__Transfer_Otsub(X0,X1)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_434])]) ).

fof(f4342,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Nat__Transfer_Otsub(X0,X1)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ),
    inference(cnf_transformation,[],[f2401]) ).

fof(f8259,plain,
    spl50_433,
    inference(avatar_split_clause,[],[f4316,f8257]) ).

fof(f8257,plain,
    ( spl50_433
  <=> ! [X0,X1] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_433])]) ).

fof(f4316,plain,
    ! [X0,X1] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)),
    inference(cnf_transformation,[],[f1447]) ).

fof(f1447,plain,
    ! [X0,X1] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)),
    inference(rectify,[],[f473]) ).

fof(f473,axiom,
    ! [X17,X3] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X17)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__0) ).

fof(f8255,plain,
    spl50_432,
    inference(avatar_split_clause,[],[f4289,f8253]) ).

fof(f8253,plain,
    ( spl50_432
  <=> ! [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,[spl50_432])]) ).

fof(f4289,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,[],[f3482]) ).

fof(f3482,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,[],[f1427]) ).

fof(f1427,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,[],[f597]) ).

fof(f597,axiom,
    ! [X33] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X33)
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X33) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__one__le__iff__zero__less) ).

fof(f8251,plain,
    spl50_431,
    inference(avatar_split_clause,[],[f4288,f8249]) ).

fof(f8249,plain,
    ( spl50_431
  <=> ! [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,[spl50_431])]) ).

fof(f4288,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,[],[f3482]) ).

fof(f8247,plain,
    spl50_430,
    inference(avatar_split_clause,[],[f4176,f8245]) ).

fof(f8245,plain,
    ( spl50_430
  <=> ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_430])]) ).

fof(f4176,plain,
    ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0)),
    inference(cnf_transformation,[],[f1324]) ).

fof(f1324,plain,
    ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0)),
    inference(rectify,[],[f468]) ).

fof(f468,axiom,
    ! [X9] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X9)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X9)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__mod__minus__le__complex__mod) ).

fof(f8243,plain,
    ( spl50_429
    | ~ spl50_3
    | ~ spl50_381 ),
    inference(avatar_split_clause,[],[f8043,f7864,f6061,f8240]) ).

fof(f8240,plain,
    ( spl50_429
  <=> c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_429])]) ).

fof(f6061,plain,
    ( spl50_3
  <=> class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_3])]) ).

fof(f7864,plain,
    ( spl50_381
  <=> ! [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,[spl50_381])]) ).

fof(f8043,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))
    | ~ spl50_3
    | ~ spl50_381 ),
    inference(resolution,[],[f7865,f6063]) ).

fof(f6063,plain,
    ( class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex)
    | ~ spl50_3 ),
    inference(avatar_component_clause,[],[f6061]) ).

fof(f7865,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)) )
    | ~ spl50_381 ),
    inference(avatar_component_clause,[],[f7864]) ).

fof(f8238,plain,
    spl50_428,
    inference(avatar_split_clause,[],[f4175,f8236]) ).

fof(f8236,plain,
    ( spl50_428
  <=> ! [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,[spl50_428])]) ).

fof(f4175,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,[],[f1323]) ).

fof(f1323,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,[],[f384]) ).

fof(f384,axiom,
    ! [X3] : 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)),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__0) ).

fof(f8234,plain,
    spl50_427,
    inference(avatar_split_clause,[],[f4174,f8232]) ).

fof(f4174,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,[],[f1322]) ).

fof(f1322,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,[],[f385]) ).

fof(f385,axiom,
    ! [X17] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__0__right) ).

fof(f8229,plain,
    spl50_426,
    inference(avatar_split_clause,[],[f4112,f8226]) ).

fof(f4112,plain,
    c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____)),
    inference(cnf_transformation,[],[f550]) ).

fof(f550,axiom,
    c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_k1n) ).

fof(f8206,plain,
    ( spl50_425
    | ~ spl50_6
    | ~ spl50_380 ),
    inference(avatar_split_clause,[],[f8042,f7860,f6076,f8203]) ).

fof(f8203,plain,
    ( spl50_425
  <=> c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_425])]) ).

fof(f7860,plain,
    ( spl50_380
  <=> ! [X0] :
        ( c_Groups_Oone__class_Oone(X0) = c_Groups_Osgn__class_Osgn(X0,c_Groups_Oone__class_Oone(X0))
        | ~ class_RealVector_Oreal__normed__algebra__1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_380])]) ).

fof(f8042,plain,
    ( c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
    | ~ spl50_6
    | ~ spl50_380 ),
    inference(resolution,[],[f7861,f6078]) ).

fof(f7861,plain,
    ( ! [X0] :
        ( ~ class_RealVector_Oreal__normed__algebra__1(X0)
        | c_Groups_Oone__class_Oone(X0) = c_Groups_Osgn__class_Osgn(X0,c_Groups_Oone__class_Oone(X0)) )
    | ~ spl50_380 ),
    inference(avatar_component_clause,[],[f7860]) ).

fof(f8156,plain,
    ( spl50_424
    | ~ spl50_4
    | ~ spl50_380 ),
    inference(avatar_split_clause,[],[f8041,f7860,f6066,f8153]) ).

fof(f8153,plain,
    ( spl50_424
  <=> c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_424])]) ).

fof(f8041,plain,
    ( c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))
    | ~ spl50_4
    | ~ spl50_380 ),
    inference(resolution,[],[f7861,f6068]) ).

fof(f8053,plain,
    ( ~ spl50_423
    | ~ spl50_331
    | ~ spl50_366 ),
    inference(avatar_split_clause,[],[f7810,f7773,f7615,f8050]) ).

fof(f8050,plain,
    ( spl50_423
  <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_423])]) ).

fof(f7615,plain,
    ( spl50_331
  <=> ! [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,[spl50_331])]) ).

fof(f7773,plain,
    ( spl50_366
  <=> ! [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,[spl50_366])]) ).

fof(f7810,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ spl50_331
    | ~ spl50_366 ),
    inference(superposition,[],[f7774,f7616]) ).

fof(f7616,plain,
    ( ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) = X0
    | ~ spl50_331 ),
    inference(avatar_component_clause,[],[f7615]) ).

fof(f7774,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)
    | ~ spl50_366 ),
    inference(avatar_component_clause,[],[f7773]) ).

fof(f8033,plain,
    ( ~ spl50_422
    | ~ spl50_324
    | spl50_371 ),
    inference(avatar_split_clause,[],[f7825,f7821,f7586,f8030]) ).

fof(f8030,plain,
    ( spl50_422
  <=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK19) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_422])]) ).

fof(f7821,plain,
    ( spl50_371
  <=> c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_371])]) ).

fof(f7825,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK19)
    | ~ spl50_324
    | spl50_371 ),
    inference(forward_demodulation,[],[f7823,f7588]) ).

fof(f7823,plain,
    ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | spl50_371 ),
    inference(avatar_component_clause,[],[f7821]) ).

fof(f8028,plain,
    spl50_421,
    inference(avatar_split_clause,[],[f5936,f8026]) ).

fof(f8026,plain,
    ( spl50_421
  <=> ! [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,[spl50_421])]) ).

fof(f5936,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,[],[f5935,f4161]) ).

fof(f5935,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,[],[f5588,f5579]) ).

fof(f5588,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,[],[f4296,f4164]) ).

fof(f4296,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,[],[f3489]) ).

fof(f3489,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,[],[f1431]) ).

fof(f1431,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,[],[f958]) ).

fof(f958,axiom,
    ! [X16] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X16,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X16 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc0) ).

fof(f8024,plain,
    spl50_420,
    inference(avatar_split_clause,[],[f5827,f8022]) ).

fof(f8022,plain,
    ( spl50_420
  <=> ! [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,[spl50_420])]) ).

fof(f5827,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,[],[f5032]) ).

fof(f5032,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,[],[f3717]) ).

fof(f8020,plain,
    spl50_419,
    inference(avatar_split_clause,[],[f5818,f8018]) ).

fof(f8018,plain,
    ( spl50_419
  <=> ! [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,[spl50_419])]) ).

fof(f5818,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,[],[f4998]) ).

fof(f4998,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,[],[f3710]) ).

fof(f8016,plain,
    spl50_418,
    inference(avatar_split_clause,[],[f5763,f8014]) ).

fof(f8014,plain,
    ( spl50_418
  <=> ! [X1] : c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_418])]) ).

fof(f5763,plain,
    ! [X1] : c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)),
    inference(equality_resolution,[],[f4697]) ).

fof(f4697,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0)
      | c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1) != X0 ),
    inference(cnf_transformation,[],[f3609]) ).

fof(f8012,plain,
    spl50_417,
    inference(avatar_split_clause,[],[f5717,f8010]) ).

fof(f8010,plain,
    ( spl50_417
  <=> ! [X1] :
        ( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Osgn__class_Osgn(X1,c_Groups_Ozero__class_Ozero(X1))
        | ~ class_Rings_Olinordered__idom(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_417])]) ).

fof(f5717,plain,
    ! [X1] :
      ( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Osgn__class_Osgn(X1,c_Groups_Ozero__class_Ozero(X1))
      | ~ class_Rings_Olinordered__idom(X1) ),
    inference(equality_resolution,[],[f4456]) ).

fof(f4456,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Osgn__class_Osgn(X1,X0)
      | c_Groups_Ozero__class_Ozero(X1) != X0
      | ~ class_Rings_Olinordered__idom(X1) ),
    inference(cnf_transformation,[],[f3531]) ).

fof(f8008,plain,
    spl50_416,
    inference(avatar_split_clause,[],[f5712,f8006]) ).

fof(f8006,plain,
    ( spl50_416
  <=> ! [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,[spl50_416])]) ).

fof(f5712,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,[],[f4417]) ).

fof(f4417,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,[],[f3515]) ).

fof(f8004,plain,
    spl50_415,
    inference(avatar_split_clause,[],[f5704,f8002]) ).

fof(f8002,plain,
    ( spl50_415
  <=> ! [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,[spl50_415])]) ).

fof(f5704,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,[],[f4374]) ).

fof(f4374,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,[],[f3505]) ).

fof(f8000,plain,
    spl50_414,
    inference(avatar_split_clause,[],[f5578,f7998]) ).

fof(f7998,plain,
    ( spl50_414
  <=> ! [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,[spl50_414])]) ).

fof(f5578,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,[],[f4155,f4164]) ).

fof(f4155,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,[],[f1303]) ).

fof(f1303,plain,
    ! [X0] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(X0)),
    inference(rectify,[],[f889]) ).

fof(f889,axiom,
    ! [X3] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__Suc) ).

fof(f7996,plain,
    spl50_413,
    inference(avatar_split_clause,[],[f4521,f7994]) ).

fof(f7994,plain,
    ( spl50_413
  <=> ! [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,[spl50_413])]) ).

fof(f4521,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,[],[f2539]) ).

fof(f2539,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,[],[f1597]) ).

fof(f1597,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,[],[f529]) ).

fof(f529,axiom,
    ! [X4,X5] :
      ( class_Rings_Ocomm__semiring__1(X5)
     => c_Groups_Oplus__class_Oplus(X5,c_Groups_Ozero__class_Ozero(X5),X4) = X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).

fof(f7992,plain,
    spl50_412,
    inference(avatar_split_clause,[],[f4520,f7990]) ).

fof(f7990,plain,
    ( spl50_412
  <=> ! [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,[spl50_412])]) ).

fof(f4520,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,[],[f2538]) ).

fof(f2538,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,[],[f1596]) ).

fof(f1596,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,[],[f530]) ).

fof(f530,axiom,
    ! [X4,X5] :
      ( class_Rings_Ocomm__semiring__1(X5)
     => c_Groups_Oplus__class_Oplus(X5,X4,c_Groups_Ozero__class_Ozero(X5)) = X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).

fof(f7988,plain,
    spl50_411,
    inference(avatar_split_clause,[],[f4519,f7986]) ).

fof(f4519,plain,
    ! [X0,X1] :
      ( c_Polynomial_Osmult(X1,c_Groups_Oone__class_Oone(X1),X0) = X0
      | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(cnf_transformation,[],[f2537]) ).

fof(f2537,plain,
    ! [X0,X1] :
      ( c_Polynomial_Osmult(X1,c_Groups_Oone__class_Oone(X1),X0) = X0
      | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(ennf_transformation,[],[f1595]) ).

fof(f1595,plain,
    ! [X0,X1] :
      ( class_Rings_Ocomm__semiring__1(X1)
     => c_Polynomial_Osmult(X1,c_Groups_Oone__class_Oone(X1),X0) = X0 ),
    inference(rectify,[],[f653]) ).

fof(f653,axiom,
    ! [X54,X5] :
      ( class_Rings_Ocomm__semiring__1(X5)
     => c_Polynomial_Osmult(X5,c_Groups_Oone__class_Oone(X5),X54) = X54 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__1__left) ).

fof(f7984,plain,
    spl50_410,
    inference(avatar_split_clause,[],[f4496,f7982]) ).

fof(f7982,plain,
    ( spl50_410
  <=> ! [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,[spl50_410])]) ).

fof(f4496,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,[],[f2516]) ).

fof(f2516,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,[],[f1574]) ).

fof(f1574,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,[],[f213]) ).

fof(f213,axiom,
    ! [X4,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => c_Groups_Oplus__class_Oplus(X5,c_Groups_Ozero__class_Ozero(X5),X4) = X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0) ).

fof(f7980,plain,
    spl50_409,
    inference(avatar_split_clause,[],[f4495,f7978]) ).

fof(f7978,plain,
    ( spl50_409
  <=> ! [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,[spl50_409])]) ).

fof(f4495,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,[],[f2515]) ).

fof(f2515,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,[],[f1573]) ).

fof(f1573,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,[],[f216]) ).

fof(f216,axiom,
    ! [X4,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => c_Groups_Oplus__class_Oplus(X5,X4,c_Groups_Ozero__class_Ozero(X5)) = X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add_Ocomm__neutral) ).

fof(f7976,plain,
    spl50_408,
    inference(avatar_split_clause,[],[f4489,f7974]) ).

fof(f4489,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,[],[f2509]) ).

fof(f2509,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,[],[f1567]) ).

fof(f1567,plain,
    ! [X0,X1] :
      ( class_Groups_Omonoid__add(X1)
     => c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X0) = X0 ),
    inference(rectify,[],[f212]) ).

fof(f212,axiom,
    ! [X4,X5] :
      ( class_Groups_Omonoid__add(X5)
     => c_Groups_Oplus__class_Oplus(X5,c_Groups_Ozero__class_Ozero(X5),X4) = X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__left) ).

fof(f7972,plain,
    spl50_407,
    inference(avatar_split_clause,[],[f4488,f7970]) ).

fof(f4488,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,[],[f2508]) ).

fof(f2508,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,[],[f1566]) ).

fof(f1566,plain,
    ! [X0,X1] :
      ( class_Groups_Omonoid__add(X1)
     => c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0 ),
    inference(rectify,[],[f215]) ).

fof(f215,axiom,
    ! [X4,X5] :
      ( class_Groups_Omonoid__add(X5)
     => c_Groups_Oplus__class_Oplus(X5,X4,c_Groups_Ozero__class_Ozero(X5)) = X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__right) ).

fof(f7968,plain,
    spl50_406,
    inference(avatar_split_clause,[],[f4477,f7966]) ).

fof(f4477,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,[],[f2500]) ).

fof(f2500,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,[],[f1558]) ).

fof(f1558,plain,
    ! [X0,X1] :
      ( class_Groups_Ogroup__add(X1)
     => c_Groups_Ominus__class_Ominus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0 ),
    inference(rectify,[],[f286]) ).

fof(f286,axiom,
    ! [X4,X5] :
      ( class_Groups_Ogroup__add(X5)
     => c_Groups_Ominus__class_Ominus(X5,X4,c_Groups_Ozero__class_Ozero(X5)) = X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__0__right) ).

fof(f7964,plain,
    spl50_405,
    inference(avatar_split_clause,[],[f4476,f7962]) ).

fof(f4476,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,[],[f2499]) ).

fof(f2499,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,[],[f1557]) ).

fof(f1557,plain,
    ! [X0,X1] :
      ( class_Groups_Ogroup__add(X1)
     => c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0)) = X0 ),
    inference(rectify,[],[f280]) ).

fof(f280,axiom,
    ! [X4,X5] :
      ( class_Groups_Ogroup__add(X5)
     => c_Groups_Ouminus__class_Ouminus(X5,c_Groups_Ouminus__class_Ouminus(X5,X4)) = X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__minus) ).

fof(f7960,plain,
    spl50_404,
    inference(avatar_split_clause,[],[f4475,f7958]) ).

fof(f4475,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,[],[f2498]) ).

fof(f2498,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,[],[f1556]) ).

fof(f1556,plain,
    ! [X0,X1] :
      ( class_Groups_Ogroup__add(X1)
     => c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ominus__class_Ominus(X1,X0,X0) ),
    inference(rectify,[],[f285]) ).

fof(f285,axiom,
    ! [X4,X5] :
      ( class_Groups_Ogroup__add(X5)
     => c_Groups_Ozero__class_Ozero(X5) = c_Groups_Ominus__class_Ominus(X5,X4,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__self) ).

fof(f7956,plain,
    spl50_403,
    inference(avatar_split_clause,[],[f4409,f7954]) ).

fof(f7954,plain,
    ( spl50_403
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK26(X0,X1))
        | ~ class_RealVector_Oreal__normed__algebra(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_403])]) ).

fof(f4409,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK26(X0,X1))
      | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(cnf_transformation,[],[f3514]) ).

fof(f3514,plain,
    ! [X0,X1] :
      ( ( ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X3)),sK26(X0,X1)))
        & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK26(X0,X1)) )
      | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK26])],[f2458,f3513]) ).

fof(f3513,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X3)),X2))
          & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) )
     => ( ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X3)),sK26(X0,X1)))
        & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK26(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f2458,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X3)),X2))
          & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) )
      | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(ennf_transformation,[],[f1519]) ).

fof(f1519,plain,
    ! [X0,X1] :
      ( class_RealVector_Oreal__normed__algebra(X1)
     => ? [X2] :
          ( ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X3)),X2))
          & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ) ),
    inference(rectify,[],[f775]) ).

fof(f775,axiom,
    ! [X9,X5] :
      ( class_RealVector_Oreal__normed__algebra(X5)
     => ? [X76] :
          ( ! [X2] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X9),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5,X2)),X76))
          & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X76) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right_Opos__bounded) ).

fof(f7952,plain,
    spl50_402,
    inference(avatar_split_clause,[],[f4407,f7950]) ).

fof(f7950,plain,
    ( spl50_402
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK25(X0,X1))
        | ~ class_RealVector_Oreal__normed__algebra(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_402])]) ).

fof(f4407,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK25(X0,X1))
      | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(cnf_transformation,[],[f3512]) ).

fof(f3512,plain,
    ! [X0,X1] :
      ( ( ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X3)),sK25(X0,X1)))
        & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK25(X0,X1)) )
      | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK25])],[f2457,f3511]) ).

fof(f3511,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X3)),X2))
          & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) )
     => ( ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X3)),sK25(X0,X1)))
        & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK25(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f2457,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X3)),X2))
          & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) )
      | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(ennf_transformation,[],[f1518]) ).

fof(f1518,plain,
    ! [X0,X1] :
      ( class_RealVector_Oreal__normed__algebra(X1)
     => ? [X2] :
          ( ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X3)),X2))
          & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ) ),
    inference(rectify,[],[f772]) ).

fof(f772,axiom,
    ! [X7,X5] :
      ( class_RealVector_Oreal__normed__algebra(X5)
     => ? [X76] :
          ( ! [X2] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X2),X7)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5,X2)),X76))
          & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X76) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left_Opos__bounded) ).

fof(f7948,plain,
    spl50_401,
    inference(avatar_split_clause,[],[f4390,f7946]) ).

fof(f7946,plain,
    ( spl50_401
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X0))
        | ~ class_RealVector_Oreal__normed__vector(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_401])]) ).

fof(f4390,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X0))
      | ~ class_RealVector_Oreal__normed__vector(X1) ),
    inference(cnf_transformation,[],[f2445]) ).

fof(f2445,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X0))
      | ~ class_RealVector_Oreal__normed__vector(X1) ),
    inference(ennf_transformation,[],[f1506]) ).

fof(f1506,plain,
    ! [X0,X1] :
      ( class_RealVector_Oreal__normed__vector(X1)
     => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X0)) ),
    inference(rectify,[],[f54]) ).

fof(f54,axiom,
    ! [X9,X5] :
      ( class_RealVector_Oreal__normed__vector(X5)
     => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5,X9)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__ge__zero) ).

fof(f7944,plain,
    spl50_400,
    inference(avatar_split_clause,[],[f4389,f7942]) ).

fof(f7942,plain,
    ( spl50_400
  <=> ! [X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | ~ class_RealVector_Oreal__normed__vector(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_400])]) ).

fof(f4389,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
      | ~ class_RealVector_Oreal__normed__vector(X1) ),
    inference(cnf_transformation,[],[f2444]) ).

fof(f2444,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
      | ~ class_RealVector_Oreal__normed__vector(X1) ),
    inference(ennf_transformation,[],[f1505]) ).

fof(f1505,plain,
    ! [X0,X1] :
      ( class_RealVector_Oreal__normed__vector(X1)
     => ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    inference(rectify,[],[f171]) ).

fof(f171,axiom,
    ! [X9,X5] :
      ( class_RealVector_Oreal__normed__vector(X5)
     => ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,X9),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__not__less__zero) ).

fof(f7940,plain,
    spl50_399,
    inference(avatar_split_clause,[],[f4379,f7938]) ).

fof(f4379,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,[],[f2429]) ).

fof(f2429,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,[],[f1496]) ).

fof(f1496,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,[],[f88]) ).

fof(f88,axiom,
    ! [X4,X5] :
      ( class_Rings_Odivision__ring__inverse__zero(X5)
     => c_Rings_Oinverse__class_Oinverse(X5,c_Rings_Oinverse__class_Oinverse(X5,X4)) = X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__inverse__eq) ).

fof(f7936,plain,
    spl50_398,
    inference(avatar_split_clause,[],[f4376,f7934]) ).

fof(f4376,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,[],[f2424]) ).

fof(f2424,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,[],[f1493]) ).

fof(f1493,plain,
    ! [X0,X1] :
      ( class_Lattices_Oboolean__algebra(X1)
     => c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0)) = X0 ),
    inference(rectify,[],[f800]) ).

fof(f800,axiom,
    ! [X9,X5] :
      ( class_Lattices_Oboolean__algebra(X5)
     => c_Groups_Ouminus__class_Ouminus(X5,c_Groups_Ouminus__class_Ouminus(X5,X9)) = X9 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__compl) ).

fof(f7932,plain,
    spl50_397,
    inference(avatar_split_clause,[],[f4315,f7930]) ).

fof(f7930,plain,
    ( spl50_397
  <=> ! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X0) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_397])]) ).

fof(f4315,plain,
    ! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X0) = X1,
    inference(cnf_transformation,[],[f1446]) ).

fof(f1446,plain,
    ! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X0) = X1,
    inference(rectify,[],[f458]) ).

fof(f458,axiom,
    ! [X3,X17] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X3),X3) = X17,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__inverse2) ).

fof(f7928,plain,
    spl50_396,
    inference(avatar_split_clause,[],[f4314,f7926]) ).

fof(f7926,plain,
    ( spl50_396
  <=> ! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X1) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_396])]) ).

fof(f4314,plain,
    ! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X1) = X0,
    inference(cnf_transformation,[],[f1445]) ).

fof(f1445,plain,
    ! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X1) = X0,
    inference(rectify,[],[f457]) ).

fof(f457,axiom,
    ! [X17,X3] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X17),X3) = X17,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__inverse) ).

fof(f7924,plain,
    spl50_395,
    inference(avatar_split_clause,[],[f4313,f7922]) ).

fof(f7920,plain,
    ( spl50_394
    | ~ spl50_291
    | ~ spl50_362 ),
    inference(avatar_split_clause,[],[f7803,f7757,f7434,f7917]) ).

fof(f7917,plain,
    ( spl50_394
  <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK45) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_394])]) ).

fof(f7803,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK45)
    | ~ spl50_291
    | ~ spl50_362 ),
    inference(resolution,[],[f7758,f7436]) ).

fof(f7915,plain,
    spl50_393,
    inference(avatar_split_clause,[],[f4312,f7913]) ).

fof(f4312,plain,
    ! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0),
    inference(cnf_transformation,[],[f1443]) ).

fof(f1443,plain,
    ! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0),
    inference(rectify,[],[f621]) ).

fof(f621,axiom,
    ! [X15,X14] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X15,X14) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X14,X15),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__commute) ).

fof(f7911,plain,
    spl50_392,
    inference(avatar_split_clause,[],[f4290,f7909]) ).

fof(f7909,plain,
    ( spl50_392
  <=> ! [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,[spl50_392])]) ).

fof(f4290,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,[],[f3483]) ).

fof(f3483,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,[],[f1428]) ).

fof(f1428,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,[],[f383]) ).

fof(f383,axiom,
    ! [X16] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X16,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X16 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__0__eq) ).

fof(f7907,plain,
    spl50_391,
    inference(avatar_split_clause,[],[f4286,f7905]) ).

fof(f7905,plain,
    ( spl50_391
  <=> ! [X0] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_391])]) ).

fof(f4286,plain,
    ! [X0] :
      ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(cnf_transformation,[],[f3481]) ).

fof(f3481,plain,
    ! [X0] :
      ( ( 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
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
    inference(nnf_transformation,[],[f1426]) ).

fof(f1426,plain,
    ! [X0] :
      ( 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,[],[f864]) ).

fof(f864,axiom,
    ! [X32] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X32,c_Groups_Oone__class_Oone(tc_Nat_Onat))
    <=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = X32 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__dvd__1__iff__1) ).

fof(f7903,plain,
    spl50_390,
    inference(avatar_split_clause,[],[f4277,f7901]) ).

fof(f7901,plain,
    ( spl50_390
  <=> ! [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,[spl50_390])]) ).

fof(f4277,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,[],[f2389]) ).

fof(f2389,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,[],[f1418]) ).

fof(f1418,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,[],[f377]) ).

fof(f377,axiom,
    ! [X3] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X3
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr0I) ).

fof(f7899,plain,
    spl50_389,
    inference(avatar_split_clause,[],[f4245,f7897]) ).

fof(f4245,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,[],[f2357]) ).

fof(f2357,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,[],[f1386]) ).

fof(f1386,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,[],[f292]) ).

fof(f292,axiom,
    ! [X5] :
      ( class_Groups_Ogroup__add(X5)
     => c_Groups_Ozero__class_Ozero(X5) = c_Groups_Ouminus__class_Ouminus(X5,c_Groups_Ozero__class_Ozero(X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__zero) ).

fof(f7895,plain,
    spl50_388,
    inference(avatar_split_clause,[],[f4204,f7893]) ).

fof(f7893,plain,
    ( spl50_388
  <=> ! [X0] :
        ( c_Groups_Ozero__class_Ozero(X0) = c_Groups_Osgn__class_Osgn(X0,c_Groups_Ozero__class_Ozero(X0))
        | ~ class_Groups_Osgn__if(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_388])]) ).

fof(f4204,plain,
    ! [X0] :
      ( c_Groups_Ozero__class_Ozero(X0) = c_Groups_Osgn__class_Osgn(X0,c_Groups_Ozero__class_Ozero(X0))
      | ~ class_Groups_Osgn__if(X0) ),
    inference(cnf_transformation,[],[f2316]) ).

fof(f2316,plain,
    ! [X0] :
      ( c_Groups_Ozero__class_Ozero(X0) = c_Groups_Osgn__class_Osgn(X0,c_Groups_Ozero__class_Ozero(X0))
      | ~ class_Groups_Osgn__if(X0) ),
    inference(ennf_transformation,[],[f1345]) ).

fof(f1345,plain,
    ! [X0] :
      ( class_Groups_Osgn__if(X0)
     => c_Groups_Ozero__class_Ozero(X0) = c_Groups_Osgn__class_Osgn(X0,c_Groups_Ozero__class_Ozero(X0)) ),
    inference(rectify,[],[f809]) ).

fof(f809,axiom,
    ! [X5] :
      ( class_Groups_Osgn__if(X5)
     => c_Groups_Ozero__class_Ozero(X5) = c_Groups_Osgn__class_Osgn(X5,c_Groups_Ozero__class_Ozero(X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn0) ).

fof(f7891,plain,
    spl50_387,
    inference(avatar_split_clause,[],[f4201,f7889]) ).

fof(f4201,plain,
    ! [X0] :
      ( c_Groups_Ozero__class_Ozero(X0) = c_Groups_Osgn__class_Osgn(X0,c_Groups_Ozero__class_Ozero(X0))
      | ~ class_RealVector_Oreal__normed__vector(X0) ),
    inference(cnf_transformation,[],[f2314]) ).

fof(f2314,plain,
    ! [X0] :
      ( c_Groups_Ozero__class_Ozero(X0) = c_Groups_Osgn__class_Osgn(X0,c_Groups_Ozero__class_Ozero(X0))
      | ~ class_RealVector_Oreal__normed__vector(X0) ),
    inference(ennf_transformation,[],[f1343]) ).

fof(f1343,plain,
    ! [X0] :
      ( class_RealVector_Oreal__normed__vector(X0)
     => c_Groups_Ozero__class_Ozero(X0) = c_Groups_Osgn__class_Osgn(X0,c_Groups_Ozero__class_Ozero(X0)) ),
    inference(rectify,[],[f808]) ).

fof(f808,axiom,
    ! [X5] :
      ( class_RealVector_Oreal__normed__vector(X5)
     => c_Groups_Ozero__class_Ozero(X5) = c_Groups_Osgn__class_Osgn(X5,c_Groups_Ozero__class_Ozero(X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__zero) ).

fof(f7887,plain,
    spl50_386,
    inference(avatar_split_clause,[],[f4200,f7885]) ).

fof(f4200,plain,
    ! [X0] :
      ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X0,c_Groups_Ozero__class_Ozero(X0))
      | ~ class_RealVector_Oreal__normed__vector(X0) ),
    inference(cnf_transformation,[],[f2313]) ).

fof(f2313,plain,
    ! [X0] :
      ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X0,c_Groups_Ozero__class_Ozero(X0))
      | ~ class_RealVector_Oreal__normed__vector(X0) ),
    inference(ennf_transformation,[],[f1342]) ).

fof(f1342,plain,
    ! [X0] :
      ( class_RealVector_Oreal__normed__vector(X0)
     => c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X0,c_Groups_Ozero__class_Ozero(X0)) ),
    inference(rectify,[],[f165]) ).

fof(f165,axiom,
    ! [X5] :
      ( class_RealVector_Oreal__normed__vector(X5)
     => c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X5,c_Groups_Ozero__class_Ozero(X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__zero) ).

fof(f7883,plain,
    spl50_385,
    inference(avatar_split_clause,[],[f4199,f7881]) ).

fof(f4199,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,[],[f2312]) ).

fof(f2312,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,[],[f1341]) ).

fof(f1341,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,[],[f122]) ).

fof(f122,axiom,
    ! [X5] :
      ( class_Rings_Odivision__ring(X5)
     => c_Groups_Oone__class_Oone(X5) = c_Rings_Oinverse__class_Oinverse(X5,c_Groups_Oone__class_Oone(X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__1) ).

fof(f7879,plain,
    spl50_384,
    inference(avatar_split_clause,[],[f4198,f7877]) ).

fof(f7877,plain,
    ( spl50_384
  <=> ! [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,[spl50_384])]) ).

fof(f4198,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,[],[f2311]) ).

fof(f2311,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,[],[f1340]) ).

fof(f1340,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,[],[f117]) ).

fof(f117,axiom,
    ! [X5] :
      ( class_Rings_Odivision__ring__inverse__zero(X5)
     => c_Groups_Ozero__class_Ozero(X5) = c_Rings_Oinverse__class_Oinverse(X5,c_Groups_Ozero__class_Ozero(X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__zero) ).

fof(f7875,plain,
    ( spl50_383
    | ~ spl50_230
    | ~ spl50_362 ),
    inference(avatar_split_clause,[],[f7801,f7757,f7189,f7872]) ).

fof(f7872,plain,
    ( spl50_383
  <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK18) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_383])]) ).

fof(f7801,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK18)
    | ~ spl50_230
    | ~ spl50_362 ),
    inference(resolution,[],[f7758,f7191]) ).

fof(f7870,plain,
    spl50_382,
    inference(avatar_split_clause,[],[f4197,f7868]) ).

fof(f4197,plain,
    ! [X0] :
      ( c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X0,c_Groups_Oone__class_Oone(X0))
      | ~ class_RealVector_Oreal__normed__algebra__1(X0) ),
    inference(cnf_transformation,[],[f2310]) ).

fof(f2310,plain,
    ! [X0] :
      ( c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X0,c_Groups_Oone__class_Oone(X0))
      | ~ class_RealVector_Oreal__normed__algebra__1(X0) ),
    inference(ennf_transformation,[],[f1339]) ).

fof(f1339,plain,
    ! [X0] :
      ( class_RealVector_Oreal__normed__algebra__1(X0)
     => c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X0,c_Groups_Oone__class_Oone(X0)) ),
    inference(rectify,[],[f120]) ).

fof(f120,axiom,
    ! [X5] :
      ( class_RealVector_Oreal__normed__algebra__1(X5)
     => c_RealVector_Onorm__class_Onorm(X5,c_Groups_Oone__class_Oone(X5)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__one) ).

fof(f7866,plain,
    spl50_381,
    inference(avatar_split_clause,[],[f4196,f7864]) ).

fof(f4196,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,[],[f2309]) ).

fof(f2309,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,[],[f1338]) ).

fof(f1338,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,[],[f118]) ).

fof(f118,axiom,
    ! [X5] :
      ( class_Fields_Ofield__inverse__zero(X5)
     => c_Groups_Ozero__class_Ozero(X5) = c_Rings_Oinverse__class_Oinverse(X5,c_Groups_Ozero__class_Ozero(X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_field__inverse__zero) ).

fof(f7862,plain,
    spl50_380,
    inference(avatar_split_clause,[],[f4195,f7860]) ).

fof(f4195,plain,
    ! [X0] :
      ( c_Groups_Oone__class_Oone(X0) = c_Groups_Osgn__class_Osgn(X0,c_Groups_Oone__class_Oone(X0))
      | ~ class_RealVector_Oreal__normed__algebra__1(X0) ),
    inference(cnf_transformation,[],[f2308]) ).

fof(f2308,plain,
    ! [X0] :
      ( c_Groups_Oone__class_Oone(X0) = c_Groups_Osgn__class_Osgn(X0,c_Groups_Oone__class_Oone(X0))
      | ~ class_RealVector_Oreal__normed__algebra__1(X0) ),
    inference(ennf_transformation,[],[f1337]) ).

fof(f1337,plain,
    ! [X0] :
      ( class_RealVector_Oreal__normed__algebra__1(X0)
     => c_Groups_Oone__class_Oone(X0) = c_Groups_Osgn__class_Osgn(X0,c_Groups_Oone__class_Oone(X0)) ),
    inference(rectify,[],[f835]) ).

fof(f835,axiom,
    ! [X5] :
      ( class_RealVector_Oreal__normed__algebra__1(X5)
     => c_Groups_Oone__class_Oone(X5) = c_Groups_Osgn__class_Osgn(X5,c_Groups_Oone__class_Oone(X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__one) ).

fof(f7858,plain,
    spl50_379,
    inference(avatar_split_clause,[],[f4173,f7856]) ).

fof(f7856,plain,
    ( spl50_379
  <=> ! [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,[spl50_379])]) ).

fof(f4173,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,[],[f1321]) ).

fof(f1321,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,[],[f422]) ).

fof(f422,axiom,
    ! [X17] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X17)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__square) ).

fof(f7854,plain,
    spl50_378,
    inference(avatar_split_clause,[],[f4172,f7852]) ).

fof(f7852,plain,
    ( spl50_378
  <=> ! [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,[spl50_378])]) ).

fof(f4172,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,[],[f1320]) ).

fof(f1320,plain,
    ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) = X0,
    inference(rectify,[],[f426]) ).

fof(f426,axiom,
    ! [X3] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X3) = X3,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__1) ).

fof(f7850,plain,
    spl50_377,
    inference(avatar_split_clause,[],[f4171,f7848]) ).

fof(f4171,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,[],[f1319]) ).

fof(f1319,plain,
    ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X0) = X0,
    inference(rectify,[],[f579]) ).

fof(f579,axiom,
    ! [X14] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X14) = X14,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__1) ).

fof(f7846,plain,
    spl50_376,
    inference(avatar_split_clause,[],[f4170,f7844]) ).

fof(f4170,plain,
    ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X0) = X0,
    inference(cnf_transformation,[],[f1318]) ).

fof(f1318,plain,
    ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X0) = X0,
    inference(rectify,[],[f210]) ).

fof(f210,axiom,
    ! [X14] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X14) = X14,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__1) ).

fof(f7842,plain,
    spl50_375,
    inference(avatar_split_clause,[],[f4169,f7840]) ).

fof(f7840,plain,
    ( spl50_375
  <=> ! [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,[spl50_375])]) ).

fof(f4169,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,[],[f1317]) ).

fof(f1317,plain,
    ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0,
    inference(rectify,[],[f424]) ).

fof(f424,axiom,
    ! [X3] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X3,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__1__right) ).

fof(f7838,plain,
    spl50_374,
    inference(avatar_split_clause,[],[f4168,f7836]) ).

fof(f4168,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,[],[f1316]) ).

fof(f1316,plain,
    ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X0,
    inference(rectify,[],[f580]) ).

fof(f580,axiom,
    ! [X14] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X14),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X14,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__1__right) ).

fof(f7834,plain,
    spl50_373,
    inference(avatar_split_clause,[],[f4167,f7832]) ).

fof(f7832,plain,
    ( spl50_373
  <=> ! [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,[spl50_373])]) ).

fof(f4167,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,[],[f1315]) ).

fof(f1315,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,[],[f591]) ).

fof(f591,axiom,
    ! [X14] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X14),X14),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__zminus__inverse2) ).

fof(f7830,plain,
    ( spl50_372
    | ~ spl50_229
    | ~ spl50_362 ),
    inference(avatar_split_clause,[],[f7800,f7757,f7184,f7827]) ).

fof(f7827,plain,
    ( spl50_372
  <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_372])]) ).

fof(f7800,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____)
    | ~ spl50_229
    | ~ spl50_362 ),
    inference(resolution,[],[f7758,f7186]) ).

fof(f7824,plain,
    ~ spl50_371,
    inference(avatar_split_clause,[],[f4111,f7821]) ).

fof(f4111,plain,
    c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(cnf_transformation,[],[f445]) ).

fof(f445,axiom,
    c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_kn) ).

fof(f7819,plain,
    ~ spl50_370,
    inference(avatar_split_clause,[],[f4110,f7816]) ).

fof(f7816,plain,
    ( spl50_370
  <=> c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_370])]) ).

fof(f4110,plain,
    c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),
    inference(cnf_transformation,[],[f555]) ).

fof(f555,axiom,
    c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_a00) ).

fof(f7787,plain,
    spl50_369,
    inference(avatar_split_clause,[],[f5871,f7785]) ).

fof(f7785,plain,
    ( spl50_369
  <=> ! [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,[spl50_369])]) ).

fof(f5871,plain,
    ! [X2,X1] : sP9(c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X1,X2,c_Groups_Ozero__class_Ozero(X2)),
    inference(equality_resolution,[],[f5870]) ).

fof(f5870,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,[],[f5271]) ).

fof(f5271,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,[],[f3804]) ).

fof(f7783,plain,
    spl50_368,
    inference(avatar_split_clause,[],[f5774,f7781]) ).

fof(f7781,plain,
    ( spl50_368
  <=> ! [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,[spl50_368])]) ).

fof(f5774,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,[],[f4737]) ).

fof(f4737,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,[],[f3628]) ).

fof(f7779,plain,
    spl50_367,
    inference(avatar_split_clause,[],[f5576,f7777]) ).

fof(f7777,plain,
    ( spl50_367
  <=> ! [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,[spl50_367])]) ).

fof(f5576,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,[],[f4153,f4164]) ).

fof(f4153,plain,
    ! [X0] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X0)),
    inference(cnf_transformation,[],[f1301]) ).

fof(f1301,plain,
    ! [X0] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X0)),
    inference(rectify,[],[f888]) ).

fof(f888,axiom,
    ! [X3] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,c_Nat_OSuc(X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lessI) ).

fof(f7775,plain,
    spl50_366,
    inference(avatar_split_clause,[],[f5575,f7773]) ).

fof(f5575,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,[],[f4150,f4164]) ).

fof(f4150,plain,
    ! [X0] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X0),X0),
    inference(cnf_transformation,[],[f1298]) ).

fof(f1298,plain,
    ! [X0] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X0),X0),
    inference(rectify,[],[f955]) ).

fof(f955,axiom,
    ! [X3] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X3),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__not__le__n) ).

fof(f7771,plain,
    spl50_365,
    inference(avatar_split_clause,[],[f5569,f7769]) ).

fof(f5569,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,[],[f4141,f4164]) ).

fof(f4141,plain,
    ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X0),
    inference(cnf_transformation,[],[f1289]) ).

fof(f1289,plain,
    ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X0),
    inference(rectify,[],[f933]) ).

fof(f933,axiom,
    ! [X17] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X17),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).

fof(f7767,plain,
    spl50_364,
    inference(avatar_split_clause,[],[f5192,f7765]) ).

fof(f7765,plain,
    ( spl50_364
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
        | ~ sP6(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_364])]) ).

fof(f5192,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
      | ~ sP6(X0,X1,X2) ),
    inference(cnf_transformation,[],[f3756]) ).

fof(f7763,plain,
    spl50_363,
    inference(avatar_split_clause,[],[f4666,f7761]) ).

fof(f7761,plain,
    ( spl50_363
  <=> ! [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,[spl50_363])]) ).

fof(f4666,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,[],[f3587]) ).

fof(f7759,plain,
    spl50_362,
    inference(avatar_split_clause,[],[f4652,f7757]) ).

fof(f4652,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) ),
    inference(cnf_transformation,[],[f3572]) ).

fof(f7755,plain,
    spl50_361,
    inference(avatar_split_clause,[],[f4579,f7753]) ).

fof(f4579,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,[],[f2604]) ).

fof(f2604,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,[],[f1647]) ).

fof(f1647,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,[],[f782]) ).

fof(f782,axiom,
    ! [X7,X9] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X9,X7)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X9,X7) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I5_J) ).

fof(f7751,plain,
    spl50_360,
    inference(avatar_split_clause,[],[f4345,f7749]) ).

fof(f7749,plain,
    ( spl50_360
  <=> ! [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,[spl50_360])]) ).

fof(f4345,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,[],[f1473]) ).

fof(f1473,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,[],[f368]) ).

fof(f368,axiom,
    ! [X3,X17] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X17)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__linear) ).

fof(f7747,plain,
    spl50_359,
    inference(avatar_split_clause,[],[f4344,f7745]) ).

fof(f7745,plain,
    ( spl50_359
  <=> ! [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,[spl50_359])]) ).

fof(f4344,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,[],[f1472]) ).

fof(f1472,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,[],[f670]) ).

fof(f670,axiom,
    ! [X15,X14] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X15,X14)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X14,X15) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__linear) ).

fof(f7743,plain,
    spl50_358,
    inference(avatar_split_clause,[],[f4343,f7741]) ).

fof(f4343,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
      | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ),
    inference(cnf_transformation,[],[f1471]) ).

fof(f1471,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
      | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ),
    inference(rectify,[],[f205]) ).

fof(f205,axiom,
    ! [X15,X14] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X15,X14)
      | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X14,X15) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__linear) ).

fof(f7739,plain,
    spl50_357,
    inference(avatar_split_clause,[],[f4249,f7737]) ).

fof(f7737,plain,
    ( spl50_357
  <=> ! [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,[spl50_357])]) ).

fof(f4249,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,[],[f2361]) ).

fof(f2361,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,[],[f1390]) ).

fof(f1390,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,[],[f143]) ).

fof(f143,axiom,
    ! [X5] :
      ( class_Rings_Olinordered__semidom(X5)
     => c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),c_Groups_Oone__class_Oone(X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__one) ).

fof(f7735,plain,
    spl50_356,
    inference(avatar_split_clause,[],[f4248,f7733]) ).

fof(f7733,plain,
    ( spl50_356
  <=> ! [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,[spl50_356])]) ).

fof(f4248,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,[],[f2360]) ).

fof(f2360,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,[],[f1389]) ).

fof(f1389,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,[],[f46]) ).

fof(f46,axiom,
    ! [X5] :
      ( class_Rings_Olinordered__semidom(X5)
     => c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),c_Groups_Oone__class_Oone(X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__one) ).

fof(f7731,plain,
    spl50_355,
    inference(avatar_split_clause,[],[f4247,f7729]) ).

fof(f7729,plain,
    ( spl50_355
  <=> ! [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,[spl50_355])]) ).

fof(f4247,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,[],[f2359]) ).

fof(f2359,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,[],[f1388]) ).

fof(f1388,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,[],[f144]) ).

fof(f144,axiom,
    ! [X5] :
      ( class_Rings_Olinordered__semidom(X5)
     => ~ c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5),c_Groups_Ozero__class_Ozero(X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__one__less__zero) ).

fof(f7727,plain,
    spl50_354,
    inference(avatar_split_clause,[],[f4246,f7725]) ).

fof(f7725,plain,
    ( spl50_354
  <=> ! [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,[spl50_354])]) ).

fof(f4246,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,[],[f2358]) ).

fof(f2358,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,[],[f1387]) ).

fof(f1387,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,[],[f47]) ).

fof(f47,axiom,
    ! [X5] :
      ( class_Rings_Olinordered__semidom(X5)
     => ~ c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oone__class_Oone(X5),c_Groups_Ozero__class_Ozero(X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__one__le__zero) ).

fof(f7723,plain,
    spl50_353,
    inference(avatar_split_clause,[],[f4202,f7721]) ).

fof(f7721,plain,
    ( spl50_353
  <=> ! [X0] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK22(X0))
        | ~ class_RealVector_Oreal__normed__algebra(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_353])]) ).

fof(f4202,plain,
    ! [X0] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK22(X0))
      | ~ class_RealVector_Oreal__normed__algebra(X0) ),
    inference(cnf_transformation,[],[f3477]) ).

fof(f3477,plain,
    ! [X0] :
      ( ( ! [X2,X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X0,X2)),c_RealVector_Onorm__class_Onorm(X0,X3))),sK22(X0)))
        & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK22(X0)) )
      | ~ class_RealVector_Oreal__normed__algebra(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK22])],[f2315,f3476]) ).

fof(f3476,plain,
    ! [X0] :
      ( ? [X1] :
          ( ! [X2,X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X0,X2)),c_RealVector_Onorm__class_Onorm(X0,X3))),X1))
          & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) )
     => ( ! [X3,X2] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X0,X2)),c_RealVector_Onorm__class_Onorm(X0,X3))),sK22(X0)))
        & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK22(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f2315,plain,
    ! [X0] :
      ( ? [X1] :
          ( ! [X2,X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X0,X2)),c_RealVector_Onorm__class_Onorm(X0,X3))),X1))
          & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) )
      | ~ class_RealVector_Oreal__normed__algebra(X0) ),
    inference(ennf_transformation,[],[f1344]) ).

fof(f1344,plain,
    ! [X0] :
      ( class_RealVector_Oreal__normed__algebra(X0)
     => ? [X1] :
          ( ! [X2,X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X0,X2)),c_RealVector_Onorm__class_Onorm(X0,X3))),X1))
          & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ) ),
    inference(rectify,[],[f774]) ).

fof(f774,axiom,
    ! [X5] :
      ( class_RealVector_Oreal__normed__algebra(X5)
     => ? [X76] :
          ( ! [X71,X77] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X71),X77)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5,X71)),c_RealVector_Onorm__class_Onorm(X5,X77))),X76))
          & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X76) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Opos__bounded) ).

fof(f7719,plain,
    spl50_352,
    inference(avatar_split_clause,[],[f4163,f7717]) ).

fof(f4163,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,[],[f1311]) ).

fof(f1311,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,[],[f448]) ).

fof(f448,axiom,
    ! [X3] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__0__eq__0) ).

fof(f7715,plain,
    ~ spl50_351,
    inference(avatar_split_clause,[],[f4109,f7712]) ).

fof(f7712,plain,
    ( spl50_351
  <=> c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_351])]) ).

fof(f4109,plain,
    c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____),
    inference(cnf_transformation,[],[f443]) ).

fof(f443,axiom,
    c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pc0) ).

fof(f7710,plain,
    ( ~ spl50_350
    | ~ spl50_331
    | ~ spl50_344 ),
    inference(avatar_split_clause,[],[f7705,f7667,f7615,f7707]) ).

fof(f7707,plain,
    ( spl50_350
  <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_350])]) ).

fof(f7705,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ spl50_331
    | ~ spl50_344 ),
    inference(superposition,[],[f7668,f7616]) ).

fof(f7693,plain,
    ( spl50_349
    | ~ spl50_321 ),
    inference(avatar_split_clause,[],[f7574,f7570,f7690]) ).

fof(f7690,plain,
    ( spl50_349
  <=> c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_q____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK19) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_349])]) ).

fof(f7570,plain,
    ( spl50_321
  <=> c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_q____) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_321])]) ).

fof(f7574,plain,
    ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_q____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK19)
    | ~ spl50_321 ),
    inference(forward_demodulation,[],[f7572,f4130]) ).

fof(f7572,plain,
    ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_q____)
    | ~ spl50_321 ),
    inference(avatar_component_clause,[],[f7570]) ).

fof(f7688,plain,
    spl50_348,
    inference(avatar_split_clause,[],[f6041,f7685]) ).

fof(f7685,plain,
    ( spl50_348
  <=> c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK19) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK46) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_348])]) ).

fof(f6041,plain,
    c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK19) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK46),
    inference(forward_demodulation,[],[f5560,f4130]) ).

fof(f5560,plain,
    c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK46),
    inference(cnf_transformation,[],[f3871]) ).

fof(f7683,plain,
    spl50_347,
    inference(avatar_split_clause,[],[f5799,f7681]) ).

fof(f7681,plain,
    ( spl50_347
  <=> ! [X2,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X2),X1,X1)
        | ~ class_Rings_Olinordered__idom(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_347])]) ).

fof(f5799,plain,
    ! [X2,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X2),X1,X1)
      | ~ class_Rings_Olinordered__idom(X2) ),
    inference(equality_resolution,[],[f4897]) ).

fof(f4897,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X2),X1,X0)
      | X0 != X1
      | ~ class_Rings_Olinordered__idom(X2) ),
    inference(cnf_transformation,[],[f3681]) ).

fof(f7679,plain,
    spl50_346,
    inference(avatar_split_clause,[],[f5694,f7676]) ).

fof(f7676,plain,
    ( spl50_346
  <=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_346])]) ).

fof(f5694,plain,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(equality_resolution,[],[f4192]) ).

fof(f4192,plain,
    ! [X0] :
      ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,X0)
      | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ),
    inference(cnf_transformation,[],[f2307]) ).

fof(f7674,plain,
    spl50_345,
    inference(avatar_split_clause,[],[f5692,f7671]) ).

fof(f7671,plain,
    ( spl50_345
  <=> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_345])]) ).

fof(f5692,plain,
    c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
    inference(equality_resolution,[],[f4186]) ).

fof(f4186,plain,
    ! [X0] :
      ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X0)
      | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X0 ),
    inference(cnf_transformation,[],[f2305]) ).

fof(f7669,plain,
    spl50_344,
    inference(avatar_split_clause,[],[f5567,f7667]) ).

fof(f5567,plain,
    ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X0,
    inference(definition_unfolding,[],[f4133,f4164]) ).

fof(f4133,plain,
    ! [X0] : c_Nat_OSuc(X0) != X0,
    inference(cnf_transformation,[],[f1281]) ).

fof(f1281,plain,
    ! [X0] : c_Nat_OSuc(X0) != X0,
    inference(rectify,[],[f934]) ).

fof(f934,axiom,
    ! [X3] : c_Nat_OSuc(X3) != X3,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).

fof(f7665,plain,
    spl50_343,
    inference(avatar_split_clause,[],[f5313,f7663]) ).

fof(f7663,plain,
    ( spl50_343
  <=> ! [X0,X3,X2,X1] :
        ( sP14(X2,X3,X0,X1)
        | ~ class_Rings_Olinordered__ring__strict(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_343])]) ).

fof(f5313,plain,
    ! [X2,X3,X0,X1] :
      ( sP14(X2,X3,X0,X1)
      | ~ class_Rings_Olinordered__ring__strict(X3) ),
    inference(cnf_transformation,[],[f3463]) ).

fof(f3463,plain,
    ! [X0,X1,X2,X3] :
      ( sP14(X2,X3,X0,X1)
      | ~ class_Rings_Olinordered__ring__strict(X3) ),
    inference(definition_folding,[],[f3127,f3462,f3461]) ).

fof(f3462,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))
      <=> sP13(X1,X0,X3,X2) )
      | ~ sP14(X2,X3,X0,X1) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP14])]) ).

fof(f3127,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,[],[f2091]) ).

fof(f2091,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,[],[f139]) ).

fof(f139,axiom,
    ! [X21,X24,X25,X5] :
      ( class_Rings_Olinordered__ring__strict(X5)
     => ( c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X25),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X25),X21))
      <=> ( ( c_Orderings_Oord__class_Oless(X5,X21,X24)
            & c_Orderings_Oord__class_Oless(X5,X25,c_Groups_Ozero__class_Ozero(X5)) )
          | ( c_Orderings_Oord__class_Oless(X5,X24,X21)
            & c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X25) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel__left__disj) ).

fof(f7661,plain,
    spl50_342,
    inference(avatar_split_clause,[],[f5304,f7659]) ).

fof(f7659,plain,
    ( spl50_342
  <=> ! [X0,X3,X2,X1] :
        ( sP12(X1,X3,X0,X2)
        | ~ class_Rings_Olinordered__ring__strict(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_342])]) ).

fof(f5304,plain,
    ! [X2,X3,X0,X1] :
      ( sP12(X1,X3,X0,X2)
      | ~ class_Rings_Olinordered__ring__strict(X3) ),
    inference(cnf_transformation,[],[f3460]) ).

fof(f3460,plain,
    ! [X0,X1,X2,X3] :
      ( sP12(X1,X3,X0,X2)
      | ~ class_Rings_Olinordered__ring__strict(X3) ),
    inference(definition_folding,[],[f3126,f3459,f3458]) ).

fof(f3459,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))
      <=> sP11(X2,X0,X3,X1) )
      | ~ sP12(X1,X3,X0,X2) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP12])]) ).

fof(f3126,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,[],[f2090]) ).

fof(f2090,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,[],[f140]) ).

fof(f140,axiom,
    ! [X21,X25,X24,X5] :
      ( class_Rings_Olinordered__ring__strict(X5)
     => ( c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X24),X25),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X21),X25))
      <=> ( ( c_Orderings_Oord__class_Oless(X5,X21,X24)
            & c_Orderings_Oord__class_Oless(X5,X25,c_Groups_Ozero__class_Ozero(X5)) )
          | ( c_Orderings_Oord__class_Oless(X5,X24,X21)
            & c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X25) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel__right__disj) ).

fof(f7657,plain,
    spl50_341,
    inference(avatar_split_clause,[],[f5274,f7655]) ).

fof(f7655,plain,
    ( spl50_341
  <=> ! [X0,X3,X2,X1] :
        ( sP10(X2,X3,X1,X0)
        | ~ class_Fields_Ofield(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_341])]) ).

fof(f5274,plain,
    ! [X2,X3,X0,X1] :
      ( sP10(X2,X3,X1,X0)
      | ~ class_Fields_Ofield(X3) ),
    inference(cnf_transformation,[],[f3457]) ).

fof(f3457,plain,
    ! [X0,X1,X2,X3] :
      ( sP10(X2,X3,X1,X0)
      | ~ class_Fields_Ofield(X3) ),
    inference(definition_folding,[],[f3099,f3456,f3455]) ).

fof(f3099,plain,
    ! [X0,X1,X2,X3] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X1),X0)
      <=> ( ( 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,[],[f2072]) ).

fof(f2072,plain,
    ! [X0,X1,X2,X3] :
      ( class_Fields_Ofield(X3)
     => ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X1),X0)
      <=> ( ( c_Groups_Ozero__class_Ozero(X3) != X2
           => 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,[],[f844]) ).

fof(f844,axiom,
    ! [X66,X64,X24,X5] :
      ( class_Fields_Ofield(X5)
     => ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5),c_Polynomial_Osmult(X5,X24,X64),X66)
      <=> ( ( c_Groups_Ozero__class_Ozero(X5) != X24
           => c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5),X64,X66) )
          & ( c_Groups_Ozero__class_Ozero(X5) = X24
           => c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = X66 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__dvd__iff) ).

fof(f7653,plain,
    spl50_340,
    inference(avatar_split_clause,[],[f4518,f7651]) ).

fof(f7651,plain,
    ( spl50_340
  <=> ! [X0,X1] :
        ( 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,[spl50_340])]) ).

fof(f4518,plain,
    ! [X0,X1] :
      ( c_Rings_Odvd__class_Odvd(X1,c_Groups_Oone__class_Oone(X1),X0)
      | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(cnf_transformation,[],[f2536]) ).

fof(f2536,plain,
    ! [X0,X1] :
      ( c_Rings_Odvd__class_Odvd(X1,c_Groups_Oone__class_Oone(X1),X0)
      | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(ennf_transformation,[],[f1594]) ).

fof(f1594,plain,
    ! [X0,X1] :
      ( class_Rings_Ocomm__semiring__1(X1)
     => c_Rings_Odvd__class_Odvd(X1,c_Groups_Oone__class_Oone(X1),X0) ),
    inference(rectify,[],[f837]) ).

fof(f837,axiom,
    ! [X4,X5] :
      ( class_Rings_Ocomm__semiring__1(X5)
     => c_Rings_Odvd__class_Odvd(X5,c_Groups_Oone__class_Oone(X5),X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__dvd) ).

fof(f7649,plain,
    spl50_339,
    inference(avatar_split_clause,[],[f4517,f7647]) ).

fof(f7647,plain,
    ( spl50_339
  <=> ! [X0,X1] :
        ( 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,[spl50_339])]) ).

fof(f4517,plain,
    ! [X0,X1] :
      ( c_Rings_Odvd__class_Odvd(X1,X0,c_Groups_Ozero__class_Ozero(X1))
      | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(cnf_transformation,[],[f2535]) ).

fof(f2535,plain,
    ! [X0,X1] :
      ( c_Rings_Odvd__class_Odvd(X1,X0,c_Groups_Ozero__class_Ozero(X1))
      | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(ennf_transformation,[],[f1593]) ).

fof(f1593,plain,
    ! [X0,X1] :
      ( class_Rings_Ocomm__semiring__1(X1)
     => c_Rings_Odvd__class_Odvd(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(rectify,[],[f805]) ).

fof(f805,axiom,
    ! [X4,X5] :
      ( class_Rings_Ocomm__semiring__1(X5)
     => c_Rings_Odvd__class_Odvd(X5,X4,c_Groups_Ozero__class_Ozero(X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__0__right) ).

fof(f7645,plain,
    spl50_338,
    inference(avatar_split_clause,[],[f4308,f7643]) ).

fof(f7643,plain,
    ( spl50_338
  <=> ! [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,[spl50_338])]) ).

fof(f4308,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,[],[f1439]) ).

fof(f1439,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,[],[f465]) ).

fof(f465,axiom,
    ! [X3,X17] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X3),X17),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__le__self) ).

fof(f7641,plain,
    spl50_337,
    inference(avatar_split_clause,[],[f4307,f7639]) ).

fof(f7639,plain,
    ( spl50_337
  <=> ! [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,[spl50_337])]) ).

fof(f4307,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,[],[f1438]) ).

fof(f1438,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,[],[f414]) ).

fof(f414,axiom,
    ! [X17,X3] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add2) ).

fof(f7637,plain,
    spl50_336,
    inference(avatar_split_clause,[],[f4306,f7635]) ).

fof(f4306,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,[],[f1437]) ).

fof(f1437,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,[],[f413]) ).

fof(f413,axiom,
    ! [X17,X3] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X17)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add1) ).

fof(f7633,plain,
    spl50_335,
    inference(avatar_split_clause,[],[f4305,f7631]) ).

fof(f7631,plain,
    ( spl50_335
  <=> ! [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,[spl50_335])]) ).

fof(f4305,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,[],[f1436]) ).

fof(f1436,plain,
    ! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X0),
    inference(rectify,[],[f397]) ).

fof(f397,axiom,
    ! [X18,X39] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X39,X18),X18),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__add__less2) ).

fof(f7629,plain,
    spl50_334,
    inference(avatar_split_clause,[],[f4304,f7627]) ).

fof(f4304,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,[],[f1435]) ).

fof(f1435,plain,
    ! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X1),
    inference(rectify,[],[f398]) ).

fof(f398,axiom,
    ! [X39,X18] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X39),X18),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__add__less1) ).

fof(f7625,plain,
    spl50_333,
    inference(avatar_split_clause,[],[f4254,f7623]) ).

fof(f7623,plain,
    ( spl50_333
  <=> ! [X0] :
        ( c_Groups_Oone__class_Oone(X0) != c_Groups_Ozero__class_Ozero(X0)
        | ~ class_Rings_Ozero__neq__one(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_333])]) ).

fof(f4254,plain,
    ! [X0] :
      ( c_Groups_Oone__class_Oone(X0) != c_Groups_Ozero__class_Ozero(X0)
      | ~ class_Rings_Ozero__neq__one(X0) ),
    inference(cnf_transformation,[],[f2366]) ).

fof(f2366,plain,
    ! [X0] :
      ( c_Groups_Oone__class_Oone(X0) != c_Groups_Ozero__class_Ozero(X0)
      | ~ class_Rings_Ozero__neq__one(X0) ),
    inference(ennf_transformation,[],[f1395]) ).

fof(f1395,plain,
    ! [X0] :
      ( class_Rings_Ozero__neq__one(X0)
     => c_Groups_Oone__class_Oone(X0) != c_Groups_Ozero__class_Ozero(X0) ),
    inference(rectify,[],[f100]) ).

fof(f100,axiom,
    ! [X5] :
      ( class_Rings_Ozero__neq__one(X5)
     => c_Groups_Ozero__class_Ozero(X5) != c_Groups_Oone__class_Oone(X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__neq__zero) ).

fof(f7621,plain,
    spl50_332,
    inference(avatar_split_clause,[],[f4230,f7619]) ).

fof(f7619,plain,
    ( spl50_332
  <=> ! [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,[spl50_332])]) ).

fof(f4230,plain,
    ! [X0] :
      ( ~ c_Polynomial_Opos__poly(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(cnf_transformation,[],[f2342]) ).

fof(f2342,plain,
    ! [X0] :
      ( ~ c_Polynomial_Opos__poly(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(ennf_transformation,[],[f1371]) ).

fof(f1371,plain,
    ! [X0] :
      ( class_Rings_Olinordered__idom(X0)
     => ~ c_Polynomial_Opos__poly(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) ),
    inference(rectify,[],[f789]) ).

fof(f789,axiom,
    ! [X5] :
      ( class_Rings_Olinordered__idom(X5)
     => ~ c_Polynomial_Opos__poly(X5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__pos__poly__0) ).

fof(f7617,plain,
    spl50_331,
    inference(avatar_split_clause,[],[f4162,f7615]) ).

fof(f4162,plain,
    ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) = X0,
    inference(cnf_transformation,[],[f1310]) ).

fof(f1310,plain,
    ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) = X0,
    inference(rectify,[],[f381]) ).

fof(f381,axiom,
    ! [X3] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3) = X3,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).

fof(f7613,plain,
    spl50_330,
    inference(avatar_split_clause,[],[f4161,f7611]) ).

fof(f7611,plain,
    ( spl50_330
  <=> ! [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,[spl50_330])]) ).

fof(f7609,plain,
    spl50_329,
    inference(avatar_split_clause,[],[f4160,f7607]) ).

fof(f7607,plain,
    ( spl50_329
  <=> ! [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,[spl50_329])]) ).

fof(f4160,plain,
    ! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) = X0,
    inference(cnf_transformation,[],[f1308]) ).

fof(f1308,plain,
    ! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) = X0,
    inference(rectify,[],[f596]) ).

fof(f596,axiom,
    ! [X14] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X14) = X14,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__0) ).

fof(f7605,plain,
    spl50_328,
    inference(avatar_split_clause,[],[f4159,f7603]) ).

fof(f7603,plain,
    ( spl50_328
  <=> ! [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,[spl50_328])]) ).

fof(f4159,plain,
    ! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X0,
    inference(cnf_transformation,[],[f1307]) ).

fof(f1307,plain,
    ! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X0,
    inference(rectify,[],[f598]) ).

fof(f598,axiom,
    ! [X14] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X14,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X14,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__0__right) ).

fof(f7601,plain,
    spl50_327,
    inference(avatar_split_clause,[],[f4158,f7599]) ).

fof(f7599,plain,
    ( spl50_327
  <=> ! [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,[spl50_327])]) ).

fof(f4158,plain,
    ! [X0] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
    inference(cnf_transformation,[],[f1306]) ).

fof(f1306,plain,
    ! [X0] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
    inference(rectify,[],[f449]) ).

fof(f449,axiom,
    ! [X17] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X17,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__nat_Odiff__0) ).

fof(f7597,plain,
    spl50_326,
    inference(avatar_split_clause,[],[f4157,f7595]) ).

fof(f7595,plain,
    ( spl50_326
  <=> ! [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,[spl50_326])]) ).

fof(f4157,plain,
    ! [X0] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) = X0,
    inference(cnf_transformation,[],[f1305]) ).

fof(f1305,plain,
    ! [X0] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) = X0,
    inference(rectify,[],[f625]) ).

fof(f625,axiom,
    ! [X14] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X14)) = X14,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zminus__zminus) ).

fof(f7593,plain,
    spl50_325,
    inference(avatar_split_clause,[],[f4156,f7591]) ).

fof(f7591,plain,
    ( spl50_325
  <=> ! [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,[spl50_325])]) ).

fof(f4156,plain,
    ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X0),
    inference(cnf_transformation,[],[f1304]) ).

fof(f1304,plain,
    ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X0),
    inference(rectify,[],[f450]) ).

fof(f450,axiom,
    ! [X17] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X17),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__self__eq__0) ).

fof(f7589,plain,
    spl50_324,
    inference(avatar_split_clause,[],[f4130,f7586]) ).

fof(f7584,plain,
    spl50_323,
    inference(avatar_split_clause,[],[f4108,f7581]) ).

fof(f7581,plain,
    ( spl50_323
  <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_323])]) ).

fof(f4108,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),
    inference(cnf_transformation,[],[f4]) ).

fof(f4,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__0960_A_060_061_Acmod_Aw_096) ).

fof(f7579,plain,
    spl50_322,
    inference(avatar_split_clause,[],[f4107,f7576]) ).

fof(f7576,plain,
    ( spl50_322
  <=> c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Complex_Oii) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Complex_Oii) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_322])]) ).

fof(f4107,plain,
    c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Complex_Oii) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Complex_Oii),
    inference(cnf_transformation,[],[f706]) ).

fof(f706,axiom,
    c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Complex_Oii) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Complex_Oii),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__i) ).

fof(f7573,plain,
    spl50_321,
    inference(avatar_split_clause,[],[f4106,f7570]) ).

fof(f7568,plain,
    spl50_320,
    inference(avatar_split_clause,[],[f4105,f7565]) ).

fof(f7565,plain,
    ( spl50_320
  <=> 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,[spl50_320])]) ).

fof(f4105,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,[],[f592]) ).

fof(f592,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/sandbox/benchmark/theBenchmark.p',fact_zminus__0) ).

fof(f7563,plain,
    spl50_319,
    inference(avatar_split_clause,[],[f4104,f7560]) ).

fof(f7560,plain,
    ( spl50_319
  <=> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_319])]) ).

fof(f4104,plain,
    c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
    inference(cnf_transformation,[],[f240]) ).

fof(f240,axiom,
    c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INVERSE__ZERO) ).

fof(f7558,plain,
    spl50_318,
    inference(avatar_split_clause,[],[f6017,f7555]) ).

fof(f7555,plain,
    ( spl50_318
  <=> 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,[spl50_318])]) ).

fof(f6017,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,[],[f5786,f5702]) ).

fof(f5786,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,[],[f4761]) ).

fof(f4761,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,[],[f3644]) ).

fof(f7553,plain,
    spl50_317,
    inference(avatar_split_clause,[],[f5838,f7551]) ).

fof(f7551,plain,
    ( spl50_317
  <=> ! [X2,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X2,X1,X1)
        | ~ class_Orderings_Oorder(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_317])]) ).

fof(f5838,plain,
    ! [X2,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X2,X1,X1)
      | ~ class_Orderings_Oorder(X2) ),
    inference(equality_resolution,[],[f5079]) ).

fof(f5079,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
      | X0 != X1
      | ~ class_Orderings_Oorder(X2) ),
    inference(cnf_transformation,[],[f3725]) ).

fof(f3725,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,[],[f3724]) ).

fof(f3724,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,[],[f2968]) ).

fof(f2968,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,[],[f1964]) ).

fof(f1964,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,[],[f714]) ).

fof(f714,axiom,
    ! [X20,X12,X5] :
      ( class_Orderings_Oorder(X5)
     => ( X12 = X20
      <=> ( c_Orderings_Oord__class_Oless__eq(X5,X20,X12)
          & c_Orderings_Oord__class_Oless__eq(X5,X12,X20) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__eq__iff) ).

fof(f7549,plain,
    spl50_316,
    inference(avatar_split_clause,[],[f5835,f7547]) ).

fof(f7547,plain,
    ( spl50_316
  <=> ! [X2,X1] :
        ( ~ c_Orderings_Oord__class_Oless(X2,X1,X1)
        | ~ class_Orderings_Oorder(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_316])]) ).

fof(f5835,plain,
    ! [X2,X1] :
      ( ~ c_Orderings_Oord__class_Oless(X2,X1,X1)
      | ~ class_Orderings_Oorder(X2) ),
    inference(equality_resolution,[],[f5074]) ).

fof(f5074,plain,
    ! [X2,X0,X1] :
      ( X0 != X1
      | ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
      | ~ class_Orderings_Oorder(X2) ),
    inference(cnf_transformation,[],[f2961]) ).

fof(f2961,plain,
    ! [X0,X1,X2] :
      ( X0 != X1
      | ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
      | ~ class_Orderings_Oorder(X2) ),
    inference(flattening,[],[f2960]) ).

fof(f2960,plain,
    ! [X0,X1,X2] :
      ( X0 != X1
      | ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
      | ~ class_Orderings_Oorder(X2) ),
    inference(ennf_transformation,[],[f1960]) ).

fof(f1960,plain,
    ! [X0,X1,X2] :
      ( class_Orderings_Oorder(X2)
     => ( c_Orderings_Oord__class_Oless(X2,X1,X0)
       => X0 != X1 ) ),
    inference(rectify,[],[f739]) ).

fof(f739,axiom,
    ! [X7,X9,X5] :
      ( class_Orderings_Oorder(X5)
     => ( c_Orderings_Oord__class_Oless(X5,X9,X7)
       => X7 != X9 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__eq) ).

fof(f7545,plain,
    spl50_315,
    inference(avatar_split_clause,[],[f5808,f7543]) ).

fof(f7543,plain,
    ( spl50_315
  <=> ! [X2,X1] :
        ( ~ c_Orderings_Oord__class_Oless(X2,X1,X1)
        | ~ class_Orderings_Olinorder(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_315])]) ).

fof(f5808,plain,
    ! [X2,X1] :
      ( ~ c_Orderings_Oord__class_Oless(X2,X1,X1)
      | ~ class_Orderings_Olinorder(X2) ),
    inference(equality_resolution,[],[f4963]) ).

fof(f4963,plain,
    ! [X2,X0,X1] :
      ( X0 != X1
      | ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
      | ~ class_Orderings_Olinorder(X2) ),
    inference(cnf_transformation,[],[f3695]) ).

fof(f3695,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,[],[f3694]) ).

fof(f3694,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,[],[f2850]) ).

fof(f2850,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,[],[f1880]) ).

fof(f1880,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,[],[f747]) ).

fof(f747,axiom,
    ! [X20,X12,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( X12 != X20
      <=> ( c_Orderings_Oord__class_Oless(X5,X20,X12)
          | c_Orderings_Oord__class_Oless(X5,X12,X20) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neq__iff) ).

fof(f7541,plain,
    spl50_314,
    inference(avatar_split_clause,[],[f4863,f7539]) ).

fof(f7539,plain,
    ( spl50_314
  <=> ! [X2,X0,X1] :
        ( sP5(X1,X2,X0)
        | ~ class_Rings_Olinordered__ring__strict(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_314])]) ).

fof(f4863,plain,
    ! [X2,X0,X1] :
      ( sP5(X1,X2,X0)
      | ~ class_Rings_Olinordered__ring__strict(X2) ),
    inference(cnf_transformation,[],[f3448]) ).

fof(f3448,plain,
    ! [X0,X1,X2] :
      ( sP5(X1,X2,X0)
      | ~ class_Rings_Olinordered__ring__strict(X2) ),
    inference(definition_folding,[],[f2743,f3447,f3446]) ).

fof(f2743,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,[],[f1812]) ).

fof(f1812,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,[],[f43]) ).

fof(f43,axiom,
    ! [X21,X24,X5] :
      ( class_Rings_Olinordered__ring__strict(X5)
     => ( c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X24),X21),c_Groups_Ozero__class_Ozero(X5))
      <=> ( ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X21)
            & c_Orderings_Oord__class_Oless__eq(X5,X24,c_Groups_Ozero__class_Ozero(X5)) )
          | ( c_Orderings_Oord__class_Oless__eq(X5,X21,c_Groups_Ozero__class_Ozero(X5))
            & c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X24) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__0__iff) ).

fof(f7537,plain,
    spl50_313,
    inference(avatar_split_clause,[],[f4854,f7535]) ).

fof(f7535,plain,
    ( spl50_313
  <=> ! [X2,X0,X1] :
        ( sP3(X1,X0,X2)
        | ~ class_Rings_Olinordered__ring__strict(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_313])]) ).

fof(f4854,plain,
    ! [X2,X0,X1] :
      ( sP3(X1,X0,X2)
      | ~ class_Rings_Olinordered__ring__strict(X2) ),
    inference(cnf_transformation,[],[f3445]) ).

fof(f3445,plain,
    ! [X0,X1,X2] :
      ( sP3(X1,X0,X2)
      | ~ class_Rings_Olinordered__ring__strict(X2) ),
    inference(definition_folding,[],[f2742,f3444,f3443]) ).

fof(f2742,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,[],[f1811]) ).

fof(f1811,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,[],[f44]) ).

fof(f44,axiom,
    ! [X21,X24,X5] :
      ( class_Rings_Olinordered__ring__strict(X5)
     => ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X24),X21))
      <=> ( ( c_Orderings_Oord__class_Oless__eq(X5,X21,c_Groups_Ozero__class_Ozero(X5))
            & c_Orderings_Oord__class_Oless__eq(X5,X24,c_Groups_Ozero__class_Ozero(X5)) )
          | ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X21)
            & c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X24) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__mult__iff) ).

fof(f7533,plain,
    spl50_312,
    inference(avatar_split_clause,[],[f4540,f7531]) ).

fof(f7531,plain,
    ( spl50_312
  <=> ! [X0,X1] :
        ( class_Groups_Ominus(tc_fun(X0,X1))
        | ~ class_Groups_Ominus(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_312])]) ).

fof(f4540,plain,
    ! [X0,X1] :
      ( class_Groups_Ominus(tc_fun(X0,X1))
      | ~ class_Groups_Ominus(X1) ),
    inference(cnf_transformation,[],[f2557]) ).

fof(f2557,plain,
    ! [X0,X1] :
      ( class_Groups_Ominus(tc_fun(X0,X1))
      | ~ class_Groups_Ominus(X1) ),
    inference(ennf_transformation,[],[f1614]) ).

fof(f1614,plain,
    ! [X0,X1] :
      ( class_Groups_Ominus(X1)
     => class_Groups_Ominus(tc_fun(X0,X1)) ),
    inference(rectify,[],[f1006]) ).

fof(f1006,axiom,
    ! [X88,X87] :
      ( class_Groups_Ominus(X87)
     => class_Groups_Ominus(tc_fun(X88,X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Groups_Ominus) ).

fof(f7529,plain,
    spl50_311,
    inference(avatar_split_clause,[],[f4536,f7527]) ).

fof(f7527,plain,
    ( spl50_311
  <=> ! [X0,X1] :
        ( class_Orderings_Oorder(tc_fun(X0,X1))
        | ~ class_Orderings_Oorder(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_311])]) ).

fof(f4536,plain,
    ! [X0,X1] :
      ( class_Orderings_Oorder(tc_fun(X0,X1))
      | ~ class_Orderings_Oorder(X1) ),
    inference(cnf_transformation,[],[f2555]) ).

fof(f2555,plain,
    ! [X0,X1] :
      ( class_Orderings_Oorder(tc_fun(X0,X1))
      | ~ class_Orderings_Oorder(X1) ),
    inference(ennf_transformation,[],[f1612]) ).

fof(f1612,plain,
    ! [X0,X1] :
      ( class_Orderings_Oorder(X1)
     => class_Orderings_Oorder(tc_fun(X0,X1)) ),
    inference(rectify,[],[f1003]) ).

fof(f1003,axiom,
    ! [X88,X87] :
      ( class_Orderings_Oorder(X87)
     => class_Orderings_Oorder(tc_fun(X88,X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Oorder) ).

fof(f7525,plain,
    spl50_310,
    inference(avatar_split_clause,[],[f4535,f7523]) ).

fof(f7523,plain,
    ( spl50_310
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X1,X0,X0)
        | ~ class_Orderings_Opreorder(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_310])]) ).

fof(f4535,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X1,X0,X0)
      | ~ class_Orderings_Opreorder(X1) ),
    inference(cnf_transformation,[],[f2554]) ).

fof(f2554,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X1,X0,X0)
      | ~ class_Orderings_Opreorder(X1) ),
    inference(ennf_transformation,[],[f1611]) ).

fof(f1611,plain,
    ! [X0,X1] :
      ( class_Orderings_Opreorder(X1)
     => c_Orderings_Oord__class_Oless__eq(X1,X0,X0) ),
    inference(rectify,[],[f709]) ).

fof(f709,axiom,
    ! [X9,X5] :
      ( class_Orderings_Opreorder(X5)
     => c_Orderings_Oord__class_Oless__eq(X5,X9,X9) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__refl) ).

fof(f7521,plain,
    spl50_309,
    inference(avatar_split_clause,[],[f4534,f7519]) ).

fof(f7519,plain,
    ( spl50_309
  <=> ! [X0,X1] :
        ( class_Orderings_Opreorder(tc_fun(X0,X1))
        | ~ class_Orderings_Opreorder(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_309])]) ).

fof(f4534,plain,
    ! [X0,X1] :
      ( class_Orderings_Opreorder(tc_fun(X0,X1))
      | ~ class_Orderings_Opreorder(X1) ),
    inference(cnf_transformation,[],[f2553]) ).

fof(f2553,plain,
    ! [X0,X1] :
      ( class_Orderings_Opreorder(tc_fun(X0,X1))
      | ~ class_Orderings_Opreorder(X1) ),
    inference(ennf_transformation,[],[f1610]) ).

fof(f1610,plain,
    ! [X0,X1] :
      ( class_Orderings_Opreorder(X1)
     => class_Orderings_Opreorder(tc_fun(X0,X1)) ),
    inference(rectify,[],[f1002]) ).

fof(f1002,axiom,
    ! [X88,X87] :
      ( class_Orderings_Opreorder(X87)
     => class_Orderings_Opreorder(tc_fun(X88,X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Opreorder) ).

fof(f7517,plain,
    spl50_308,
    inference(avatar_split_clause,[],[f4533,f7515]) ).

fof(f7515,plain,
    ( spl50_308
  <=> ! [X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless(X1,X0,X0)
        | ~ class_Orderings_Opreorder(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_308])]) ).

fof(f4533,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(X1,X0,X0)
      | ~ class_Orderings_Opreorder(X1) ),
    inference(cnf_transformation,[],[f2552]) ).

fof(f2552,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(X1,X0,X0)
      | ~ class_Orderings_Opreorder(X1) ),
    inference(ennf_transformation,[],[f1609]) ).

fof(f1609,plain,
    ! [X0,X1] :
      ( class_Orderings_Opreorder(X1)
     => ~ c_Orderings_Oord__class_Oless(X1,X0,X0) ),
    inference(rectify,[],[f748]) ).

fof(f748,axiom,
    ! [X9,X5] :
      ( class_Orderings_Opreorder(X5)
     => ~ c_Orderings_Oord__class_Oless(X5,X9,X9) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__irrefl) ).

fof(f7513,plain,
    spl50_307,
    inference(avatar_split_clause,[],[f4532,f7511]) ).

fof(f7511,plain,
    ( spl50_307
  <=> ! [X0,X1] :
        ( class_Orderings_Oord(tc_fun(X0,X1))
        | ~ class_Orderings_Oord(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_307])]) ).

fof(f4532,plain,
    ! [X0,X1] :
      ( class_Orderings_Oord(tc_fun(X0,X1))
      | ~ class_Orderings_Oord(X1) ),
    inference(cnf_transformation,[],[f2551]) ).

fof(f2551,plain,
    ! [X0,X1] :
      ( class_Orderings_Oord(tc_fun(X0,X1))
      | ~ class_Orderings_Oord(X1) ),
    inference(ennf_transformation,[],[f1608]) ).

fof(f1608,plain,
    ! [X0,X1] :
      ( class_Orderings_Oord(X1)
     => class_Orderings_Oord(tc_fun(X0,X1)) ),
    inference(rectify,[],[f1004]) ).

fof(f1004,axiom,
    ! [X88,X87] :
      ( class_Orderings_Oord(X87)
     => class_Orderings_Oord(tc_fun(X88,X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).

fof(f7509,plain,
    spl50_306,
    inference(avatar_split_clause,[],[f4531,f7507]) ).

fof(f7507,plain,
    ( spl50_306
  <=> ! [X0,X1] :
        ( class_Groups_Ouminus(tc_fun(X0,X1))
        | ~ class_Groups_Ouminus(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_306])]) ).

fof(f4531,plain,
    ! [X0,X1] :
      ( class_Groups_Ouminus(tc_fun(X0,X1))
      | ~ class_Groups_Ouminus(X1) ),
    inference(cnf_transformation,[],[f2550]) ).

fof(f2550,plain,
    ! [X0,X1] :
      ( class_Groups_Ouminus(tc_fun(X0,X1))
      | ~ class_Groups_Ouminus(X1) ),
    inference(ennf_transformation,[],[f1607]) ).

fof(f1607,plain,
    ! [X0,X1] :
      ( class_Groups_Ouminus(X1)
     => class_Groups_Ouminus(tc_fun(X0,X1)) ),
    inference(rectify,[],[f1005]) ).

fof(f1005,axiom,
    ! [X88,X87] :
      ( class_Groups_Ouminus(X87)
     => class_Groups_Ouminus(tc_fun(X88,X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Groups_Ouminus) ).

fof(f7505,plain,
    spl50_305,
    inference(avatar_split_clause,[],[f4516,f7503]) ).

fof(f7503,plain,
    ( spl50_305
  <=> ! [X0,X1] :
        ( c_Rings_Odvd__class_Odvd(X1,X0,X0)
        | ~ class_Rings_Ocomm__semiring__1(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_305])]) ).

fof(f4516,plain,
    ! [X0,X1] :
      ( c_Rings_Odvd__class_Odvd(X1,X0,X0)
      | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(cnf_transformation,[],[f2534]) ).

fof(f2534,plain,
    ! [X0,X1] :
      ( c_Rings_Odvd__class_Odvd(X1,X0,X0)
      | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(ennf_transformation,[],[f1592]) ).

fof(f1592,plain,
    ! [X0,X1] :
      ( class_Rings_Ocomm__semiring__1(X1)
     => c_Rings_Odvd__class_Odvd(X1,X0,X0) ),
    inference(rectify,[],[f813]) ).

fof(f813,axiom,
    ! [X4,X5] :
      ( class_Rings_Ocomm__semiring__1(X5)
     => c_Rings_Odvd__class_Odvd(X5,X4,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__refl) ).

fof(f7501,plain,
    spl50_304,
    inference(avatar_split_clause,[],[f4375,f7499]) ).

fof(f7499,plain,
    ( spl50_304
  <=> ! [X0,X1] :
        ( class_Lattices_Oboolean__algebra(tc_fun(X0,X1))
        | ~ class_Lattices_Oboolean__algebra(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_304])]) ).

fof(f4375,plain,
    ! [X0,X1] :
      ( class_Lattices_Oboolean__algebra(tc_fun(X0,X1))
      | ~ class_Lattices_Oboolean__algebra(X1) ),
    inference(cnf_transformation,[],[f2423]) ).

fof(f2423,plain,
    ! [X0,X1] :
      ( class_Lattices_Oboolean__algebra(tc_fun(X0,X1))
      | ~ class_Lattices_Oboolean__algebra(X1) ),
    inference(ennf_transformation,[],[f1492]) ).

fof(f1492,plain,
    ! [X0,X1] :
      ( class_Lattices_Oboolean__algebra(X1)
     => class_Lattices_Oboolean__algebra(tc_fun(X0,X1)) ),
    inference(rectify,[],[f1001]) ).

fof(f1001,axiom,
    ! [X88,X87] :
      ( class_Lattices_Oboolean__algebra(X87)
     => class_Lattices_Oboolean__algebra(tc_fun(X88,X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Oboolean__algebra) ).

fof(f7497,plain,
    spl50_303,
    inference(avatar_split_clause,[],[f4103,f7494]) ).

fof(f7494,plain,
    ( spl50_303
  <=> 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,[spl50_303])]) ).

fof(f4103,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,[],[f595]) ).

fof(f595,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/sandbox/benchmark/theBenchmark.p',fact_int__0__less__1) ).

fof(f7492,plain,
    spl50_302,
    inference(avatar_split_clause,[],[f4101,f7489]) ).

fof(f7489,plain,
    ( spl50_302
  <=> 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,[spl50_302])]) ).

fof(f4101,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,[],[f695]) ).

fof(f695,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/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).

fof(f7487,plain,
    ~ spl50_301,
    inference(avatar_split_clause,[],[f4098,f7484]) ).

fof(f7484,plain,
    ( spl50_301
  <=> c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_301])]) ).

fof(f4098,plain,
    ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____)),
    inference(cnf_transformation,[],[f557]) ).

fof(f557,axiom,
    ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_qnc) ).

fof(f7482,plain,
    ~ spl50_300,
    inference(avatar_split_clause,[],[f4097,f7479]) ).

fof(f7479,plain,
    ( spl50_300
  <=> c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_300])]) ).

fof(f4097,plain,
    ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____)),
    inference(cnf_transformation,[],[f270]) ).

fof(f270,axiom,
    ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less_Oprems) ).

fof(f7477,plain,
    ~ spl50_299,
    inference(avatar_split_clause,[],[f4096,f7474]) ).

fof(f7474,plain,
    ( spl50_299
  <=> c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_299])]) ).

fof(f4096,plain,
    ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p)),
    inference(cnf_transformation,[],[f191]) ).

fof(f191,axiom,
    ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_assms) ).

fof(f7472,plain,
    ( ~ spl50_298
    | spl50_297 ),
    inference(avatar_split_clause,[],[f7467,f7463,f7469]) ).

fof(f7463,plain,
    ( spl50_297
  <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_297])]) ).

fof(f7467,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))))
    | spl50_297 ),
    inference(forward_demodulation,[],[f7465,f4326]) ).

fof(f7465,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____)))
    | spl50_297 ),
    inference(avatar_component_clause,[],[f7463]) ).

fof(f7466,plain,
    ~ spl50_297,
    inference(avatar_split_clause,[],[f3875,f7463]) ).

fof(f3875,plain,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))),
    inference(cnf_transformation,[],[f1274]) ).

fof(f1274,plain,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))),
    inference(flattening,[],[f1273]) ).

fof(f1273,negated_conjecture,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))),
    inference(negated_conjecture,[],[f1272]) ).

fof(f1272,conjecture,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

fof(f7461,plain,
    spl50_296,
    inference(avatar_split_clause,[],[f5987,f7458]) ).

fof(f7458,plain,
    ( spl50_296
  <=> sP1(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_296])]) ).

fof(f5987,plain,
    sP1(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(forward_demodulation,[],[f5986,f4161]) ).

fof(f5986,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,[],[f5773,f4313]) ).

fof(f5773,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,[],[f5772]) ).

fof(f5772,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,[],[f5658]) ).

fof(f5658,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,[],[f4717,f4164]) ).

fof(f4717,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,[],[f3618]) ).

fof(f7456,plain,
    spl50_295,
    inference(avatar_split_clause,[],[f5985,f7453]) ).

fof(f7453,plain,
    ( spl50_295
  <=> sP1(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_295])]) ).

fof(f5985,plain,
    sP1(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(forward_demodulation,[],[f5984,f4161]) ).

fof(f5984,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,[],[f5771,f4313]) ).

fof(f5771,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,[],[f5770]) ).

fof(f5770,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,[],[f5657]) ).

fof(f5657,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,[],[f4718,f4164]) ).

fof(f4718,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,[],[f3618]) ).

fof(f7451,plain,
    spl50_294,
    inference(avatar_split_clause,[],[f5971,f7448]) ).

fof(f7448,plain,
    ( spl50_294
  <=> sP0(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_294])]) ).

fof(f5971,plain,
    sP0(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(forward_demodulation,[],[f5970,f4161]) ).

fof(f5970,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,[],[f5769,f4313]) ).

fof(f5769,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,[],[f5768]) ).

fof(f5768,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,[],[f5651]) ).

fof(f5651,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,[],[f4709,f4164]) ).

fof(f4709,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,[],[f3615]) ).

fof(f7446,plain,
    spl50_293,
    inference(avatar_split_clause,[],[f5969,f7443]) ).

fof(f7443,plain,
    ( spl50_293
  <=> sP0(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_293])]) ).

fof(f5969,plain,
    sP0(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(forward_demodulation,[],[f5968,f4161]) ).

fof(f5968,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,[],[f5767,f4313]) ).

fof(f5767,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,[],[f5766]) ).

fof(f5766,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,[],[f5650]) ).

fof(f5650,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,[],[f4710,f4164]) ).

fof(f4710,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,[],[f3615]) ).

fof(f7441,plain,
    spl50_292,
    inference(avatar_split_clause,[],[f5916,f7439]) ).

fof(f7439,plain,
    ( spl50_292
  <=> ! [X0] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_292])]) ).

fof(f5916,plain,
    ! [X0] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),
    inference(forward_demodulation,[],[f5577,f5566]) ).

fof(f5566,plain,
    c_Groups_Oone__class_Oone(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(definition_unfolding,[],[f4100,f4164]) ).

fof(f4100,plain,
    c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(cnf_transformation,[],[f946]) ).

fof(f946,axiom,
    c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_One__nat__def) ).

fof(f5577,plain,
    ! [X0] : c_Rings_Odvd__class_Odvd(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,[],[f4154,f4164]) ).

fof(f4154,plain,
    ! [X0] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0),
    inference(cnf_transformation,[],[f1302]) ).

fof(f1302,plain,
    ! [X0] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0),
    inference(rectify,[],[f890]) ).

fof(f890,axiom,
    ! [X38] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X38),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__1__left) ).

fof(f7437,plain,
    spl50_291,
    inference(avatar_split_clause,[],[f5558,f7434]) ).

fof(f5558,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK45),
    inference(cnf_transformation,[],[f3869]) ).

fof(f7432,plain,
    spl50_290,
    inference(avatar_split_clause,[],[f4274,f7430]) ).

fof(f7430,plain,
    ( spl50_290
  <=> ! [X0] :
        ( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Ocomm__semiring__1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_290])]) ).

fof(f4274,plain,
    ! [X0] :
      ( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__semiring__1(X0) ),
    inference(cnf_transformation,[],[f2386]) ).

fof(f2386,plain,
    ! [X0] :
      ( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__semiring__1(X0) ),
    inference(ennf_transformation,[],[f1415]) ).

fof(f1415,plain,
    ! [X0] :
      ( class_Rings_Ocomm__semiring__1(X0)
     => class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1243]) ).

fof(f1243,axiom,
    ! [X87] :
      ( class_Rings_Ocomm__semiring__1(X87)
     => class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__1) ).

fof(f7428,plain,
    spl50_289,
    inference(avatar_split_clause,[],[f4273,f7426]) ).

fof(f7426,plain,
    ( spl50_289
  <=> ! [X0] :
        ( class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Ocomm__semiring__1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_289])]) ).

fof(f4273,plain,
    ! [X0] :
      ( class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__semiring__1(X0) ),
    inference(cnf_transformation,[],[f2385]) ).

fof(f2385,plain,
    ! [X0] :
      ( class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__semiring__1(X0) ),
    inference(ennf_transformation,[],[f1414]) ).

fof(f1414,plain,
    ! [X0] :
      ( class_Rings_Ocomm__semiring__1(X0)
     => class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1251]) ).

fof(f1251,axiom,
    ! [X87] :
      ( class_Rings_Ocomm__semiring__1(X87)
     => class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Omonoid__mult) ).

fof(f7424,plain,
    spl50_288,
    inference(avatar_split_clause,[],[f4272,f7422]) ).

fof(f7422,plain,
    ( spl50_288
  <=> ! [X0] :
        ( class_Power_Opower(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Ocomm__semiring__1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_288])]) ).

fof(f4272,plain,
    ! [X0] :
      ( class_Power_Opower(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__semiring__1(X0) ),
    inference(cnf_transformation,[],[f2384]) ).

fof(f2384,plain,
    ! [X0] :
      ( class_Power_Opower(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__semiring__1(X0) ),
    inference(ennf_transformation,[],[f1413]) ).

fof(f1413,plain,
    ! [X0] :
      ( class_Rings_Ocomm__semiring__1(X0)
     => class_Power_Opower(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1266]) ).

fof(f1266,axiom,
    ! [X87] :
      ( class_Rings_Ocomm__semiring__1(X87)
     => class_Power_Opower(tc_Polynomial_Opoly(X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Power_Opower) ).

fof(f7420,plain,
    spl50_287,
    inference(avatar_split_clause,[],[f4271,f7418]) ).

fof(f7418,plain,
    ( spl50_287
  <=> ! [X0] :
        ( class_Rings_Odvd(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Ocomm__semiring__1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_287])]) ).

fof(f4271,plain,
    ! [X0] :
      ( class_Rings_Odvd(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__semiring__1(X0) ),
    inference(cnf_transformation,[],[f2383]) ).

fof(f2383,plain,
    ! [X0] :
      ( class_Rings_Odvd(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__semiring__1(X0) ),
    inference(ennf_transformation,[],[f1412]) ).

fof(f1412,plain,
    ! [X0] :
      ( class_Rings_Ocomm__semiring__1(X0)
     => class_Rings_Odvd(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1271]) ).

fof(f1271,axiom,
    ! [X87] :
      ( class_Rings_Ocomm__semiring__1(X87)
     => class_Rings_Odvd(tc_Polynomial_Opoly(X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Odvd) ).

fof(f7416,plain,
    spl50_286,
    inference(avatar_split_clause,[],[f4270,f7414]) ).

fof(f7414,plain,
    ( spl50_286
  <=> ! [X0] :
        ( class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Ocomm__semiring__1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_286])]) ).

fof(f4270,plain,
    ! [X0] :
      ( class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__semiring__1(X0) ),
    inference(cnf_transformation,[],[f2382]) ).

fof(f2382,plain,
    ! [X0] :
      ( class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__semiring__1(X0) ),
    inference(ennf_transformation,[],[f1411]) ).

fof(f1411,plain,
    ! [X0] :
      ( class_Rings_Ocomm__semiring__1(X0)
     => class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1236]) ).

fof(f1236,axiom,
    ! [X87] :
      ( class_Rings_Ocomm__semiring__1(X87)
     => class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult) ).

fof(f7412,plain,
    spl50_285,
    inference(avatar_split_clause,[],[f4269,f7410]) ).

fof(f7410,plain,
    ( spl50_285
  <=> ! [X0] :
        ( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Ocomm__semiring__1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_285])]) ).

fof(f4269,plain,
    ! [X0] :
      ( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__semiring__1(X0) ),
    inference(cnf_transformation,[],[f2381]) ).

fof(f2381,plain,
    ! [X0] :
      ( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__semiring__1(X0) ),
    inference(ennf_transformation,[],[f1410]) ).

fof(f1410,plain,
    ! [X0] :
      ( class_Rings_Ocomm__semiring__1(X0)
     => class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1247]) ).

fof(f1247,axiom,
    ! [X87] :
      ( class_Rings_Ocomm__semiring__1(X87)
     => class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ozero__neq__one) ).

fof(f7408,plain,
    spl50_284,
    inference(avatar_split_clause,[],[f4268,f7406]) ).

fof(f7406,plain,
    ( spl50_284
  <=> ! [X0] :
        ( class_Groups_Oone(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Ocomm__semiring__1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_284])]) ).

fof(f4268,plain,
    ! [X0] :
      ( class_Groups_Oone(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__semiring__1(X0) ),
    inference(cnf_transformation,[],[f2380]) ).

fof(f2380,plain,
    ! [X0] :
      ( class_Groups_Oone(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__semiring__1(X0) ),
    inference(ennf_transformation,[],[f1409]) ).

fof(f1409,plain,
    ! [X0] :
      ( class_Rings_Ocomm__semiring__1(X0)
     => class_Groups_Oone(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1270]) ).

fof(f1270,axiom,
    ! [X87] :
      ( class_Rings_Ocomm__semiring__1(X87)
     => class_Groups_Oone(tc_Polynomial_Opoly(X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oone) ).

fof(f7404,plain,
    spl50_283,
    inference(avatar_split_clause,[],[f4267,f7402]) ).

fof(f7402,plain,
    ( spl50_283
  <=> ! [X0] :
        ( class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Ocomm__semiring__0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_283])]) ).

fof(f4267,plain,
    ! [X0] :
      ( class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__semiring__0(X0) ),
    inference(cnf_transformation,[],[f2379]) ).

fof(f2379,plain,
    ! [X0] :
      ( class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__semiring__0(X0) ),
    inference(ennf_transformation,[],[f1408]) ).

fof(f1408,plain,
    ! [X0] :
      ( class_Rings_Ocomm__semiring__0(X0)
     => class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1244]) ).

fof(f1244,axiom,
    ! [X87] :
      ( class_Rings_Ocomm__semiring__0(X87)
     => class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__0) ).

fof(f7400,plain,
    spl50_282,
    inference(avatar_split_clause,[],[f4266,f7398]) ).

fof(f7398,plain,
    ( spl50_282
  <=> ! [X0] :
        ( class_Rings_Osemiring__0(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Ocomm__semiring__0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_282])]) ).

fof(f4266,plain,
    ! [X0] :
      ( class_Rings_Osemiring__0(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__semiring__0(X0) ),
    inference(cnf_transformation,[],[f2378]) ).

fof(f2378,plain,
    ! [X0] :
      ( class_Rings_Osemiring__0(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__semiring__0(X0) ),
    inference(ennf_transformation,[],[f1407]) ).

fof(f1407,plain,
    ! [X0] :
      ( class_Rings_Ocomm__semiring__0(X0)
     => class_Rings_Osemiring__0(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1254]) ).

fof(f1254,axiom,
    ! [X87] :
      ( class_Rings_Ocomm__semiring__0(X87)
     => class_Rings_Osemiring__0(tc_Polynomial_Opoly(X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Osemiring__0) ).

fof(f7396,plain,
    spl50_281,
    inference(avatar_split_clause,[],[f4265,f7394]) ).

fof(f7394,plain,
    ( spl50_281
  <=> ! [X0] :
        ( class_Rings_Omult__zero(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Ocomm__semiring__0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_281])]) ).

fof(f4265,plain,
    ! [X0] :
      ( class_Rings_Omult__zero(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__semiring__0(X0) ),
    inference(cnf_transformation,[],[f2377]) ).

fof(f2377,plain,
    ! [X0] :
      ( class_Rings_Omult__zero(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__semiring__0(X0) ),
    inference(ennf_transformation,[],[f1406]) ).

fof(f1406,plain,
    ! [X0] :
      ( class_Rings_Ocomm__semiring__0(X0)
     => class_Rings_Omult__zero(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1256]) ).

fof(f1256,axiom,
    ! [X87] :
      ( class_Rings_Ocomm__semiring__0(X87)
     => class_Rings_Omult__zero(tc_Polynomial_Opoly(X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Omult__zero) ).

fof(f7392,plain,
    spl50_280,
    inference(avatar_split_clause,[],[f4264,f7390]) ).

fof(f7390,plain,
    ( spl50_280
  <=> ! [X0] :
        ( class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Ocomm__semiring__0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_280])]) ).

fof(f4264,plain,
    ! [X0] :
      ( class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__semiring__0(X0) ),
    inference(cnf_transformation,[],[f2376]) ).

fof(f2376,plain,
    ! [X0] :
      ( class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__semiring__0(X0) ),
    inference(ennf_transformation,[],[f1405]) ).

fof(f1405,plain,
    ! [X0] :
      ( class_Rings_Ocomm__semiring__0(X0)
     => class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1245]) ).

fof(f1245,axiom,
    ! [X87] :
      ( class_Rings_Ocomm__semiring__0(X87)
     => class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring) ).

fof(f7388,plain,
    spl50_279,
    inference(avatar_split_clause,[],[f4263,f7386]) ).

fof(f7386,plain,
    ( spl50_279
  <=> ! [X0] :
        ( class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Ocomm__semiring__0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_279])]) ).

fof(f4263,plain,
    ! [X0] :
      ( class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__semiring__0(X0) ),
    inference(cnf_transformation,[],[f2375]) ).

fof(f2375,plain,
    ! [X0] :
      ( class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__semiring__0(X0) ),
    inference(ennf_transformation,[],[f1404]) ).

fof(f1404,plain,
    ! [X0] :
      ( class_Rings_Ocomm__semiring__0(X0)
     => class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1235]) ).

fof(f1235,axiom,
    ! [X87] :
      ( class_Rings_Ocomm__semiring__0(X87)
     => class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__semigroup__mult) ).

fof(f7384,plain,
    spl50_278,
    inference(avatar_split_clause,[],[f4262,f7382]) ).

fof(f7382,plain,
    ( spl50_278
  <=> ! [X0] :
        ( class_Rings_Osemiring(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Ocomm__semiring__0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_278])]) ).

fof(f4262,plain,
    ! [X0] :
      ( class_Rings_Osemiring(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__semiring__0(X0) ),
    inference(cnf_transformation,[],[f2374]) ).

fof(f2374,plain,
    ! [X0] :
      ( class_Rings_Osemiring(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__semiring__0(X0) ),
    inference(ennf_transformation,[],[f1403]) ).

fof(f1403,plain,
    ! [X0] :
      ( class_Rings_Ocomm__semiring__0(X0)
     => class_Rings_Osemiring(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1260]) ).

fof(f1260,axiom,
    ! [X87] :
      ( class_Rings_Ocomm__semiring__0(X87)
     => class_Rings_Osemiring(tc_Polynomial_Opoly(X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Osemiring) ).

fof(f7380,plain,
    spl50_277,
    inference(avatar_split_clause,[],[f4260,f7378]) ).

fof(f7378,plain,
    ( spl50_277
  <=> ! [X0] :
        ( class_Groups_Ozero(tc_Polynomial_Opoly(X0))
        | ~ class_Groups_Ozero(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_277])]) ).

fof(f4260,plain,
    ! [X0] :
      ( class_Groups_Ozero(tc_Polynomial_Opoly(X0))
      | ~ class_Groups_Ozero(X0) ),
    inference(cnf_transformation,[],[f2372]) ).

fof(f2372,plain,
    ! [X0] :
      ( class_Groups_Ozero(tc_Polynomial_Opoly(X0))
      | ~ class_Groups_Ozero(X0) ),
    inference(ennf_transformation,[],[f1401]) ).

fof(f1401,plain,
    ! [X0] :
      ( class_Groups_Ozero(X0)
     => class_Groups_Ozero(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1267]) ).

fof(f1267,axiom,
    ! [X87] :
      ( class_Groups_Ozero(X87)
     => class_Groups_Ozero(tc_Polynomial_Opoly(X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ozero) ).

fof(f7376,plain,
    spl50_276,
    inference(avatar_split_clause,[],[f4259,f7374]) ).

fof(f7374,plain,
    ( spl50_276
  <=> ! [X0] :
        ( class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X0))
        | ~ class_Groups_Ocomm__monoid__add(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_276])]) ).

fof(f4259,plain,
    ! [X0] :
      ( class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X0))
      | ~ class_Groups_Ocomm__monoid__add(X0) ),
    inference(cnf_transformation,[],[f2371]) ).

fof(f2371,plain,
    ! [X0] :
      ( class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X0))
      | ~ class_Groups_Ocomm__monoid__add(X0) ),
    inference(ennf_transformation,[],[f1400]) ).

fof(f1400,plain,
    ! [X0] :
      ( class_Groups_Ocomm__monoid__add(X0)
     => class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1240]) ).

fof(f1240,axiom,
    ! [X87] :
      ( class_Groups_Ocomm__monoid__add(X87)
     => class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocomm__monoid__add) ).

fof(f7372,plain,
    spl50_275,
    inference(avatar_split_clause,[],[f4258,f7370]) ).

fof(f7370,plain,
    ( spl50_275
  <=> ! [X0] :
        ( class_Groups_Omonoid__add(tc_Polynomial_Opoly(X0))
        | ~ class_Groups_Ocomm__monoid__add(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_275])]) ).

fof(f4258,plain,
    ! [X0] :
      ( class_Groups_Omonoid__add(tc_Polynomial_Opoly(X0))
      | ~ class_Groups_Ocomm__monoid__add(X0) ),
    inference(cnf_transformation,[],[f2370]) ).

fof(f2370,plain,
    ! [X0] :
      ( class_Groups_Omonoid__add(tc_Polynomial_Opoly(X0))
      | ~ class_Groups_Ocomm__monoid__add(X0) ),
    inference(ennf_transformation,[],[f1399]) ).

fof(f1399,plain,
    ! [X0] :
      ( class_Groups_Ocomm__monoid__add(X0)
     => class_Groups_Omonoid__add(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1253]) ).

fof(f1253,axiom,
    ! [X87] :
      ( class_Groups_Ocomm__monoid__add(X87)
     => class_Groups_Omonoid__add(tc_Polynomial_Opoly(X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Omonoid__add) ).

fof(f7368,plain,
    spl50_274,
    inference(avatar_split_clause,[],[f4257,f7366]) ).

fof(f7366,plain,
    ( spl50_274
  <=> ! [X0] :
        ( class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X0))
        | ~ class_Groups_Ocomm__monoid__add(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_274])]) ).

fof(f4257,plain,
    ! [X0] :
      ( class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X0))
      | ~ class_Groups_Ocomm__monoid__add(X0) ),
    inference(cnf_transformation,[],[f2369]) ).

fof(f2369,plain,
    ! [X0] :
      ( class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X0))
      | ~ class_Groups_Ocomm__monoid__add(X0) ),
    inference(ennf_transformation,[],[f1398]) ).

fof(f1398,plain,
    ! [X0] :
      ( class_Groups_Ocomm__monoid__add(X0)
     => class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1237]) ).

fof(f1237,axiom,
    ! [X87] :
      ( class_Groups_Ocomm__monoid__add(X87)
     => class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__semigroup__add) ).

fof(f7364,plain,
    spl50_273,
    inference(avatar_split_clause,[],[f4253,f7362]) ).

fof(f7362,plain,
    ( spl50_273
  <=> ! [X0] :
        ( class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X0))
        | ~ class_Groups_Ocancel__comm__monoid__add(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_273])]) ).

fof(f4253,plain,
    ! [X0] :
      ( class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X0))
      | ~ class_Groups_Ocancel__comm__monoid__add(X0) ),
    inference(cnf_transformation,[],[f2365]) ).

fof(f2365,plain,
    ! [X0] :
      ( class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X0))
      | ~ class_Groups_Ocancel__comm__monoid__add(X0) ),
    inference(ennf_transformation,[],[f1394]) ).

fof(f1394,plain,
    ! [X0] :
      ( class_Groups_Ocancel__comm__monoid__add(X0)
     => class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1232]) ).

fof(f1232,axiom,
    ! [X87] :
      ( class_Groups_Ocancel__comm__monoid__add(X87)
     => class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add) ).

fof(f7360,plain,
    spl50_272,
    inference(avatar_split_clause,[],[f4252,f7358]) ).

fof(f7358,plain,
    ( spl50_272
  <=> ! [X0] :
        ( class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X0))
        | ~ class_Groups_Ocancel__comm__monoid__add(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_272])]) ).

fof(f4252,plain,
    ! [X0] :
      ( class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X0))
      | ~ class_Groups_Ocancel__comm__monoid__add(X0) ),
    inference(cnf_transformation,[],[f2364]) ).

fof(f2364,plain,
    ! [X0] :
      ( class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X0))
      | ~ class_Groups_Ocancel__comm__monoid__add(X0) ),
    inference(ennf_transformation,[],[f1393]) ).

fof(f1393,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,
    ! [X87] :
      ( class_Groups_Ocancel__comm__monoid__add(X87)
     => class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add) ).

fof(f7356,plain,
    spl50_271,
    inference(avatar_split_clause,[],[f4251,f7354]) ).

fof(f7354,plain,
    ( spl50_271
  <=> ! [X0] :
        ( class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X0))
        | ~ class_Groups_Ocancel__comm__monoid__add(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_271])]) ).

fof(f4251,plain,
    ! [X0] :
      ( class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X0))
      | ~ class_Groups_Ocancel__comm__monoid__add(X0) ),
    inference(cnf_transformation,[],[f2363]) ).

fof(f2363,plain,
    ! [X0] :
      ( class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X0))
      | ~ class_Groups_Ocancel__comm__monoid__add(X0) ),
    inference(ennf_transformation,[],[f1392]) ).

fof(f1392,plain,
    ! [X0] :
      ( class_Groups_Ocancel__comm__monoid__add(X0)
     => class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1224]) ).

fof(f1224,axiom,
    ! [X87] :
      ( class_Groups_Ocancel__comm__monoid__add(X87)
     => class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add) ).

fof(f7352,plain,
    spl50_270,
    inference(avatar_split_clause,[],[f4243,f7350]) ).

fof(f7350,plain,
    ( spl50_270
  <=> ! [X0] :
        ( class_Groups_Ominus(tc_Polynomial_Opoly(X0))
        | ~ class_Groups_Oab__group__add(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_270])]) ).

fof(f4243,plain,
    ! [X0] :
      ( class_Groups_Ominus(tc_Polynomial_Opoly(X0))
      | ~ class_Groups_Oab__group__add(X0) ),
    inference(cnf_transformation,[],[f2355]) ).

fof(f2355,plain,
    ! [X0] :
      ( class_Groups_Ominus(tc_Polynomial_Opoly(X0))
      | ~ class_Groups_Oab__group__add(X0) ),
    inference(ennf_transformation,[],[f1384]) ).

fof(f1384,plain,
    ! [X0] :
      ( class_Groups_Oab__group__add(X0)
     => class_Groups_Ominus(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1265]) ).

fof(f1265,axiom,
    ! [X87] :
      ( class_Groups_Oab__group__add(X87)
     => class_Groups_Ominus(tc_Polynomial_Opoly(X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ominus) ).

fof(f7348,plain,
    spl50_269,
    inference(avatar_split_clause,[],[f4242,f7346]) ).

fof(f7346,plain,
    ( spl50_269
  <=> ! [X0] :
        ( class_Groups_Ouminus(tc_Polynomial_Opoly(X0))
        | ~ class_Groups_Oab__group__add(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_269])]) ).

fof(f4242,plain,
    ! [X0] :
      ( class_Groups_Ouminus(tc_Polynomial_Opoly(X0))
      | ~ class_Groups_Oab__group__add(X0) ),
    inference(cnf_transformation,[],[f2354]) ).

fof(f2354,plain,
    ! [X0] :
      ( class_Groups_Ouminus(tc_Polynomial_Opoly(X0))
      | ~ class_Groups_Oab__group__add(X0) ),
    inference(ennf_transformation,[],[f1383]) ).

fof(f1383,plain,
    ! [X0] :
      ( class_Groups_Oab__group__add(X0)
     => class_Groups_Ouminus(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1262]) ).

fof(f1262,axiom,
    ! [X87] :
      ( class_Groups_Oab__group__add(X87)
     => class_Groups_Ouminus(tc_Polynomial_Opoly(X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ouminus) ).

fof(f7344,plain,
    spl50_268,
    inference(avatar_split_clause,[],[f4241,f7342]) ).

fof(f7342,plain,
    ( spl50_268
  <=> ! [X0] :
        ( class_Groups_Ogroup__add(tc_Polynomial_Opoly(X0))
        | ~ class_Groups_Oab__group__add(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_268])]) ).

fof(f4241,plain,
    ! [X0] :
      ( class_Groups_Ogroup__add(tc_Polynomial_Opoly(X0))
      | ~ class_Groups_Oab__group__add(X0) ),
    inference(cnf_transformation,[],[f2353]) ).

fof(f2353,plain,
    ! [X0] :
      ( class_Groups_Ogroup__add(tc_Polynomial_Opoly(X0))
      | ~ class_Groups_Oab__group__add(X0) ),
    inference(ennf_transformation,[],[f1382]) ).

fof(f1382,plain,
    ! [X0] :
      ( class_Groups_Oab__group__add(X0)
     => class_Groups_Ogroup__add(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1255]) ).

fof(f1255,axiom,
    ! [X87] :
      ( class_Groups_Oab__group__add(X87)
     => class_Groups_Ogroup__add(tc_Polynomial_Opoly(X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ogroup__add) ).

fof(f7340,plain,
    spl50_267,
    inference(avatar_split_clause,[],[f4240,f7338]) ).

fof(f7338,plain,
    ( spl50_267
  <=> ! [X0] :
        ( class_Groups_Oab__group__add(tc_Polynomial_Opoly(X0))
        | ~ class_Groups_Oab__group__add(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_267])]) ).

fof(f4240,plain,
    ! [X0] :
      ( class_Groups_Oab__group__add(tc_Polynomial_Opoly(X0))
      | ~ class_Groups_Oab__group__add(X0) ),
    inference(cnf_transformation,[],[f2352]) ).

fof(f2352,plain,
    ! [X0] :
      ( class_Groups_Oab__group__add(tc_Polynomial_Opoly(X0))
      | ~ class_Groups_Oab__group__add(X0) ),
    inference(ennf_transformation,[],[f1381]) ).

fof(f1381,plain,
    ! [X0] :
      ( class_Groups_Oab__group__add(X0)
     => class_Groups_Oab__group__add(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1246]) ).

fof(f1246,axiom,
    ! [X87] :
      ( class_Groups_Oab__group__add(X87)
     => class_Groups_Oab__group__add(tc_Polynomial_Opoly(X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__group__add) ).

fof(f7336,plain,
    spl50_266,
    inference(avatar_split_clause,[],[f4239,f7334]) ).

fof(f7334,plain,
    ( spl50_266
  <=> ! [X0] :
        ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Oidom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_266])]) ).

fof(f4239,plain,
    ! [X0] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Oidom(X0) ),
    inference(cnf_transformation,[],[f2351]) ).

fof(f2351,plain,
    ! [X0] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Oidom(X0) ),
    inference(ennf_transformation,[],[f1380]) ).

fof(f1380,plain,
    ! [X0] :
      ( class_Rings_Oidom(X0)
     => class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1215]) ).

fof(f1215,axiom,
    ! [X87] :
      ( class_Rings_Oidom(X87)
     => class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).

fof(f7332,plain,
    spl50_265,
    inference(avatar_split_clause,[],[f4238,f7330]) ).

fof(f7330,plain,
    ( spl50_265
  <=> ! [X0] :
        ( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Oidom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_265])]) ).

fof(f4238,plain,
    ! [X0] :
      ( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Oidom(X0) ),
    inference(cnf_transformation,[],[f2350]) ).

fof(f2350,plain,
    ! [X0] :
      ( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Oidom(X0) ),
    inference(ennf_transformation,[],[f1379]) ).

fof(f1379,plain,
    ! [X0] :
      ( class_Rings_Oidom(X0)
     => class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1239]) ).

fof(f1239,axiom,
    ! [X87] :
      ( class_Rings_Oidom(X87)
     => class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ono__zero__divisors) ).

fof(f7328,plain,
    spl50_264,
    inference(avatar_split_clause,[],[f4237,f7326]) ).

fof(f7326,plain,
    ( spl50_264
  <=> ! [X0] :
        ( class_Rings_Oidom(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Oidom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_264])]) ).

fof(f4237,plain,
    ! [X0] :
      ( class_Rings_Oidom(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Oidom(X0) ),
    inference(cnf_transformation,[],[f2349]) ).

fof(f2349,plain,
    ! [X0] :
      ( class_Rings_Oidom(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Oidom(X0) ),
    inference(ennf_transformation,[],[f1378]) ).

fof(f1378,plain,
    ! [X0] :
      ( class_Rings_Oidom(X0)
     => class_Rings_Oidom(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1269]) ).

fof(f1269,axiom,
    ! [X87] :
      ( class_Rings_Oidom(X87)
     => class_Rings_Oidom(tc_Polynomial_Opoly(X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oidom) ).

fof(f7324,plain,
    spl50_263,
    inference(avatar_split_clause,[],[f4236,f7322]) ).

fof(f7322,plain,
    ( spl50_263
  <=> ! [X0] :
        ( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Oidom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_263])]) ).

fof(f4236,plain,
    ! [X0] :
      ( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Oidom(X0) ),
    inference(cnf_transformation,[],[f2348]) ).

fof(f2348,plain,
    ! [X0] :
      ( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Oidom(X0) ),
    inference(ennf_transformation,[],[f1377]) ).

fof(f1377,plain,
    ! [X0] :
      ( class_Rings_Oidom(X0)
     => class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1225]) ).

fof(f1225,axiom,
    ! [X87] :
      ( class_Rings_Oidom(X87)
     => class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors) ).

fof(f7320,plain,
    spl50_262,
    inference(avatar_split_clause,[],[f4235,f7318]) ).

fof(f7318,plain,
    ( spl50_262
  <=> ! [X0] :
        ( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Oidom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_262])]) ).

fof(f4235,plain,
    ! [X0] :
      ( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Oidom(X0) ),
    inference(cnf_transformation,[],[f2347]) ).

fof(f2347,plain,
    ! [X0] :
      ( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Oidom(X0) ),
    inference(ennf_transformation,[],[f1376]) ).

fof(f1376,plain,
    ! [X0] :
      ( class_Rings_Oidom(X0)
     => class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1228]) ).

fof(f1228,axiom,
    ! [X87] :
      ( class_Rings_Oidom(X87)
     => class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors) ).

fof(f7316,plain,
    spl50_261,
    inference(avatar_split_clause,[],[f4234,f7314]) ).

fof(f7314,plain,
    ( spl50_261
  <=> ! [X0] :
        ( class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Ocomm__ring(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_261])]) ).

fof(f4234,plain,
    ! [X0] :
      ( class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__ring(X0) ),
    inference(cnf_transformation,[],[f2346]) ).

fof(f2346,plain,
    ! [X0] :
      ( class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__ring(X0) ),
    inference(ennf_transformation,[],[f1375]) ).

fof(f1375,plain,
    ! [X0] :
      ( class_Rings_Ocomm__ring(X0)
     => class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1257]) ).

fof(f1257,axiom,
    ! [X87] :
      ( class_Rings_Ocomm__ring(X87)
     => class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__ring) ).

fof(f7312,plain,
    spl50_260,
    inference(avatar_split_clause,[],[f4233,f7310]) ).

fof(f7310,plain,
    ( spl50_260
  <=> ! [X0] :
        ( class_Rings_Oring(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Ocomm__ring(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_260])]) ).

fof(f4233,plain,
    ! [X0] :
      ( class_Rings_Oring(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__ring(X0) ),
    inference(cnf_transformation,[],[f2345]) ).

fof(f2345,plain,
    ! [X0] :
      ( class_Rings_Oring(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__ring(X0) ),
    inference(ennf_transformation,[],[f1374]) ).

fof(f1374,plain,
    ! [X0] :
      ( class_Rings_Ocomm__ring(X0)
     => class_Rings_Oring(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1268]) ).

fof(f1268,axiom,
    ! [X87] :
      ( class_Rings_Ocomm__ring(X87)
     => class_Rings_Oring(tc_Polynomial_Opoly(X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring) ).

fof(f7308,plain,
    spl50_259,
    inference(avatar_split_clause,[],[f4232,f7306]) ).

fof(f7306,plain,
    ( spl50_259
  <=> ! [X0] :
        ( class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Ocomm__ring__1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_259])]) ).

fof(f4232,plain,
    ! [X0] :
      ( class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__ring__1(X0) ),
    inference(cnf_transformation,[],[f2344]) ).

fof(f2344,plain,
    ! [X0] :
      ( class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__ring__1(X0) ),
    inference(ennf_transformation,[],[f1373]) ).

fof(f1373,plain,
    ! [X0] :
      ( class_Rings_Ocomm__ring__1(X0)
     => class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1252]) ).

fof(f1252,axiom,
    ! [X87] :
      ( class_Rings_Ocomm__ring__1(X87)
     => class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__ring__1) ).

fof(f7304,plain,
    spl50_258,
    inference(avatar_split_clause,[],[f4231,f7302]) ).

fof(f7302,plain,
    ( spl50_258
  <=> ! [X0] :
        ( class_Rings_Oring__1(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Ocomm__ring__1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_258])]) ).

fof(f4231,plain,
    ! [X0] :
      ( class_Rings_Oring__1(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__ring__1(X0) ),
    inference(cnf_transformation,[],[f2343]) ).

fof(f2343,plain,
    ! [X0] :
      ( class_Rings_Oring__1(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__ring__1(X0) ),
    inference(ennf_transformation,[],[f1372]) ).

fof(f1372,plain,
    ! [X0] :
      ( class_Rings_Ocomm__ring__1(X0)
     => class_Rings_Oring__1(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1264]) ).

fof(f1264,axiom,
    ! [X87] :
      ( class_Rings_Ocomm__ring__1(X87)
     => class_Rings_Oring__1(tc_Polynomial_Opoly(X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__1) ).

fof(f7300,plain,
    spl50_257,
    inference(avatar_split_clause,[],[f4229,f7298]) ).

fof(f7298,plain,
    ( spl50_257
  <=> ! [X0] :
        ( class_Orderings_Oorder(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Olinordered__idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_257])]) ).

fof(f4229,plain,
    ! [X0] :
      ( class_Orderings_Oorder(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(cnf_transformation,[],[f2341]) ).

fof(f2341,plain,
    ! [X0] :
      ( class_Orderings_Oorder(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(ennf_transformation,[],[f1370]) ).

fof(f1370,plain,
    ! [X0] :
      ( class_Rings_Olinordered__idom(X0)
     => class_Orderings_Oorder(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1258]) ).

fof(f1258,axiom,
    ! [X87] :
      ( class_Rings_Olinordered__idom(X87)
     => class_Orderings_Oorder(tc_Polynomial_Opoly(X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Oorder) ).

fof(f7296,plain,
    spl50_256,
    inference(avatar_split_clause,[],[f4228,f7294]) ).

fof(f7294,plain,
    ( spl50_256
  <=> ! [X0] :
        ( class_Orderings_Opreorder(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Olinordered__idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_256])]) ).

fof(f4228,plain,
    ! [X0] :
      ( class_Orderings_Opreorder(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(cnf_transformation,[],[f2340]) ).

fof(f2340,plain,
    ! [X0] :
      ( class_Orderings_Opreorder(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(ennf_transformation,[],[f1369]) ).

fof(f1369,plain,
    ! [X0] :
      ( class_Rings_Olinordered__idom(X0)
     => class_Orderings_Opreorder(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1249]) ).

fof(f1249,axiom,
    ! [X87] :
      ( class_Rings_Olinordered__idom(X87)
     => class_Orderings_Opreorder(tc_Polynomial_Opoly(X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Opreorder) ).

fof(f7292,plain,
    spl50_255,
    inference(avatar_split_clause,[],[f4227,f7290]) ).

fof(f7290,plain,
    ( spl50_255
  <=> ! [X0] :
        ( class_Orderings_Oord(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Olinordered__idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_255])]) ).

fof(f4227,plain,
    ! [X0] :
      ( class_Orderings_Oord(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(cnf_transformation,[],[f2339]) ).

fof(f2339,plain,
    ! [X0] :
      ( class_Orderings_Oord(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(ennf_transformation,[],[f1368]) ).

fof(f1368,plain,
    ! [X0] :
      ( class_Rings_Olinordered__idom(X0)
     => class_Orderings_Oord(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1261]) ).

fof(f1261,axiom,
    ! [X87] :
      ( class_Rings_Olinordered__idom(X87)
     => class_Orderings_Oord(tc_Polynomial_Opoly(X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Oord) ).

fof(f7288,plain,
    spl50_254,
    inference(avatar_split_clause,[],[f4226,f7286]) ).

fof(f7286,plain,
    ( spl50_254
  <=> ! [X0] :
        ( class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Olinordered__idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_254])]) ).

fof(f4226,plain,
    ! [X0] :
      ( class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(cnf_transformation,[],[f2338]) ).

fof(f2338,plain,
    ! [X0] :
      ( class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(ennf_transformation,[],[f1367]) ).

fof(f1367,plain,
    ! [X0] :
      ( class_Rings_Olinordered__idom(X0)
     => class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1234]) ).

fof(f1234,axiom,
    ! [X87] :
      ( class_Rings_Olinordered__idom(X87)
     => class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semidom) ).

fof(f7284,plain,
    spl50_253,
    inference(avatar_split_clause,[],[f4225,f7282]) ).

fof(f7282,plain,
    ( spl50_253
  <=> ! [X0] :
        ( class_Orderings_Olinorder(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Olinordered__idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_253])]) ).

fof(f4225,plain,
    ! [X0] :
      ( class_Orderings_Olinorder(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(cnf_transformation,[],[f2337]) ).

fof(f2337,plain,
    ! [X0] :
      ( class_Orderings_Olinorder(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(ennf_transformation,[],[f1366]) ).

fof(f1366,plain,
    ! [X0] :
      ( class_Rings_Olinordered__idom(X0)
     => class_Orderings_Olinorder(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1250]) ).

fof(f1250,axiom,
    ! [X87] :
      ( class_Rings_Olinordered__idom(X87)
     => class_Orderings_Olinorder(tc_Polynomial_Opoly(X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Olinorder) ).

fof(f7280,plain,
    spl50_252,
    inference(avatar_split_clause,[],[f4224,f7278]) ).

fof(f7278,plain,
    ( spl50_252
  <=> ! [X0] :
        ( class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Olinordered__idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_252])]) ).

fof(f4224,plain,
    ! [X0] :
      ( class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(cnf_transformation,[],[f2336]) ).

fof(f2336,plain,
    ! [X0] :
      ( class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(ennf_transformation,[],[f1365]) ).

fof(f1365,plain,
    ! [X0] :
      ( class_Rings_Olinordered__idom(X0)
     => class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1220]) ).

fof(f1220,axiom,
    ! [X87] :
      ( class_Rings_Olinordered__idom(X87)
     => class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict) ).

fof(f7276,plain,
    spl50_251,
    inference(avatar_split_clause,[],[f4223,f7274]) ).

fof(f7274,plain,
    ( spl50_251
  <=> ! [X0] :
        ( class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Olinordered__idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_251])]) ).

fof(f4223,plain,
    ! [X0] :
      ( class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(cnf_transformation,[],[f2335]) ).

fof(f2335,plain,
    ! [X0] :
      ( class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(ennf_transformation,[],[f1364]) ).

fof(f1364,plain,
    ! [X0] :
      ( class_Rings_Olinordered__idom(X0)
     => class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1222]) ).

fof(f1222,axiom,
    ! [X87] :
      ( class_Rings_Olinordered__idom(X87)
     => class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add) ).

fof(f7272,plain,
    spl50_250,
    inference(avatar_split_clause,[],[f4222,f7270]) ).

fof(f7270,plain,
    ( spl50_250
  <=> ! [X0] :
        ( class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Olinordered__idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_250])]) ).

fof(f4222,plain,
    ! [X0] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(cnf_transformation,[],[f2334]) ).

fof(f2334,plain,
    ! [X0] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(ennf_transformation,[],[f1363]) ).

fof(f1363,plain,
    ! [X0] :
      ( class_Rings_Olinordered__idom(X0)
     => class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1217]) ).

fof(f1217,axiom,
    ! [X87] :
      ( class_Rings_Olinordered__idom(X87)
     => class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le) ).

fof(f7268,plain,
    spl50_249,
    inference(avatar_split_clause,[],[f4221,f7266]) ).

fof(f7266,plain,
    ( spl50_249
  <=> ! [X0] :
        ( class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Olinordered__idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_249])]) ).

fof(f4221,plain,
    ! [X0] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(cnf_transformation,[],[f2333]) ).

fof(f2333,plain,
    ! [X0] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(ennf_transformation,[],[f1362]) ).

fof(f1362,plain,
    ! [X0] :
      ( class_Rings_Olinordered__idom(X0)
     => class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1216]) ).

fof(f1216,axiom,
    ! [X87] :
      ( class_Rings_Olinordered__idom(X87)
     => class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add) ).

fof(f7264,plain,
    spl50_248,
    inference(avatar_split_clause,[],[f4220,f7262]) ).

fof(f7262,plain,
    ( spl50_248
  <=> ! [X0] :
        ( class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Olinordered__idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_248])]) ).

fof(f4220,plain,
    ! [X0] :
      ( class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(cnf_transformation,[],[f2332]) ).

fof(f2332,plain,
    ! [X0] :
      ( class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(ennf_transformation,[],[f1361]) ).

fof(f1361,plain,
    ! [X0] :
      ( class_Rings_Olinordered__idom(X0)
     => class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1226]) ).

fof(f1226,axiom,
    ! [X87] :
      ( class_Rings_Olinordered__idom(X87)
     => class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring) ).

fof(f7260,plain,
    spl50_247,
    inference(avatar_split_clause,[],[f4219,f7258]) ).

fof(f7258,plain,
    ( spl50_247
  <=> ! [X0] :
        ( class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Olinordered__idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_247])]) ).

fof(f4219,plain,
    ! [X0] :
      ( class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(cnf_transformation,[],[f2331]) ).

fof(f2331,plain,
    ! [X0] :
      ( class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(ennf_transformation,[],[f1360]) ).

fof(f1360,plain,
    ! [X0] :
      ( class_Rings_Olinordered__idom(X0)
     => class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1238]) ).

fof(f1238,axiom,
    ! [X87] :
      ( class_Rings_Olinordered__idom(X87)
     => class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__semiring) ).

fof(f7256,plain,
    spl50_246,
    inference(avatar_split_clause,[],[f4218,f7254]) ).

fof(f7254,plain,
    ( spl50_246
  <=> ! [X0] :
        ( class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Olinordered__idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_246])]) ).

fof(f4218,plain,
    ! [X0] :
      ( class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(cnf_transformation,[],[f2330]) ).

fof(f2330,plain,
    ! [X0] :
      ( class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(ennf_transformation,[],[f1359]) ).

fof(f1359,plain,
    ! [X0] :
      ( class_Rings_Olinordered__idom(X0)
     => class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1221]) ).

fof(f1221,axiom,
    ! [X87] :
      ( class_Rings_Olinordered__idom(X87)
     => class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add) ).

fof(f7252,plain,
    spl50_245,
    inference(avatar_split_clause,[],[f4217,f7250]) ).

fof(f7250,plain,
    ( spl50_245
  <=> ! [X0] :
        ( class_Int_Oring__char__0(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Olinordered__idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_245])]) ).

fof(f4217,plain,
    ! [X0] :
      ( class_Int_Oring__char__0(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(cnf_transformation,[],[f2329]) ).

fof(f2329,plain,
    ! [X0] :
      ( class_Int_Oring__char__0(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(ennf_transformation,[],[f1358]) ).

fof(f1358,plain,
    ! [X0] :
      ( class_Rings_Olinordered__idom(X0)
     => class_Int_Oring__char__0(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1259]) ).

fof(f1259,axiom,
    ! [X87] :
      ( class_Rings_Olinordered__idom(X87)
     => class_Int_Oring__char__0(tc_Polynomial_Opoly(X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Int_Oring__char__0) ).

fof(f7248,plain,
    spl50_244,
    inference(avatar_split_clause,[],[f4216,f7246]) ).

fof(f7246,plain,
    ( spl50_244
  <=> ! [X0] :
        ( class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Olinordered__idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_244])]) ).

fof(f4216,plain,
    ! [X0] :
      ( class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(cnf_transformation,[],[f2328]) ).

fof(f2328,plain,
    ! [X0] :
      ( class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(ennf_transformation,[],[f1357]) ).

fof(f1357,plain,
    ! [X0] :
      ( class_Rings_Olinordered__idom(X0)
     => class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1233]) ).

fof(f1233,axiom,
    ! [X87] :
      ( class_Rings_Olinordered__idom(X87)
     => class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring) ).

fof(f7244,plain,
    spl50_243,
    inference(avatar_split_clause,[],[f4215,f7242]) ).

fof(f7242,plain,
    ( spl50_243
  <=> ! [X0] :
        ( class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Olinordered__idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_243])]) ).

fof(f4215,plain,
    ! [X0] :
      ( class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(cnf_transformation,[],[f2327]) ).

fof(f2327,plain,
    ! [X0] :
      ( class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(ennf_transformation,[],[f1356]) ).

fof(f1356,plain,
    ! [X0] :
      ( class_Rings_Olinordered__idom(X0)
     => class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1218]) ).

fof(f1218,axiom,
    ! [X87] :
      ( class_Rings_Olinordered__idom(X87)
     => class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict) ).

fof(f7240,plain,
    spl50_242,
    inference(avatar_split_clause,[],[f4214,f7238]) ).

fof(f7238,plain,
    ( spl50_242
  <=> ! [X0] :
        ( class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Olinordered__idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_242])]) ).

fof(f4214,plain,
    ! [X0] :
      ( class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(cnf_transformation,[],[f2326]) ).

fof(f2326,plain,
    ! [X0] :
      ( class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(ennf_transformation,[],[f1355]) ).

fof(f1355,plain,
    ! [X0] :
      ( class_Rings_Olinordered__idom(X0)
     => class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1229]) ).

fof(f1229,axiom,
    ! [X87] :
      ( class_Rings_Olinordered__idom(X87)
     => class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__comm__semiring) ).

fof(f7236,plain,
    spl50_241,
    inference(avatar_split_clause,[],[f4213,f7234]) ).

fof(f7234,plain,
    ( spl50_241
  <=> ! [X0] :
        ( class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Olinordered__idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_241])]) ).

fof(f4213,plain,
    ! [X0] :
      ( class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(cnf_transformation,[],[f2325]) ).

fof(f2325,plain,
    ! [X0] :
      ( class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(ennf_transformation,[],[f1354]) ).

fof(f1354,plain,
    ! [X0] :
      ( class_Rings_Olinordered__idom(X0)
     => class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1242]) ).

fof(f1242,axiom,
    ! [X87] :
      ( class_Rings_Olinordered__idom(X87)
     => class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__idom) ).

fof(f7232,plain,
    spl50_240,
    inference(avatar_split_clause,[],[f4212,f7230]) ).

fof(f7230,plain,
    ( spl50_240
  <=> ! [X0] :
        ( class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Olinordered__idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_240])]) ).

fof(f4212,plain,
    ! [X0] :
      ( class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(cnf_transformation,[],[f2324]) ).

fof(f2324,plain,
    ! [X0] :
      ( class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(ennf_transformation,[],[f1353]) ).

fof(f1353,plain,
    ! [X0] :
      ( class_Rings_Olinordered__idom(X0)
     => class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1231]) ).

fof(f1231,axiom,
    ! [X87] :
      ( class_Rings_Olinordered__idom(X87)
     => class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__group__add) ).

fof(f7228,plain,
    spl50_239,
    inference(avatar_split_clause,[],[f4211,f7226]) ).

fof(f7226,plain,
    ( spl50_239
  <=> ! [X0] :
        ( class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Olinordered__idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_239])]) ).

fof(f4211,plain,
    ! [X0] :
      ( class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(cnf_transformation,[],[f2323]) ).

fof(f2323,plain,
    ! [X0] :
      ( class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(ennf_transformation,[],[f1352]) ).

fof(f1352,plain,
    ! [X0] :
      ( class_Rings_Olinordered__idom(X0)
     => class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1227]) ).

fof(f1227,axiom,
    ! [X87] :
      ( class_Rings_Olinordered__idom(X87)
     => class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__ring__strict) ).

fof(f7224,plain,
    spl50_238,
    inference(avatar_split_clause,[],[f4210,f7222]) ).

fof(f7222,plain,
    ( spl50_238
  <=> ! [X0] :
        ( class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Olinordered__idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_238])]) ).

fof(f4210,plain,
    ! [X0] :
      ( class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(cnf_transformation,[],[f2322]) ).

fof(f2322,plain,
    ! [X0] :
      ( class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(ennf_transformation,[],[f1351]) ).

fof(f1351,plain,
    ! [X0] :
      ( class_Rings_Olinordered__idom(X0)
     => class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1223]) ).

fof(f1223,axiom,
    ! [X87] :
      ( class_Rings_Olinordered__idom(X87)
     => class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add) ).

fof(f7220,plain,
    spl50_237,
    inference(avatar_split_clause,[],[f4209,f7218]) ).

fof(f7218,plain,
    ( spl50_237
  <=> ! [X0] :
        ( class_Rings_Oordered__ring(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Olinordered__idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_237])]) ).

fof(f4209,plain,
    ! [X0] :
      ( class_Rings_Oordered__ring(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(cnf_transformation,[],[f2321]) ).

fof(f2321,plain,
    ! [X0] :
      ( class_Rings_Oordered__ring(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(ennf_transformation,[],[f1350]) ).

fof(f1350,plain,
    ! [X0] :
      ( class_Rings_Olinordered__idom(X0)
     => class_Rings_Oordered__ring(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1248]) ).

fof(f1248,axiom,
    ! [X87] :
      ( class_Rings_Olinordered__idom(X87)
     => class_Rings_Oordered__ring(tc_Polynomial_Opoly(X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__ring) ).

fof(f7216,plain,
    spl50_236,
    inference(avatar_split_clause,[],[f4208,f7214]) ).

fof(f7214,plain,
    ( spl50_236
  <=> ! [X0] :
        ( class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Olinordered__idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_236])]) ).

fof(f4208,plain,
    ! [X0] :
      ( class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(cnf_transformation,[],[f2320]) ).

fof(f2320,plain,
    ! [X0] :
      ( class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(ennf_transformation,[],[f1349]) ).

fof(f1349,plain,
    ! [X0] :
      ( class_Rings_Olinordered__idom(X0)
     => class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1241]) ).

fof(f1241,axiom,
    ! [X87] :
      ( class_Rings_Olinordered__idom(X87)
     => class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__ring) ).

fof(f7212,plain,
    spl50_235,
    inference(avatar_split_clause,[],[f4207,f7210]) ).

fof(f7210,plain,
    ( spl50_235
  <=> ! [X0] :
        ( class_Groups_Osgn__if(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Olinordered__idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_235])]) ).

fof(f4207,plain,
    ! [X0] :
      ( class_Groups_Osgn__if(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(cnf_transformation,[],[f2319]) ).

fof(f2319,plain,
    ! [X0] :
      ( class_Groups_Osgn__if(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(ennf_transformation,[],[f1348]) ).

fof(f1348,plain,
    ! [X0] :
      ( class_Rings_Olinordered__idom(X0)
     => class_Groups_Osgn__if(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1263]) ).

fof(f1263,axiom,
    ! [X87] :
      ( class_Rings_Olinordered__idom(X87)
     => class_Groups_Osgn__if(tc_Polynomial_Opoly(X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Osgn__if) ).

fof(f7208,plain,
    spl50_234,
    inference(avatar_split_clause,[],[f4206,f7206]) ).

fof(f7206,plain,
    ( spl50_234
  <=> ! [X0] :
        ( class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Olinordered__idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_234])]) ).

fof(f4206,plain,
    ! [X0] :
      ( class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(cnf_transformation,[],[f2318]) ).

fof(f2318,plain,
    ! [X0] :
      ( class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(ennf_transformation,[],[f1347]) ).

fof(f1347,plain,
    ! [X0] :
      ( class_Rings_Olinordered__idom(X0)
     => class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1219]) ).

fof(f1219,axiom,
    ! [X87] :
      ( class_Rings_Olinordered__idom(X87)
     => class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict) ).

fof(f7204,plain,
    spl50_233,
    inference(avatar_split_clause,[],[f4205,f7202]) ).

fof(f7202,plain,
    ( spl50_233
  <=> ! [X0] :
        ( class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X0))
        | ~ class_Rings_Olinordered__idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_233])]) ).

fof(f4205,plain,
    ! [X0] :
      ( class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(cnf_transformation,[],[f2317]) ).

fof(f2317,plain,
    ! [X0] :
      ( class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(ennf_transformation,[],[f1346]) ).

fof(f1346,plain,
    ! [X0] :
      ( class_Rings_Olinordered__idom(X0)
     => class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1230]) ).

fof(f1230,axiom,
    ! [X87] :
      ( class_Rings_Olinordered__idom(X87)
     => class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__1) ).

fof(f7200,plain,
    spl50_232,
    inference(avatar_split_clause,[],[f4151,f7198]) ).

fof(f7198,plain,
    ( spl50_232
  <=> ! [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,[spl50_232])]) ).

fof(f4151,plain,
    ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0),
    inference(cnf_transformation,[],[f1299]) ).

fof(f1299,plain,
    ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0),
    inference(rectify,[],[f266]) ).

fof(f266,axiom,
    ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le0) ).

fof(f7196,plain,
    spl50_231,
    inference(avatar_split_clause,[],[f4147,f7194]) ).

fof(f4147,plain,
    ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(cnf_transformation,[],[f1295]) ).

fof(f1295,plain,
    ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(rectify,[],[f267]) ).

fof(f267,axiom,
    ! [X3] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__zeroE) ).

fof(f7192,plain,
    spl50_230,
    inference(avatar_split_clause,[],[f4128,f7189]) ).

fof(f4128,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK18),
    inference(cnf_transformation,[],[f3471]) ).

fof(f7187,plain,
    spl50_229,
    inference(avatar_split_clause,[],[f4095,f7184]) ).

fof(f4095,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____),
    inference(cnf_transformation,[],[f2]) ).

fof(f2,axiom,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_m_I1_J) ).

fof(f7182,plain,
    ~ spl50_228,
    inference(avatar_split_clause,[],[f4094,f7179]) ).

fof(f7179,plain,
    ( spl50_228
  <=> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_228])]) ).

fof(f4094,plain,
    c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f207]) ).

fof(f207,axiom,
    c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__zero__not__eq__one) ).

fof(f7177,plain,
    ~ spl50_227,
    inference(avatar_split_clause,[],[f4093,f7174]) ).

fof(f7174,plain,
    ( spl50_227
  <=> c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_227])]) ).

fof(f4093,plain,
    c_Groups_Oone__class_Oone(tc_Int_Oint) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(cnf_transformation,[],[f593]) ).

fof(f593,axiom,
    c_Groups_Oone__class_Oone(tc_Int_Oint) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__0__neq__1) ).

fof(f7172,plain,
    spl50_226,
    inference(avatar_split_clause,[],[f5755,f7170]) ).

fof(f7170,plain,
    ( spl50_226
  <=> ! [X1] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_226])]) ).

fof(f5755,plain,
    ! [X1] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X1),
    inference(equality_resolution,[],[f4667]) ).

fof(f4667,plain,
    ! [X0,X1] :
      ( X0 != X1
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
    inference(cnf_transformation,[],[f3587]) ).

fof(f7168,plain,
    spl50_225,
    inference(avatar_split_clause,[],[f5754,f7166]) ).

fof(f7166,plain,
    ( spl50_225
  <=> ! [X1] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_225])]) ).

fof(f5754,plain,
    ! [X1] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X1),
    inference(equality_resolution,[],[f4662]) ).

fof(f4662,plain,
    ! [X0,X1] :
      ( X0 != X1
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) ),
    inference(cnf_transformation,[],[f3584]) ).

fof(f3584,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
        | X0 = X1
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) )
      & ( ( X0 != X1
          & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) )
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) ) ),
    inference(flattening,[],[f3583]) ).

fof(f3583,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
        | X0 = X1
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) )
      & ( ( X0 != X1
          & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) )
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) ) ),
    inference(nnf_transformation,[],[f1703]) ).

fof(f1703,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
    <=> ( X0 != X1
        & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ) ),
    inference(rectify,[],[f235]) ).

fof(f235,axiom,
    ! [X20,X12] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X12,X20)
    <=> ( X12 != X20
        & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X12,X20) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__less__def) ).

fof(f7164,plain,
    ~ spl50_224,
    inference(avatar_split_clause,[],[f5563,f7161]) ).

fof(f7161,plain,
    ( spl50_224
  <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = sK47 ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_224])]) ).

fof(f5563,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != sK47,
    inference(cnf_transformation,[],[f3874]) ).

fof(f7159,plain,
    ~ spl50_223,
    inference(avatar_split_clause,[],[f5562,f7156]) ).

fof(f7156,plain,
    ( spl50_223
  <=> c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = sK48 ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_223])]) ).

fof(f5562,plain,
    c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != sK48,
    inference(cnf_transformation,[],[f3874]) ).

fof(f7154,plain,
    spl50_222,
    inference(avatar_split_clause,[],[f4140,f7152]) ).

fof(f7152,plain,
    ( spl50_222
  <=> ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_222])]) ).

fof(f4140,plain,
    ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X0),
    inference(cnf_transformation,[],[f1288]) ).

fof(f1288,plain,
    ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X0),
    inference(rectify,[],[f369]) ).

fof(f369,axiom,
    ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__refl) ).

fof(f7150,plain,
    spl50_221,
    inference(avatar_split_clause,[],[f4139,f7148]) ).

fof(f4139,plain,
    ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X0),
    inference(cnf_transformation,[],[f1287]) ).

fof(f1287,plain,
    ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X0),
    inference(rectify,[],[f669]) ).

fof(f669,axiom,
    ! [X15] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X15,X15),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__refl) ).

fof(f7146,plain,
    spl50_220,
    inference(avatar_split_clause,[],[f4138,f7144]) ).

fof(f7144,plain,
    ( spl50_220
  <=> ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_220])]) ).

fof(f4138,plain,
    ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X0),
    inference(cnf_transformation,[],[f1286]) ).

fof(f1286,plain,
    ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X0),
    inference(rectify,[],[f206]) ).

fof(f206,axiom,
    ! [X15] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X15,X15),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__refl) ).

fof(f7142,plain,
    spl50_219,
    inference(avatar_split_clause,[],[f4137,f7140]) ).

fof(f7140,plain,
    ( spl50_219
  <=> ! [X0] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_219])]) ).

fof(f4137,plain,
    ! [X0] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,X0),
    inference(cnf_transformation,[],[f1285]) ).

fof(f1285,plain,
    ! [X0] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,X0),
    inference(rectify,[],[f886]) ).

fof(f886,axiom,
    ! [X9] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X9),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oorder__refl) ).

fof(f7138,plain,
    spl50_218,
    inference(avatar_split_clause,[],[f4135,f7136]) ).

fof(f4135,plain,
    ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X0),
    inference(cnf_transformation,[],[f1283]) ).

fof(f1283,plain,
    ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X0),
    inference(rectify,[],[f359]) ).

fof(f359,axiom,
    ! [X3] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl) ).

fof(f7134,plain,
    ~ spl50_217,
    inference(avatar_split_clause,[],[f4092,f7131]) ).

fof(f7131,plain,
    ( spl50_217
  <=> c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Complex_Oii ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_217])]) ).

fof(f4092,plain,
    c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Complex_Oii,
    inference(cnf_transformation,[],[f701]) ).

fof(f701,axiom,
    c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Complex_Oii,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__i__not__zero) ).

fof(f7129,plain,
    ~ spl50_216,
    inference(avatar_split_clause,[],[f4091,f7126]) ).

fof(f7126,plain,
    ( spl50_216
  <=> c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v_a____ ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_216])]) ).

fof(f4091,plain,
    c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != v_a____,
    inference(cnf_transformation,[],[f18]) ).

fof(f18,axiom,
    c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != v_a____,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_kas_I1_J) ).

fof(f7124,plain,
    ~ spl50_215,
    inference(avatar_split_clause,[],[f4090,f7121]) ).

fof(f7121,plain,
    ( spl50_215
  <=> c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Complex_Oii ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_215])]) ).

fof(f4090,plain,
    c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) != c_Complex_Oii,
    inference(cnf_transformation,[],[f702]) ).

fof(f702,axiom,
    c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) != c_Complex_Oii,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__i__not__one) ).

fof(f7119,plain,
    ~ spl50_214,
    inference(avatar_split_clause,[],[f4089,f7116]) ).

fof(f7116,plain,
    ( spl50_214
  <=> v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_214])]) ).

fof(f4089,plain,
    v_k____ != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(cnf_transformation,[],[f5]) ).

fof(f5,axiom,
    v_k____ != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_kas_I2_J) ).

fof(f7114,plain,
    ~ spl50_213,
    inference(avatar_split_clause,[],[f4088,f7111]) ).

fof(f4088,plain,
    v_w____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f3]) ).

fof(f3,axiom,
    v_w____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_w0) ).

fof(f7109,plain,
    spl50_212,
    inference(avatar_split_clause,[],[f4087,f7106]) ).

fof(f7106,plain,
    ( spl50_212
  <=> class_Groups_Ominus(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_212])]) ).

fof(f4087,plain,
    class_Groups_Ominus(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1096]) ).

fof(f1096,axiom,
    class_Groups_Ominus(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ominus) ).

fof(f7104,plain,
    spl50_211,
    inference(avatar_split_clause,[],[f4086,f7101]) ).

fof(f7101,plain,
    ( spl50_211
  <=> class_Groups_Ominus(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_211])]) ).

fof(f4086,plain,
    class_Groups_Ominus(tc_Int_Oint),
    inference(cnf_transformation,[],[f1057]) ).

fof(f1057,axiom,
    class_Groups_Ominus(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ominus) ).

fof(f7099,plain,
    spl50_210,
    inference(avatar_split_clause,[],[f4085,f7096]) ).

fof(f7096,plain,
    ( spl50_210
  <=> class_Groups_Ominus(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_210])]) ).

fof(f4085,plain,
    class_Groups_Ominus(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1166]) ).

fof(f1166,axiom,
    class_Groups_Ominus(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ominus) ).

fof(f7094,plain,
    spl50_209,
    inference(avatar_split_clause,[],[f4084,f7091]) ).

fof(f7091,plain,
    ( spl50_209
  <=> class_Groups_Ominus(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_209])]) ).

fof(f4084,plain,
    class_Groups_Ominus(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1207]) ).

fof(f1207,axiom,
    class_Groups_Ominus(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ominus) ).

fof(f7089,plain,
    spl50_208,
    inference(avatar_split_clause,[],[f4083,f7086]) ).

fof(f7086,plain,
    ( spl50_208
  <=> class_Groups_Ominus(tc_HOL_Obool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_208])]) ).

fof(f4083,plain,
    class_Groups_Ominus(tc_HOL_Obool),
    inference(cnf_transformation,[],[f1106]) ).

fof(f1106,axiom,
    class_Groups_Ominus(tc_HOL_Obool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Groups_Ominus) ).

fof(f7084,plain,
    spl50_207,
    inference(avatar_split_clause,[],[f4082,f7081]) ).

fof(f7081,plain,
    ( spl50_207
  <=> class_Orderings_Oorder(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_207])]) ).

fof(f4082,plain,
    class_Orderings_Oorder(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1093]) ).

fof(f1093,axiom,
    class_Orderings_Oorder(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).

fof(f7079,plain,
    spl50_206,
    inference(avatar_split_clause,[],[f4081,f7076]) ).

fof(f7076,plain,
    ( spl50_206
  <=> class_Orderings_Oorder(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_206])]) ).

fof(f4081,plain,
    class_Orderings_Oorder(tc_Int_Oint),
    inference(cnf_transformation,[],[f1050]) ).

fof(f1050,axiom,
    class_Orderings_Oorder(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oorder) ).

fof(f7074,plain,
    spl50_205,
    inference(avatar_split_clause,[],[f4080,f7071]) ).

fof(f4080,plain,
    class_Orderings_Oorder(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1159]) ).

fof(f1159,axiom,
    class_Orderings_Oorder(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Oorder) ).

fof(f7069,plain,
    spl50_204,
    inference(avatar_split_clause,[],[f4079,f7066]) ).

fof(f7066,plain,
    ( spl50_204
  <=> class_Orderings_Oorder(tc_HOL_Obool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_204])]) ).

fof(f4079,plain,
    class_Orderings_Oorder(tc_HOL_Obool),
    inference(cnf_transformation,[],[f1103]) ).

fof(f1103,axiom,
    class_Orderings_Oorder(tc_HOL_Obool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oorder) ).

fof(f7064,plain,
    spl50_203,
    inference(avatar_split_clause,[],[f4078,f7061]) ).

fof(f7061,plain,
    ( spl50_203
  <=> class_Orderings_Opreorder(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_203])]) ).

fof(f4078,plain,
    class_Orderings_Opreorder(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1087]) ).

fof(f1087,axiom,
    class_Orderings_Opreorder(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).

fof(f7059,plain,
    spl50_202,
    inference(avatar_split_clause,[],[f4077,f7056]) ).

fof(f7056,plain,
    ( spl50_202
  <=> class_Orderings_Opreorder(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_202])]) ).

fof(f4077,plain,
    class_Orderings_Opreorder(tc_Int_Oint),
    inference(cnf_transformation,[],[f1041]) ).

fof(f1041,axiom,
    class_Orderings_Opreorder(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Opreorder) ).

fof(f7054,plain,
    spl50_201,
    inference(avatar_split_clause,[],[f4076,f7051]) ).

fof(f4076,plain,
    class_Orderings_Opreorder(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1150]) ).

fof(f1150,axiom,
    class_Orderings_Opreorder(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Opreorder) ).

fof(f7049,plain,
    spl50_200,
    inference(avatar_split_clause,[],[f4075,f7046]) ).

fof(f7046,plain,
    ( spl50_200
  <=> class_Orderings_Opreorder(tc_HOL_Obool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_200])]) ).

fof(f4075,plain,
    class_Orderings_Opreorder(tc_HOL_Obool),
    inference(cnf_transformation,[],[f1102]) ).

fof(f1102,axiom,
    class_Orderings_Opreorder(tc_HOL_Obool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Opreorder) ).

fof(f7044,plain,
    spl50_199,
    inference(avatar_split_clause,[],[f4074,f7041]) ).

fof(f7041,plain,
    ( spl50_199
  <=> class_Orderings_Oord(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_199])]) ).

fof(f4074,plain,
    class_Orderings_Oord(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1095]) ).

fof(f1095,axiom,
    class_Orderings_Oord(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).

fof(f7039,plain,
    spl50_198,
    inference(avatar_split_clause,[],[f4073,f7036]) ).

fof(f7036,plain,
    ( spl50_198
  <=> class_Orderings_Oord(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_198])]) ).

fof(f4073,plain,
    class_Orderings_Oord(tc_Int_Oint),
    inference(cnf_transformation,[],[f1053]) ).

fof(f1053,axiom,
    class_Orderings_Oord(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oord) ).

fof(f7034,plain,
    spl50_197,
    inference(avatar_split_clause,[],[f4072,f7031]) ).

fof(f7031,plain,
    ( spl50_197
  <=> class_Orderings_Oord(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_197])]) ).

fof(f4072,plain,
    class_Orderings_Oord(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1162]) ).

fof(f1162,axiom,
    class_Orderings_Oord(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Oord) ).

fof(f7029,plain,
    spl50_196,
    inference(avatar_split_clause,[],[f4071,f7026]) ).

fof(f7026,plain,
    ( spl50_196
  <=> class_Orderings_Oord(tc_HOL_Obool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_196])]) ).

fof(f4071,plain,
    class_Orderings_Oord(tc_HOL_Obool),
    inference(cnf_transformation,[],[f1104]) ).

fof(f1104,axiom,
    class_Orderings_Oord(tc_HOL_Obool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oord) ).

fof(f7024,plain,
    spl50_195,
    inference(avatar_split_clause,[],[f4070,f7021]) ).

fof(f7021,plain,
    ( spl50_195
  <=> class_Groups_Ouminus(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_195])]) ).

fof(f4070,plain,
    class_Groups_Ouminus(tc_Int_Oint),
    inference(cnf_transformation,[],[f1054]) ).

fof(f1054,axiom,
    class_Groups_Ouminus(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ouminus) ).

fof(f7019,plain,
    spl50_194,
    inference(avatar_split_clause,[],[f4069,f7016]) ).

fof(f7016,plain,
    ( spl50_194
  <=> class_Groups_Ouminus(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_194])]) ).

fof(f4069,plain,
    class_Groups_Ouminus(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1163]) ).

fof(f1163,axiom,
    class_Groups_Ouminus(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ouminus) ).

fof(f7014,plain,
    spl50_193,
    inference(avatar_split_clause,[],[f4068,f7011]) ).

fof(f7011,plain,
    ( spl50_193
  <=> class_Groups_Ouminus(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_193])]) ).

fof(f4068,plain,
    class_Groups_Ouminus(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1205]) ).

fof(f1205,axiom,
    class_Groups_Ouminus(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ouminus) ).

fof(f7009,plain,
    spl50_192,
    inference(avatar_split_clause,[],[f4067,f7006]) ).

fof(f7006,plain,
    ( spl50_192
  <=> class_Groups_Ouminus(tc_HOL_Obool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_192])]) ).

fof(f4067,plain,
    class_Groups_Ouminus(tc_HOL_Obool),
    inference(cnf_transformation,[],[f1105]) ).

fof(f1105,axiom,
    class_Groups_Ouminus(tc_HOL_Obool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Groups_Ouminus) ).

fof(f7004,plain,
    spl50_191,
    inference(avatar_split_clause,[],[f4066,f7001]) ).

fof(f4066,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/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).

fof(f6999,plain,
    spl50_190,
    inference(avatar_split_clause,[],[f4065,f6996]) ).

fof(f4065,plain,
    class_Rings_Ocomm__semiring__1(tc_Int_Oint),
    inference(cnf_transformation,[],[f1035]) ).

fof(f1035,axiom,
    class_Rings_Ocomm__semiring__1(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__1) ).

fof(f6994,plain,
    spl50_189,
    inference(avatar_split_clause,[],[f4064,f6991]) ).

fof(f4064,plain,
    class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1143]) ).

fof(f1143,axiom,
    class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__1) ).

fof(f6989,plain,
    spl50_188,
    inference(avatar_split_clause,[],[f4063,f6986]) ).

fof(f4063,plain,
    class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1190]) ).

fof(f1190,axiom,
    class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).

fof(f6984,plain,
    spl50_187,
    inference(avatar_split_clause,[],[f4062,f6981]) ).

fof(f6981,plain,
    ( spl50_187
  <=> class_Rings_Ocomm__semiring__0(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_187])]) ).

fof(f4062,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/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__0) ).

fof(f6979,plain,
    spl50_186,
    inference(avatar_split_clause,[],[f4061,f6976]) ).

fof(f6976,plain,
    ( spl50_186
  <=> class_Rings_Ocomm__semiring__0(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_186])]) ).

fof(f4061,plain,
    class_Rings_Ocomm__semiring__0(tc_Int_Oint),
    inference(cnf_transformation,[],[f1036]) ).

fof(f1036,axiom,
    class_Rings_Ocomm__semiring__0(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__0) ).

fof(f6974,plain,
    spl50_185,
    inference(avatar_split_clause,[],[f4060,f6971]) ).

fof(f6971,plain,
    ( spl50_185
  <=> class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_185])]) ).

fof(f4060,plain,
    class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1144]) ).

fof(f1144,axiom,
    class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__0) ).

fof(f6969,plain,
    spl50_184,
    inference(avatar_split_clause,[],[f4059,f6966]) ).

fof(f6966,plain,
    ( spl50_184
  <=> class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_184])]) ).

fof(f4059,plain,
    class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1191]) ).

fof(f1191,axiom,
    class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__0) ).

fof(f6964,plain,
    spl50_183,
    inference(avatar_split_clause,[],[f4058,f6961]) ).

fof(f6961,plain,
    ( spl50_183
  <=> class_Groups_Ozero(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_183])]) ).

fof(f4058,plain,
    class_Groups_Ozero(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1098]) ).

fof(f1098,axiom,
    class_Groups_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ozero) ).

fof(f6959,plain,
    spl50_182,
    inference(avatar_split_clause,[],[f4057,f6956]) ).

fof(f6956,plain,
    ( spl50_182
  <=> class_Groups_Ozero(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_182])]) ).

fof(f4057,plain,
    class_Groups_Ozero(tc_Int_Oint),
    inference(cnf_transformation,[],[f1059]) ).

fof(f1059,axiom,
    class_Groups_Ozero(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ozero) ).

fof(f6954,plain,
    spl50_181,
    inference(avatar_split_clause,[],[f4056,f6951]) ).

fof(f6951,plain,
    ( spl50_181
  <=> class_Groups_Ozero(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_181])]) ).

fof(f4056,plain,
    class_Groups_Ozero(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1169]) ).

fof(f1169,axiom,
    class_Groups_Ozero(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ozero) ).

fof(f6949,plain,
    spl50_180,
    inference(avatar_split_clause,[],[f4055,f6946]) ).

fof(f6946,plain,
    ( spl50_180
  <=> class_Groups_Ozero(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_180])]) ).

fof(f4055,plain,
    class_Groups_Ozero(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1210]) ).

fof(f1210,axiom,
    class_Groups_Ozero(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ozero) ).

fof(f6944,plain,
    spl50_179,
    inference(avatar_split_clause,[],[f4054,f6941]) ).

fof(f6941,plain,
    ( spl50_179
  <=> class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_179])]) ).

fof(f4054,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/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__add) ).

fof(f6939,plain,
    spl50_178,
    inference(avatar_split_clause,[],[f4053,f6936]) ).

fof(f6936,plain,
    ( spl50_178
  <=> class_Groups_Omonoid__mult(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_178])]) ).

fof(f4053,plain,
    class_Groups_Omonoid__mult(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1089]) ).

fof(f1089,axiom,
    class_Groups_Omonoid__mult(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__mult) ).

fof(f6934,plain,
    spl50_177,
    inference(avatar_split_clause,[],[f4052,f6931]) ).

fof(f6931,plain,
    ( spl50_177
  <=> class_Groups_Omonoid__mult(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_177])]) ).

fof(f4052,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/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__mult) ).

fof(f6929,plain,
    spl50_176,
    inference(avatar_split_clause,[],[f4051,f6926]) ).

fof(f6926,plain,
    ( spl50_176
  <=> class_Groups_Ocomm__monoid__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_176])]) ).

fof(f4051,plain,
    class_Groups_Ocomm__monoid__add(tc_Int_Oint),
    inference(cnf_transformation,[],[f1032]) ).

fof(f1032,axiom,
    class_Groups_Ocomm__monoid__add(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__add) ).

fof(f6924,plain,
    spl50_175,
    inference(avatar_split_clause,[],[f4050,f6921]) ).

fof(f6921,plain,
    ( spl50_175
  <=> class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_175])]) ).

fof(f4050,plain,
    class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1140]) ).

fof(f1140,axiom,
    class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocomm__monoid__add) ).

fof(f6919,plain,
    spl50_174,
    inference(avatar_split_clause,[],[f4049,f6916]) ).

fof(f6916,plain,
    ( spl50_174
  <=> class_Groups_Omonoid__mult(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_174])]) ).

fof(f4049,plain,
    class_Groups_Omonoid__mult(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1152]) ).

fof(f1152,axiom,
    class_Groups_Omonoid__mult(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__mult) ).

fof(f6914,plain,
    spl50_173,
    inference(avatar_split_clause,[],[f4048,f6911]) ).

fof(f6911,plain,
    ( spl50_173
  <=> class_Groups_Omonoid__mult(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_173])]) ).

fof(f4048,plain,
    class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1196]) ).

fof(f1196,axiom,
    class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Omonoid__mult) ).

fof(f6909,plain,
    spl50_172,
    inference(avatar_split_clause,[],[f4047,f6906]) ).

fof(f6906,plain,
    ( spl50_172
  <=> class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_172])]) ).

fof(f4047,plain,
    class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1189]) ).

fof(f1189,axiom,
    class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocomm__monoid__add) ).

fof(f6904,plain,
    spl50_171,
    inference(avatar_split_clause,[],[f4046,f6901]) ).

fof(f6901,plain,
    ( spl50_171
  <=> class_Power_Opower(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_171])]) ).

fof(f4046,plain,
    class_Power_Opower(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1097]) ).

fof(f1097,axiom,
    class_Power_Opower(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Power_Opower) ).

fof(f6899,plain,
    spl50_170,
    inference(avatar_split_clause,[],[f4045,f6896]) ).

fof(f6896,plain,
    ( spl50_170
  <=> class_Power_Opower(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_170])]) ).

fof(f4045,plain,
    class_Power_Opower(tc_Int_Oint),
    inference(cnf_transformation,[],[f1058]) ).

fof(f1058,axiom,
    class_Power_Opower(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Power_Opower) ).

fof(f6894,plain,
    spl50_169,
    inference(avatar_split_clause,[],[f4044,f6891]) ).

fof(f6891,plain,
    ( spl50_169
  <=> class_Power_Opower(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_169])]) ).

fof(f4044,plain,
    class_Power_Opower(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1168]) ).

fof(f1168,axiom,
    class_Power_Opower(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Power_Opower) ).

fof(f6889,plain,
    spl50_168,
    inference(avatar_split_clause,[],[f4043,f6886]) ).

fof(f6886,plain,
    ( spl50_168
  <=> class_Power_Opower(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_168])]) ).

fof(f4043,plain,
    class_Power_Opower(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1209]) ).

fof(f1209,axiom,
    class_Power_Opower(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Power_Opower) ).

fof(f6884,plain,
    spl50_167,
    inference(avatar_split_clause,[],[f4042,f6881]) ).

fof(f6881,plain,
    ( spl50_167
  <=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_167])]) ).

fof(f4042,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/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).

fof(f6879,plain,
    spl50_166,
    inference(avatar_split_clause,[],[f4041,f6876]) ).

fof(f4041,plain,
    class_Rings_Odvd(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1100]) ).

fof(f1100,axiom,
    class_Rings_Odvd(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Odvd) ).

fof(f6874,plain,
    spl50_165,
    inference(avatar_split_clause,[],[f4040,f6871]) ).

fof(f6871,plain,
    ( spl50_165
  <=> class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_165])]) ).

fof(f4040,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/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).

fof(f6869,plain,
    spl50_164,
    inference(avatar_split_clause,[],[f4039,f6866]) ).

fof(f6866,plain,
    ( spl50_164
  <=> class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_164])]) ).

fof(f4039,plain,
    class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
    inference(cnf_transformation,[],[f1024]) ).

fof(f1024,axiom,
    class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__semigroup__add) ).

fof(f6864,plain,
    spl50_163,
    inference(avatar_split_clause,[],[f4038,f6861]) ).

fof(f6861,plain,
    ( spl50_163
  <=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_163])]) ).

fof(f4038,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
    inference(cnf_transformation,[],[f1007]) ).

fof(f1007,axiom,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).

fof(f6859,plain,
    spl50_162,
    inference(avatar_split_clause,[],[f4037,f6856]) ).

fof(f4037,plain,
    class_Rings_Odvd(tc_Int_Oint),
    inference(cnf_transformation,[],[f1063]) ).

fof(f1063,axiom,
    class_Rings_Odvd(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Odvd) ).

fof(f6854,plain,
    spl50_161,
    inference(avatar_split_clause,[],[f4036,f6851]) ).

fof(f6851,plain,
    ( spl50_161
  <=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_161])]) ).

fof(f4036,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1107]) ).

fof(f1107,axiom,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).

fof(f6849,plain,
    spl50_160,
    inference(avatar_split_clause,[],[f4035,f6846]) ).

fof(f4035,plain,
    class_Rings_Odvd(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1173]) ).

fof(f1173,axiom,
    class_Rings_Odvd(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Odvd) ).

fof(f6844,plain,
    spl50_159,
    inference(avatar_split_clause,[],[f4034,f6841]) ).

fof(f6841,plain,
    ( spl50_159
  <=> class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_159])]) ).

fof(f4034,plain,
    class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1130]) ).

fof(f1130,axiom,
    class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__semigroup__add) ).

fof(f6839,plain,
    spl50_158,
    inference(avatar_split_clause,[],[f4033,f6836]) ).

fof(f6836,plain,
    ( spl50_158
  <=> class_Rings_Odvd(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_158])]) ).

fof(f4033,plain,
    class_Rings_Odvd(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1214]) ).

fof(f1214,axiom,
    class_Rings_Odvd(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odvd) ).

fof(f6834,plain,
    spl50_157,
    inference(avatar_split_clause,[],[f4032,f6831]) ).

fof(f6831,plain,
    ( spl50_157
  <=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_157])]) ).

fof(f4032,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1174]) ).

fof(f1174,axiom,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).

fof(f6829,plain,
    spl50_156,
    inference(avatar_split_clause,[],[f4031,f6826]) ).

fof(f6826,plain,
    ( spl50_156
  <=> class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_156])]) ).

fof(f4031,plain,
    class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1183]) ).

fof(f1183,axiom,
    class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add) ).

fof(f6824,plain,
    spl50_155,
    inference(avatar_split_clause,[],[f4030,f6821]) ).

fof(f6821,plain,
    ( spl50_155
  <=> class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_155])]) ).

fof(f4030,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/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__mult) ).

fof(f6819,plain,
    spl50_154,
    inference(avatar_split_clause,[],[f4029,f6816]) ).

fof(f6816,plain,
    ( spl50_154
  <=> class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_154])]) ).

fof(f4029,plain,
    class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat),
    inference(cnf_transformation,[],[f999]) ).

fof(f999,axiom,
    class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__comm__monoid__add) ).

fof(f6814,plain,
    spl50_153,
    inference(avatar_split_clause,[],[f4028,f6811]) ).

fof(f6811,plain,
    ( spl50_153
  <=> class_Rings_Omult__zero(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_153])]) ).

fof(f4028,plain,
    class_Rings_Omult__zero(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1092]) ).

fof(f1092,axiom,
    class_Rings_Omult__zero(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Omult__zero) ).

fof(f6809,plain,
    spl50_152,
    inference(avatar_split_clause,[],[f4027,f6806]) ).

fof(f6806,plain,
    ( spl50_152
  <=> class_Rings_Osemiring__0(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_152])]) ).

fof(f4027,plain,
    class_Rings_Osemiring__0(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1091]) ).

fof(f1091,axiom,
    class_Rings_Osemiring__0(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__0) ).

fof(f6804,plain,
    spl50_151,
    inference(avatar_split_clause,[],[f4026,f6801]) ).

fof(f6801,plain,
    ( spl50_151
  <=> class_Rings_Ono__zero__divisors(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_151])]) ).

fof(f4026,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/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ono__zero__divisors) ).

fof(f6799,plain,
    spl50_150,
    inference(avatar_split_clause,[],[f4025,f6796]) ).

fof(f6796,plain,
    ( spl50_150
  <=> class_Rings_Ozero__neq__one(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_150])]) ).

fof(f4025,plain,
    class_Rings_Ozero__neq__one(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1086]) ).

fof(f1086,axiom,
    class_Rings_Ozero__neq__one(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ozero__neq__one) ).

fof(f6794,plain,
    spl50_149,
    inference(avatar_split_clause,[],[f4024,f6791]) ).

fof(f6791,plain,
    ( spl50_149
  <=> class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_149])]) ).

fof(f4024,plain,
    class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
    inference(cnf_transformation,[],[f1028]) ).

fof(f1028,axiom,
    class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__mult) ).

fof(f6789,plain,
    spl50_148,
    inference(avatar_split_clause,[],[f4023,f6786]) ).

fof(f6786,plain,
    ( spl50_148
  <=> class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_148])]) ).

fof(f4023,plain,
    class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint),
    inference(cnf_transformation,[],[f1000]) ).

fof(f1000,axiom,
    class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__comm__monoid__add) ).

fof(f6784,plain,
    spl50_147,
    inference(avatar_split_clause,[],[f4022,f6781]) ).

fof(f6781,plain,
    ( spl50_147
  <=> class_Rings_Osemiring__0(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_147])]) ).

fof(f4022,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/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring__0) ).

fof(f6779,plain,
    spl50_146,
    inference(avatar_split_clause,[],[f4021,f6776]) ).

fof(f6776,plain,
    ( spl50_146
  <=> class_Rings_Ono__zero__divisors(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_146])]) ).

fof(f4021,plain,
    class_Rings_Ono__zero__divisors(tc_Int_Oint),
    inference(cnf_transformation,[],[f1031]) ).

fof(f1031,axiom,
    class_Rings_Ono__zero__divisors(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ono__zero__divisors) ).

fof(f6774,plain,
    spl50_145,
    inference(avatar_split_clause,[],[f4020,f6771]) ).

fof(f6771,plain,
    ( spl50_145
  <=> class_Rings_Ozero__neq__one(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_145])]) ).

fof(f4020,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/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ozero__neq__one) ).

fof(f6769,plain,
    spl50_144,
    inference(avatar_split_clause,[],[f4019,f6766]) ).

fof(f6766,plain,
    ( spl50_144
  <=> class_Rings_Omult__zero(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_144])]) ).

fof(f4019,plain,
    class_Rings_Omult__zero(tc_Int_Oint),
    inference(cnf_transformation,[],[f1048]) ).

fof(f1048,axiom,
    class_Rings_Omult__zero(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Omult__zero) ).

fof(f6764,plain,
    spl50_143,
    inference(avatar_split_clause,[],[f4018,f6761]) ).

fof(f6761,plain,
    ( spl50_143
  <=> class_Rings_Omult__zero(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_143])]) ).

fof(f4018,plain,
    class_Rings_Omult__zero(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1157]) ).

fof(f1157,axiom,
    class_Rings_Omult__zero(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Omult__zero) ).

fof(f6759,plain,
    spl50_142,
    inference(avatar_split_clause,[],[f4017,f6756]) ).

fof(f6756,plain,
    ( spl50_142
  <=> class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_142])]) ).

fof(f4017,plain,
    class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1135]) ).

fof(f1135,axiom,
    class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocomm__monoid__mult) ).

fof(f6754,plain,
    spl50_141,
    inference(avatar_split_clause,[],[f4016,f6751]) ).

fof(f6751,plain,
    ( spl50_141
  <=> class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_141])]) ).

fof(f4016,plain,
    class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f998]) ).

fof(f998,axiom,
    class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__comm__monoid__add) ).

fof(f6749,plain,
    spl50_140,
    inference(avatar_split_clause,[],[f4015,f6746]) ).

fof(f6746,plain,
    ( spl50_140
  <=> class_Rings_Osemiring__0(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_140])]) ).

fof(f4015,plain,
    class_Rings_Osemiring__0(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1155]) ).

fof(f1155,axiom,
    class_Rings_Osemiring__0(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring__0) ).

fof(f6744,plain,
    spl50_139,
    inference(avatar_split_clause,[],[f4014,f6741]) ).

fof(f6741,plain,
    ( spl50_139
  <=> class_Rings_Ono__zero__divisors(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_139])]) ).

fof(f4014,plain,
    class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1139]) ).

fof(f1139,axiom,
    class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ono__zero__divisors) ).

fof(f6739,plain,
    spl50_138,
    inference(avatar_split_clause,[],[f4013,f6736]) ).

fof(f6736,plain,
    ( spl50_138
  <=> class_Rings_Ozero__neq__one(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_138])]) ).

fof(f4013,plain,
    class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1148]) ).

fof(f1148,axiom,
    class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ozero__neq__one) ).

fof(f6734,plain,
    spl50_137,
    inference(avatar_split_clause,[],[f4012,f6731]) ).

fof(f6731,plain,
    ( spl50_137
  <=> class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_137])]) ).

fof(f4012,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/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add) ).

fof(f6729,plain,
    spl50_136,
    inference(avatar_split_clause,[],[f4011,f6726]) ).

fof(f6726,plain,
    ( spl50_136
  <=> class_Rings_Osemiring__0(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_136])]) ).

fof(f4011,plain,
    class_Rings_Osemiring__0(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1199]) ).

fof(f1199,axiom,
    class_Rings_Osemiring__0(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring__0) ).

fof(f6724,plain,
    spl50_135,
    inference(avatar_split_clause,[],[f4010,f6721]) ).

fof(f6721,plain,
    ( spl50_135
  <=> class_Rings_Ozero__neq__one(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_135])]) ).

fof(f4010,plain,
    class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1195]) ).

fof(f1195,axiom,
    class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ozero__neq__one) ).

fof(f6719,plain,
    spl50_134,
    inference(avatar_split_clause,[],[f4009,f6716]) ).

fof(f6716,plain,
    ( spl50_134
  <=> class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_134])]) ).

fof(f4009,plain,
    class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1186]) ).

fof(f1186,axiom,
    class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult) ).

fof(f6714,plain,
    spl50_133,
    inference(avatar_split_clause,[],[f4008,f6711]) ).

fof(f6711,plain,
    ( spl50_133
  <=> class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_133])]) ).

fof(f4008,plain,
    class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1188]) ).

fof(f1188,axiom,
    class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ono__zero__divisors) ).

fof(f6709,plain,
    spl50_132,
    inference(avatar_split_clause,[],[f4007,f6706]) ).

fof(f6706,plain,
    ( spl50_132
  <=> class_Rings_Omult__zero(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_132])]) ).

fof(f4007,plain,
    class_Rings_Omult__zero(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1201]) ).

fof(f1201,axiom,
    class_Rings_Omult__zero(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Omult__zero) ).

fof(f6704,plain,
    spl50_131,
    inference(avatar_split_clause,[],[f4006,f6701]) ).

fof(f6701,plain,
    ( spl50_131
  <=> class_Groups_Omonoid__add(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_131])]) ).

fof(f4006,plain,
    class_Groups_Omonoid__add(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1090]) ).

fof(f1090,axiom,
    class_Groups_Omonoid__add(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__add) ).

fof(f6699,plain,
    spl50_130,
    inference(avatar_split_clause,[],[f4005,f6696]) ).

fof(f6696,plain,
    ( spl50_130
  <=> class_Groups_Omonoid__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_130])]) ).

fof(f4005,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/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__add) ).

fof(f6694,plain,
    spl50_129,
    inference(avatar_split_clause,[],[f4004,f6691]) ).

fof(f4004,plain,
    class_Groups_Omonoid__add(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1154]) ).

fof(f1154,axiom,
    class_Groups_Omonoid__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__add) ).

fof(f6689,plain,
    spl50_128,
    inference(avatar_split_clause,[],[f4003,f6686]) ).

fof(f4003,plain,
    class_Groups_Omonoid__add(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1198]) ).

fof(f1198,axiom,
    class_Groups_Omonoid__add(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Omonoid__add) ).

fof(f6684,plain,
    spl50_127,
    inference(avatar_split_clause,[],[f4002,f6681]) ).

fof(f6681,plain,
    ( spl50_127
  <=> class_Rings_Ocomm__semiring(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_127])]) ).

fof(f4002,plain,
    class_Rings_Ocomm__semiring(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1085]) ).

fof(f1085,axiom,
    class_Rings_Ocomm__semiring(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring) ).

fof(f6679,plain,
    spl50_126,
    inference(avatar_split_clause,[],[f4001,f6676]) ).

fof(f6676,plain,
    ( spl50_126
  <=> class_Groups_Oone(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_126])]) ).

fof(f4001,plain,
    class_Groups_Oone(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1099]) ).

fof(f1099,axiom,
    class_Groups_Oone(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oone) ).

fof(f6674,plain,
    spl50_125,
    inference(avatar_split_clause,[],[f4000,f6671]) ).

fof(f6671,plain,
    ( spl50_125
  <=> class_Rings_Osemiring(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_125])]) ).

fof(f4000,plain,
    class_Rings_Osemiring(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1094]) ).

fof(f1094,axiom,
    class_Rings_Osemiring(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring) ).

fof(f6669,plain,
    spl50_124,
    inference(avatar_split_clause,[],[f3999,f6666]) ).

fof(f6666,plain,
    ( spl50_124
  <=> class_Groups_Oab__semigroup__add(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_124])]) ).

fof(f3999,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/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__add) ).

fof(f6664,plain,
    spl50_123,
    inference(avatar_split_clause,[],[f3998,f6661]) ).

fof(f6661,plain,
    ( spl50_123
  <=> class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_123])]) ).

fof(f3998,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/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__mult) ).

fof(f6659,plain,
    spl50_122,
    inference(avatar_split_clause,[],[f3997,f6656]) ).

fof(f6656,plain,
    ( spl50_122
  <=> class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_122])]) ).

fof(f3997,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/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) ).

fof(f6654,plain,
    spl50_121,
    inference(avatar_split_clause,[],[f3996,f6651]) ).

fof(f6651,plain,
    ( spl50_121
  <=> class_Groups_Oone(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_121])]) ).

fof(f3996,plain,
    class_Groups_Oone(tc_Int_Oint),
    inference(cnf_transformation,[],[f1062]) ).

fof(f1062,axiom,
    class_Groups_Oone(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oone) ).

fof(f6649,plain,
    spl50_120,
    inference(avatar_split_clause,[],[f3995,f6646]) ).

fof(f6646,plain,
    ( spl50_120
  <=> class_Rings_Osemiring(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_120])]) ).

fof(f3995,plain,
    class_Rings_Osemiring(tc_Int_Oint),
    inference(cnf_transformation,[],[f1052]) ).

fof(f1052,axiom,
    class_Rings_Osemiring(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring) ).

fof(f6644,plain,
    spl50_119,
    inference(avatar_split_clause,[],[f3994,f6641]) ).

fof(f6641,plain,
    ( spl50_119
  <=> class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_119])]) ).

fof(f3994,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
    inference(cnf_transformation,[],[f1016]) ).

fof(f1016,axiom,
    class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__ab__semigroup__add) ).

fof(f6639,plain,
    spl50_118,
    inference(avatar_split_clause,[],[f3993,f6636]) ).

fof(f6636,plain,
    ( spl50_118
  <=> class_Groups_Oab__semigroup__mult(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_118])]) ).

fof(f3993,plain,
    class_Groups_Oab__semigroup__mult(tc_Int_Oint),
    inference(cnf_transformation,[],[f1027]) ).

fof(f1027,axiom,
    class_Groups_Oab__semigroup__mult(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__mult) ).

fof(f6634,plain,
    spl50_117,
    inference(avatar_split_clause,[],[f3992,f6631]) ).

fof(f6631,plain,
    ( spl50_117
  <=> class_Groups_Oab__semigroup__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_117])]) ).

fof(f3992,plain,
    class_Groups_Oab__semigroup__add(tc_Int_Oint),
    inference(cnf_transformation,[],[f1029]) ).

fof(f1029,axiom,
    class_Groups_Oab__semigroup__add(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__add) ).

fof(f6629,plain,
    spl50_116,
    inference(avatar_split_clause,[],[f3991,f6626]) ).

fof(f6626,plain,
    ( spl50_116
  <=> class_Rings_Ocomm__semiring(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_116])]) ).

fof(f3991,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/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring) ).

fof(f6624,plain,
    spl50_115,
    inference(avatar_split_clause,[],[f3990,f6621]) ).

fof(f6621,plain,
    ( spl50_115
  <=> class_Rings_Ocomm__semiring(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_115])]) ).

fof(f3990,plain,
    class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1146]) ).

fof(f1146,axiom,
    class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring) ).

fof(f6619,plain,
    spl50_114,
    inference(avatar_split_clause,[],[f3989,f6616]) ).

fof(f6616,plain,
    ( spl50_114
  <=> class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_114])]) ).

fof(f3989,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1121]) ).

fof(f1121,axiom,
    class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add) ).

fof(f6614,plain,
    spl50_113,
    inference(avatar_split_clause,[],[f3988,f6611]) ).

fof(f6611,plain,
    ( spl50_113
  <=> class_Rings_Osemiring(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_113])]) ).

fof(f3988,plain,
    class_Rings_Osemiring(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1161]) ).

fof(f1161,axiom,
    class_Rings_Osemiring(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring) ).

fof(f6609,plain,
    spl50_112,
    inference(avatar_split_clause,[],[f3987,f6606]) ).

fof(f6606,plain,
    ( spl50_112
  <=> class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_112])]) ).

fof(f3987,plain,
    class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1134]) ).

fof(f1134,axiom,
    class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__semigroup__mult) ).

fof(f6604,plain,
    spl50_111,
    inference(avatar_split_clause,[],[f3986,f6601]) ).

fof(f6601,plain,
    ( spl50_111
  <=> class_Groups_Oone(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_111])]) ).

fof(f3986,plain,
    class_Groups_Oone(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1172]) ).

fof(f1172,axiom,
    class_Groups_Oone(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oone) ).

fof(f6599,plain,
    spl50_110,
    inference(avatar_split_clause,[],[f3985,f6596]) ).

fof(f6596,plain,
    ( spl50_110
  <=> class_Groups_Oab__semigroup__add(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_110])]) ).

fof(f3985,plain,
    class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1136]) ).

fof(f1136,axiom,
    class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__semigroup__add) ).

fof(f6594,plain,
    spl50_109,
    inference(avatar_split_clause,[],[f3984,f6591]) ).

fof(f6591,plain,
    ( spl50_109
  <=> class_Groups_Oone(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_109])]) ).

fof(f3984,plain,
    class_Groups_Oone(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1213]) ).

fof(f1213,axiom,
    class_Groups_Oone(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oone) ).

fof(f6589,plain,
    spl50_108,
    inference(avatar_split_clause,[],[f3983,f6586]) ).

fof(f6586,plain,
    ( spl50_108
  <=> class_Rings_Osemiring(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_108])]) ).

fof(f3983,plain,
    class_Rings_Osemiring(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1204]) ).

fof(f1204,axiom,
    class_Rings_Osemiring(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring) ).

fof(f6584,plain,
    spl50_107,
    inference(avatar_split_clause,[],[f3982,f6581]) ).

fof(f6581,plain,
    ( spl50_107
  <=> class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_107])]) ).

fof(f3982,plain,
    class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1185]) ).

fof(f1185,axiom,
    class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__semigroup__mult) ).

fof(f6579,plain,
    spl50_106,
    inference(avatar_split_clause,[],[f3981,f6576]) ).

fof(f6576,plain,
    ( spl50_106
  <=> class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_106])]) ).

fof(f3981,plain,
    class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1187]) ).

fof(f1187,axiom,
    class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__semigroup__add) ).

fof(f6574,plain,
    spl50_105,
    inference(avatar_split_clause,[],[f3980,f6571]) ).

fof(f6571,plain,
    ( spl50_105
  <=> class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_105])]) ).

fof(f3980,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1179]) ).

fof(f1179,axiom,
    class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add) ).

fof(f6569,plain,
    spl50_104,
    inference(avatar_split_clause,[],[f3979,f6566]) ).

fof(f6566,plain,
    ( spl50_104
  <=> class_Rings_Ocomm__semiring(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_104])]) ).

fof(f3979,plain,
    class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1193]) ).

fof(f1193,axiom,
    class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring) ).

fof(f6564,plain,
    spl50_103,
    inference(avatar_split_clause,[],[f3978,f6561]) ).

fof(f6561,plain,
    ( spl50_103
  <=> class_Rings_Olinordered__semidom(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_103])]) ).

fof(f3978,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/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semidom) ).

fof(f6559,plain,
    spl50_102,
    inference(avatar_split_clause,[],[f3977,f6556]) ).

fof(f6556,plain,
    ( spl50_102
  <=> class_Rings_Olinordered__semidom(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_102])]) ).

fof(f3977,plain,
    class_Rings_Olinordered__semidom(tc_Int_Oint),
    inference(cnf_transformation,[],[f1026]) ).

fof(f1026,axiom,
    class_Rings_Olinordered__semidom(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semidom) ).

fof(f6554,plain,
    spl50_101,
    inference(avatar_split_clause,[],[f3976,f6551]) ).

fof(f6551,plain,
    ( spl50_101
  <=> class_Rings_Olinordered__semidom(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_101])]) ).

fof(f3976,plain,
    class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1133]) ).

fof(f1133,axiom,
    class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semidom) ).

fof(f6549,plain,
    spl50_100,
    inference(avatar_split_clause,[],[f3975,f6546]) ).

fof(f3975,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/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ogroup__add) ).

fof(f6544,plain,
    spl50_99,
    inference(avatar_split_clause,[],[f3974,f6541]) ).

fof(f3974,plain,
    class_Groups_Ogroup__add(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1156]) ).

fof(f1156,axiom,
    class_Groups_Ogroup__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ogroup__add) ).

fof(f6539,plain,
    spl50_98,
    inference(avatar_split_clause,[],[f3973,f6536]) ).

fof(f3973,plain,
    class_Groups_Ogroup__add(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1200]) ).

fof(f1200,axiom,
    class_Groups_Ogroup__add(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ogroup__add) ).

fof(f6534,plain,
    spl50_97,
    inference(avatar_split_clause,[],[f3972,f6531]) ).

fof(f6531,plain,
    ( spl50_97
  <=> class_Groups_Oab__group__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_97])]) ).

fof(f3972,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/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__group__add) ).

fof(f6529,plain,
    spl50_96,
    inference(avatar_split_clause,[],[f3971,f6526]) ).

fof(f6526,plain,
    ( spl50_96
  <=> class_Groups_Oab__group__add(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_96])]) ).

fof(f3971,plain,
    class_Groups_Oab__group__add(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1147]) ).

fof(f1147,axiom,
    class_Groups_Oab__group__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__group__add) ).

fof(f6524,plain,
    spl50_95,
    inference(avatar_split_clause,[],[f3970,f6521]) ).

fof(f6521,plain,
    ( spl50_95
  <=> class_Groups_Oab__group__add(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_95])]) ).

fof(f3970,plain,
    class_Groups_Oab__group__add(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1194]) ).

fof(f1194,axiom,
    class_Groups_Oab__group__add(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__group__add) ).

fof(f6519,plain,
    spl50_94,
    inference(avatar_split_clause,[],[f3969,f6516]) ).

fof(f6516,plain,
    ( spl50_94
  <=> class_Rings_Oidom(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_94])]) ).

fof(f3969,plain,
    class_Rings_Oidom(tc_Int_Oint),
    inference(cnf_transformation,[],[f1061]) ).

fof(f1061,axiom,
    class_Rings_Oidom(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oidom) ).

fof(f6514,plain,
    spl50_93,
    inference(avatar_split_clause,[],[f3968,f6511]) ).

fof(f6511,plain,
    ( spl50_93
  <=> class_Rings_Oidom(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_93])]) ).

fof(f3968,plain,
    class_Rings_Oidom(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1171]) ).

fof(f1171,axiom,
    class_Rings_Oidom(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oidom) ).

fof(f6509,plain,
    spl50_92,
    inference(avatar_split_clause,[],[f3967,f6506]) ).

fof(f6506,plain,
    ( spl50_92
  <=> class_Rings_Oidom(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_92])]) ).

fof(f3967,plain,
    class_Rings_Oidom(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1212]) ).

fof(f1212,axiom,
    class_Rings_Oidom(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oidom) ).

fof(f6504,plain,
    spl50_91,
    inference(avatar_split_clause,[],[f3966,f6501]) ).

fof(f6501,plain,
    ( spl50_91
  <=> class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_91])]) ).

fof(f3966,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/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring__strict) ).

fof(f6499,plain,
    spl50_90,
    inference(avatar_split_clause,[],[f3965,f6496]) ).

fof(f6496,plain,
    ( spl50_90
  <=> class_Orderings_Olinorder(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_90])]) ).

fof(f3965,plain,
    class_Orderings_Olinorder(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1088]) ).

fof(f1088,axiom,
    class_Orderings_Olinorder(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).

fof(f6494,plain,
    spl50_89,
    inference(avatar_split_clause,[],[f3964,f6491]) ).

fof(f6491,plain,
    ( spl50_89
  <=> class_Orderings_Olinorder(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_89])]) ).

fof(f3964,plain,
    class_Orderings_Olinorder(tc_Int_Oint),
    inference(cnf_transformation,[],[f1042]) ).

fof(f1042,axiom,
    class_Orderings_Olinorder(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Olinorder) ).

fof(f6489,plain,
    spl50_88,
    inference(avatar_split_clause,[],[f3963,f6486]) ).

fof(f6486,plain,
    ( spl50_88
  <=> class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_88])]) ).

fof(f3963,plain,
    class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
    inference(cnf_transformation,[],[f1012]) ).

fof(f1012,axiom,
    class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__strict) ).

fof(f6484,plain,
    spl50_87,
    inference(avatar_split_clause,[],[f3962,f6481]) ).

fof(f6481,plain,
    ( spl50_87
  <=> class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_87])]) ).

fof(f3962,plain,
    class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1114]) ).

fof(f1114,axiom,
    class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__strict) ).

fof(f6479,plain,
    spl50_86,
    inference(avatar_split_clause,[],[f3961,f6476]) ).

fof(f3961,plain,
    class_Orderings_Olinorder(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1151]) ).

fof(f1151,axiom,
    class_Orderings_Olinorder(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Olinorder) ).

fof(f6474,plain,
    spl50_85,
    inference(avatar_split_clause,[],[f3960,f6471]) ).

fof(f6471,plain,
    ( spl50_85
  <=> class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_85])]) ).

fof(f3960,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/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__comm__monoid__add) ).

fof(f6469,plain,
    spl50_84,
    inference(avatar_split_clause,[],[f3959,f6466]) ).

fof(f6466,plain,
    ( spl50_84
  <=> class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_84])]) ).

fof(f3959,plain,
    class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
    inference(cnf_transformation,[],[f1014]) ).

fof(f1014,axiom,
    class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__comm__monoid__add) ).

fof(f6464,plain,
    spl50_83,
    inference(avatar_split_clause,[],[f3958,f6461]) ).

fof(f6461,plain,
    ( spl50_83
  <=> class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_83])]) ).

fof(f3958,plain,
    class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1119]) ).

fof(f1119,axiom,
    class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add) ).

fof(f6459,plain,
    spl50_82,
    inference(avatar_split_clause,[],[f3957,f6456]) ).

fof(f6456,plain,
    ( spl50_82
  <=> class_Rings_Ocomm__ring(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_82])]) ).

fof(f3957,plain,
    class_Rings_Ocomm__ring(tc_Int_Oint),
    inference(cnf_transformation,[],[f1049]) ).

fof(f1049,axiom,
    class_Rings_Ocomm__ring(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring) ).

fof(f6454,plain,
    spl50_81,
    inference(avatar_split_clause,[],[f3956,f6451]) ).

fof(f6451,plain,
    ( spl50_81
  <=> class_Rings_Ocomm__ring(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_81])]) ).

fof(f3956,plain,
    class_Rings_Ocomm__ring(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1158]) ).

fof(f1158,axiom,
    class_Rings_Ocomm__ring(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__ring) ).

fof(f6449,plain,
    spl50_80,
    inference(avatar_split_clause,[],[f3955,f6446]) ).

fof(f6446,plain,
    ( spl50_80
  <=> class_Rings_Ocomm__ring(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_80])]) ).

fof(f3955,plain,
    class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1202]) ).

fof(f1202,axiom,
    class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__ring) ).

fof(f6444,plain,
    spl50_79,
    inference(avatar_split_clause,[],[f3954,f6441]) ).

fof(f6441,plain,
    ( spl50_79
  <=> class_Rings_Ocomm__ring__1(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_79])]) ).

fof(f3954,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/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring__1) ).

fof(f6439,plain,
    spl50_78,
    inference(avatar_split_clause,[],[f3953,f6436]) ).

fof(f6436,plain,
    ( spl50_78
  <=> class_Rings_Ocomm__ring__1(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_78])]) ).

fof(f3953,plain,
    class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1153]) ).

fof(f1153,axiom,
    class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__ring__1) ).

fof(f6434,plain,
    spl50_77,
    inference(avatar_split_clause,[],[f3952,f6431]) ).

fof(f6431,plain,
    ( spl50_77
  <=> class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_77])]) ).

fof(f3952,plain,
    class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1197]) ).

fof(f1197,axiom,
    class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__ring__1) ).

fof(f6429,plain,
    spl50_76,
    inference(avatar_split_clause,[],[f3951,f6426]) ).

fof(f6426,plain,
    ( spl50_76
  <=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_76])]) ).

fof(f3951,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/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le) ).

fof(f6424,plain,
    spl50_75,
    inference(avatar_split_clause,[],[f3950,f6421]) ).

fof(f6421,plain,
    ( spl50_75
  <=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_75])]) ).

fof(f3950,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
    inference(cnf_transformation,[],[f1009]) ).

fof(f1009,axiom,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le) ).

fof(f6419,plain,
    spl50_74,
    inference(avatar_split_clause,[],[f3949,f6416]) ).

fof(f6416,plain,
    ( spl50_74
  <=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_74])]) ).

fof(f3949,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1109]) ).

fof(f1109,axiom,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le) ).

fof(f6414,plain,
    spl50_73,
    inference(avatar_split_clause,[],[f3948,f6411]) ).

fof(f6411,plain,
    ( spl50_73
  <=> class_Rings_Oring(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_73])]) ).

fof(f3948,plain,
    class_Rings_Oring(tc_Int_Oint),
    inference(cnf_transformation,[],[f1060]) ).

fof(f1060,axiom,
    class_Rings_Oring(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring) ).

fof(f6409,plain,
    spl50_72,
    inference(avatar_split_clause,[],[f3947,f6406]) ).

fof(f6406,plain,
    ( spl50_72
  <=> class_Rings_Oring(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_72])]) ).

fof(f3947,plain,
    class_Rings_Oring(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1170]) ).

fof(f1170,axiom,
    class_Rings_Oring(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring) ).

fof(f6404,plain,
    spl50_71,
    inference(avatar_split_clause,[],[f3946,f6401]) ).

fof(f6401,plain,
    ( spl50_71
  <=> class_Rings_Oring(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_71])]) ).

fof(f3946,plain,
    class_Rings_Oring(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1211]) ).

fof(f1211,axiom,
    class_Rings_Oring(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring) ).

fof(f6399,plain,
    spl50_70,
    inference(avatar_split_clause,[],[f3945,f6396]) ).

fof(f6396,plain,
    ( spl50_70
  <=> class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_70])]) ).

fof(f3945,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/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__cancel__semiring) ).

fof(f6394,plain,
    spl50_69,
    inference(avatar_split_clause,[],[f3944,f6391]) ).

fof(f6391,plain,
    ( spl50_69
  <=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_69])]) ).

fof(f3944,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/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) ).

fof(f6389,plain,
    spl50_68,
    inference(avatar_split_clause,[],[f3943,f6386]) ).

fof(f6386,plain,
    ( spl50_68
  <=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_68])]) ).

fof(f3943,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
    inference(cnf_transformation,[],[f1008]) ).

fof(f1008,axiom,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add) ).

fof(f6384,plain,
    spl50_67,
    inference(avatar_split_clause,[],[f3942,f6381]) ).

fof(f6381,plain,
    ( spl50_67
  <=> class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_67])]) ).

fof(f3942,plain,
    class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
    inference(cnf_transformation,[],[f1018]) ).

fof(f1018,axiom,
    class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__cancel__semiring) ).

fof(f6379,plain,
    spl50_66,
    inference(avatar_split_clause,[],[f3941,f6376]) ).

fof(f6376,plain,
    ( spl50_66
  <=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_66])]) ).

fof(f3941,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1108]) ).

fof(f1108,axiom,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add) ).

fof(f6374,plain,
    spl50_65,
    inference(avatar_split_clause,[],[f3940,f6371]) ).

fof(f6371,plain,
    ( spl50_65
  <=> class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_65])]) ).

fof(f3940,plain,
    class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1123]) ).

fof(f1123,axiom,
    class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__cancel__semiring) ).

fof(f6369,plain,
    spl50_64,
    inference(avatar_split_clause,[],[f3939,f6366]) ).

fof(f6366,plain,
    ( spl50_64
  <=> class_Rings_Oordered__semiring(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_64])]) ).

fof(f3939,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/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__semiring) ).

fof(f6364,plain,
    spl50_63,
    inference(avatar_split_clause,[],[f3938,f6361]) ).

fof(f6361,plain,
    ( spl50_63
  <=> class_Rings_Oordered__semiring(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_63])]) ).

fof(f3938,plain,
    class_Rings_Oordered__semiring(tc_Int_Oint),
    inference(cnf_transformation,[],[f1030]) ).

fof(f1030,axiom,
    class_Rings_Oordered__semiring(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__semiring) ).

fof(f6359,plain,
    spl50_62,
    inference(avatar_split_clause,[],[f3937,f6356]) ).

fof(f6356,plain,
    ( spl50_62
  <=> class_Rings_Oordered__semiring(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_62])]) ).

fof(f3937,plain,
    class_Rings_Oordered__semiring(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1138]) ).

fof(f1138,axiom,
    class_Rings_Oordered__semiring(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__semiring) ).

fof(f6354,plain,
    spl50_61,
    inference(avatar_split_clause,[],[f3936,f6351]) ).

fof(f6351,plain,
    ( spl50_61
  <=> class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_61])]) ).

fof(f3936,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/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) ).

fof(f6349,plain,
    spl50_60,
    inference(avatar_split_clause,[],[f3935,f6346]) ).

fof(f6346,plain,
    ( spl50_60
  <=> class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_60])]) ).

fof(f3935,plain,
    class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
    inference(cnf_transformation,[],[f1013]) ).

fof(f1013,axiom,
    class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add) ).

fof(f6344,plain,
    spl50_59,
    inference(avatar_split_clause,[],[f3934,f6341]) ).

fof(f6341,plain,
    ( spl50_59
  <=> class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_59])]) ).

fof(f3934,plain,
    class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1117]) ).

fof(f1117,axiom,
    class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add) ).

fof(f6339,plain,
    spl50_58,
    inference(avatar_split_clause,[],[f3933,f6336]) ).

fof(f6336,plain,
    ( spl50_58
  <=> class_Rings_Olinordered__semiring(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_58])]) ).

fof(f3933,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/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring) ).

fof(f6334,plain,
    spl50_57,
    inference(avatar_split_clause,[],[f3932,f6331]) ).

fof(f6331,plain,
    ( spl50_57
  <=> class_Rings_Oring__1(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_57])]) ).

fof(f3932,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/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1) ).

fof(f6329,plain,
    spl50_56,
    inference(avatar_split_clause,[],[f3931,f6326]) ).

fof(f6326,plain,
    ( spl50_56
  <=> class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_56])]) ).

fof(f3931,plain,
    class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
    inference(cnf_transformation,[],[f1017]) ).

fof(f1017,axiom,
    class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1__no__zero__divisors) ).

fof(f6324,plain,
    spl50_55,
    inference(avatar_split_clause,[],[f3930,f6321]) ).

fof(f6321,plain,
    ( spl50_55
  <=> class_Rings_Olinordered__semiring(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_55])]) ).

fof(f3930,plain,
    class_Rings_Olinordered__semiring(tc_Int_Oint),
    inference(cnf_transformation,[],[f1025]) ).

fof(f1025,axiom,
    class_Rings_Olinordered__semiring(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring) ).

fof(f6319,plain,
    spl50_54,
    inference(avatar_split_clause,[],[f3929,f6316]) ).

fof(f6316,plain,
    ( spl50_54
  <=> class_Int_Oring__char__0(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_54])]) ).

fof(f3929,plain,
    class_Int_Oring__char__0(tc_Int_Oint),
    inference(cnf_transformation,[],[f1051]) ).

fof(f1051,axiom,
    class_Int_Oring__char__0(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Int_Oring__char__0) ).

fof(f6314,plain,
    spl50_53,
    inference(avatar_split_clause,[],[f3928,f6311]) ).

fof(f6311,plain,
    ( spl50_53
  <=> class_Rings_Oring__1(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_53])]) ).

fof(f3928,plain,
    class_Rings_Oring__1(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1165]) ).

fof(f1165,axiom,
    class_Rings_Oring__1(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__1) ).

fof(f6309,plain,
    spl50_52,
    inference(avatar_split_clause,[],[f3927,f6306]) ).

fof(f6306,plain,
    ( spl50_52
  <=> class_Rings_Olinordered__semiring(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_52])]) ).

fof(f3927,plain,
    class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1131]) ).

fof(f1131,axiom,
    class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring) ).

fof(f6304,plain,
    spl50_51,
    inference(avatar_split_clause,[],[f3926,f6301]) ).

fof(f6301,plain,
    ( spl50_51
  <=> class_Int_Oring__char__0(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_51])]) ).

fof(f3926,plain,
    class_Int_Oring__char__0(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1160]) ).

fof(f1160,axiom,
    class_Int_Oring__char__0(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Int_Oring__char__0) ).

fof(f6299,plain,
    spl50_50,
    inference(avatar_split_clause,[],[f3925,f6296]) ).

fof(f6296,plain,
    ( spl50_50
  <=> class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_50])]) ).

fof(f3925,plain,
    class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1122]) ).

fof(f1122,axiom,
    class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors) ).

fof(f6294,plain,
    spl50_49,
    inference(avatar_split_clause,[],[f3924,f6291]) ).

fof(f6291,plain,
    ( spl50_49
  <=> class_Rings_Oring__1(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_49])]) ).

fof(f3924,plain,
    class_Rings_Oring__1(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1206]) ).

fof(f1206,axiom,
    class_Rings_Oring__1(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__1) ).

fof(f6289,plain,
    spl50_48,
    inference(avatar_split_clause,[],[f3923,f6286]) ).

fof(f3923,plain,
    class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1180]) ).

fof(f1180,axiom,
    class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors) ).

fof(f6284,plain,
    spl50_47,
    inference(avatar_split_clause,[],[f3922,f6281]) ).

fof(f6281,plain,
    ( spl50_47
  <=> class_Int_Oring__char__0(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_47])]) ).

fof(f3922,plain,
    class_Int_Oring__char__0(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1203]) ).

fof(f1203,axiom,
    class_Int_Oring__char__0(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Int_Oring__char__0) ).

fof(f6279,plain,
    spl50_46,
    inference(avatar_split_clause,[],[f3921,f6276]) ).

fof(f6276,plain,
    ( spl50_46
  <=> class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_46])]) ).

fof(f3921,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/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__comm__semiring) ).

fof(f6274,plain,
    spl50_45,
    inference(avatar_split_clause,[],[f3920,f6271]) ).

fof(f6271,plain,
    ( spl50_45
  <=> class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_45])]) ).

fof(f3920,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/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict) ).

fof(f6269,plain,
    spl50_44,
    inference(avatar_split_clause,[],[f3919,f6266]) ).

fof(f6266,plain,
    ( spl50_44
  <=> class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_44])]) ).

fof(f3919,plain,
    class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
    inference(cnf_transformation,[],[f1020]) ).

fof(f1020,axiom,
    class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__no__zero__divisors) ).

fof(f6264,plain,
    spl50_43,
    inference(avatar_split_clause,[],[f3918,f6261]) ).

fof(f6261,plain,
    ( spl50_43
  <=> class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_43])]) ).

fof(f3918,plain,
    class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
    inference(cnf_transformation,[],[f1010]) ).

fof(f1010,axiom,
    class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__comm__semiring__strict) ).

fof(f6259,plain,
    spl50_42,
    inference(avatar_split_clause,[],[f3917,f6256]) ).

fof(f6256,plain,
    ( spl50_42
  <=> class_Rings_Oordered__comm__semiring(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_42])]) ).

fof(f3917,plain,
    class_Rings_Oordered__comm__semiring(tc_Int_Oint),
    inference(cnf_transformation,[],[f1021]) ).

fof(f1021,axiom,
    class_Rings_Oordered__comm__semiring(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__comm__semiring) ).

fof(f6254,plain,
    spl50_41,
    inference(avatar_split_clause,[],[f3916,f6251]) ).

fof(f6251,plain,
    ( spl50_41
  <=> class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_41])]) ).

fof(f3916,plain,
    class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1127]) ).

fof(f1127,axiom,
    class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__comm__semiring) ).

fof(f6249,plain,
    spl50_40,
    inference(avatar_split_clause,[],[f3915,f6246]) ).

fof(f6246,plain,
    ( spl50_40
  <=> class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_40])]) ).

fof(f3915,plain,
    class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1126]) ).

fof(f1126,axiom,
    class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__no__zero__divisors) ).

fof(f6244,plain,
    spl50_39,
    inference(avatar_split_clause,[],[f3914,f6241]) ).

fof(f6241,plain,
    ( spl50_39
  <=> class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_39])]) ).

fof(f3914,plain,
    class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1110]) ).

fof(f1110,axiom,
    class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict) ).

fof(f6239,plain,
    spl50_38,
    inference(avatar_split_clause,[],[f3913,f6236]) ).

fof(f6236,plain,
    ( spl50_38
  <=> class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_38])]) ).

fof(f3913,plain,
    class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1182]) ).

fof(f1182,axiom,
    class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors) ).

fof(f6234,plain,
    spl50_37,
    inference(avatar_split_clause,[],[f3912,f6231]) ).

fof(f6231,plain,
    ( spl50_37
  <=> class_Rings_Olinordered__idom(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_37])]) ).

fof(f3912,plain,
    class_Rings_Olinordered__idom(tc_Int_Oint),
    inference(cnf_transformation,[],[f1034]) ).

fof(f1034,axiom,
    class_Rings_Olinordered__idom(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__idom) ).

fof(f6229,plain,
    spl50_36,
    inference(avatar_split_clause,[],[f3911,f6226]) ).

fof(f6226,plain,
    ( spl50_36
  <=> class_Rings_Olinordered__idom(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_36])]) ).

fof(f3911,plain,
    class_Rings_Olinordered__idom(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1142]) ).

fof(f1142,axiom,
    class_Rings_Olinordered__idom(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__idom) ).

fof(f6224,plain,
    spl50_35,
    inference(avatar_split_clause,[],[f3910,f6221]) ).

fof(f6221,plain,
    ( spl50_35
  <=> class_Groups_Oordered__ab__group__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_35])]) ).

fof(f3910,plain,
    class_Groups_Oordered__ab__group__add(tc_Int_Oint),
    inference(cnf_transformation,[],[f1023]) ).

fof(f1023,axiom,
    class_Groups_Oordered__ab__group__add(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__group__add) ).

fof(f6219,plain,
    spl50_34,
    inference(avatar_split_clause,[],[f3909,f6216]) ).

fof(f6216,plain,
    ( spl50_34
  <=> class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_34])]) ).

fof(f3909,plain,
    class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1129]) ).

fof(f1129,axiom,
    class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__group__add) ).

fof(f6214,plain,
    spl50_33,
    inference(avatar_split_clause,[],[f3908,f6211]) ).

fof(f6211,plain,
    ( spl50_33
  <=> class_Rings_Olinordered__ring__strict(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_33])]) ).

fof(f3908,plain,
    class_Rings_Olinordered__ring__strict(tc_Int_Oint),
    inference(cnf_transformation,[],[f1019]) ).

fof(f1019,axiom,
    class_Rings_Olinordered__ring__strict(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring__strict) ).

fof(f6209,plain,
    spl50_32,
    inference(avatar_split_clause,[],[f3907,f6206]) ).

fof(f6206,plain,
    ( spl50_32
  <=> class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_32])]) ).

fof(f3907,plain,
    class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1125]) ).

fof(f1125,axiom,
    class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__ring__strict) ).

fof(f6204,plain,
    spl50_31,
    inference(avatar_split_clause,[],[f3906,f6201]) ).

fof(f6201,plain,
    ( spl50_31
  <=> class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_31])]) ).

fof(f3906,plain,
    class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
    inference(cnf_transformation,[],[f1015]) ).

fof(f1015,axiom,
    class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Olinordered__ab__group__add) ).

fof(f6199,plain,
    spl50_30,
    inference(avatar_split_clause,[],[f3905,f6196]) ).

fof(f6196,plain,
    ( spl50_30
  <=> class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_30])]) ).

fof(f3905,plain,
    class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1120]) ).

fof(f1120,axiom,
    class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Olinordered__ab__group__add) ).

fof(f6194,plain,
    spl50_29,
    inference(avatar_split_clause,[],[f3904,f6191]) ).

fof(f6191,plain,
    ( spl50_29
  <=> class_Rings_Oordered__ring(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_29])]) ).

fof(f3904,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/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring) ).

fof(f6189,plain,
    spl50_28,
    inference(avatar_split_clause,[],[f3903,f6186]) ).

fof(f6186,plain,
    ( spl50_28
  <=> class_Rings_Oordered__ring(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_28])]) ).

fof(f3903,plain,
    class_Rings_Oordered__ring(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1149]) ).

fof(f1149,axiom,
    class_Rings_Oordered__ring(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__ring) ).

fof(f6184,plain,
    spl50_27,
    inference(avatar_split_clause,[],[f3902,f6181]) ).

fof(f6181,plain,
    ( spl50_27
  <=> class_Rings_Olinordered__ring(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_27])]) ).

fof(f3902,plain,
    class_Rings_Olinordered__ring(tc_Int_Oint),
    inference(cnf_transformation,[],[f1033]) ).

fof(f1033,axiom,
    class_Rings_Olinordered__ring(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring) ).

fof(f6179,plain,
    spl50_26,
    inference(avatar_split_clause,[],[f3901,f6176]) ).

fof(f6176,plain,
    ( spl50_26
  <=> class_Rings_Olinordered__ring(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_26])]) ).

fof(f3901,plain,
    class_Rings_Olinordered__ring(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1141]) ).

fof(f1141,axiom,
    class_Rings_Olinordered__ring(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__ring) ).

fof(f6174,plain,
    spl50_25,
    inference(avatar_split_clause,[],[f3900,f6171]) ).

fof(f6171,plain,
    ( spl50_25
  <=> class_Groups_Osgn__if(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_25])]) ).

fof(f3900,plain,
    class_Groups_Osgn__if(tc_Int_Oint),
    inference(cnf_transformation,[],[f1055]) ).

fof(f1055,axiom,
    class_Groups_Osgn__if(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Osgn__if) ).

fof(f6169,plain,
    spl50_24,
    inference(avatar_split_clause,[],[f3899,f6166]) ).

fof(f6166,plain,
    ( spl50_24
  <=> class_Groups_Osgn__if(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_24])]) ).

fof(f3899,plain,
    class_Groups_Osgn__if(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1164]) ).

fof(f1164,axiom,
    class_Groups_Osgn__if(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Osgn__if) ).

fof(f6164,plain,
    spl50_23,
    inference(avatar_split_clause,[],[f3898,f6161]) ).

fof(f6161,plain,
    ( spl50_23
  <=> class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_23])]) ).

fof(f3898,plain,
    class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
    inference(cnf_transformation,[],[f1011]) ).

fof(f1011,axiom,
    class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1__strict) ).

fof(f6159,plain,
    spl50_22,
    inference(avatar_split_clause,[],[f3897,f6156]) ).

fof(f6156,plain,
    ( spl50_22
  <=> class_Rings_Olinordered__semiring__1(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_22])]) ).

fof(f3897,plain,
    class_Rings_Olinordered__semiring__1(tc_Int_Oint),
    inference(cnf_transformation,[],[f1022]) ).

fof(f1022,axiom,
    class_Rings_Olinordered__semiring__1(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1) ).

fof(f6154,plain,
    spl50_21,
    inference(avatar_split_clause,[],[f3896,f6151]) ).

fof(f6151,plain,
    ( spl50_21
  <=> class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_21])]) ).

fof(f3896,plain,
    class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1112]) ).

fof(f1112,axiom,
    class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict) ).

fof(f6149,plain,
    spl50_20,
    inference(avatar_split_clause,[],[f3895,f6146]) ).

fof(f6146,plain,
    ( spl50_20
  <=> class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_20])]) ).

fof(f3895,plain,
    class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1128]) ).

fof(f1128,axiom,
    class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__1) ).

fof(f6144,plain,
    spl50_19,
    inference(avatar_split_clause,[],[f3894,f6141]) ).

fof(f6141,plain,
    ( spl50_19
  <=> class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_19])]) ).

fof(f3894,plain,
    class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1118]) ).

fof(f1118,axiom,
    class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).

fof(f6139,plain,
    spl50_18,
    inference(avatar_split_clause,[],[f3893,f6136]) ).

fof(f6136,plain,
    ( spl50_18
  <=> class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_18])]) ).

fof(f3893,plain,
    class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1178]) ).

fof(f1178,axiom,
    class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).

fof(f6134,plain,
    spl50_17,
    inference(avatar_split_clause,[],[f3892,f6131]) ).

fof(f3892,plain,
    class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1124]) ).

fof(f1124,axiom,
    class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).

fof(f6129,plain,
    spl50_16,
    inference(avatar_split_clause,[],[f3891,f6126]) ).

fof(f3891,plain,
    class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1181]) ).

fof(f1181,axiom,
    class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).

fof(f6124,plain,
    spl50_15,
    inference(avatar_split_clause,[],[f3890,f6121]) ).

fof(f3890,plain,
    class_Rings_Odivision__ring(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1145]) ).

fof(f1145,axiom,
    class_Rings_Odivision__ring(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Odivision__ring) ).

fof(f6119,plain,
    spl50_14,
    inference(avatar_split_clause,[],[f3889,f6116]) ).

fof(f3889,plain,
    class_Rings_Odivision__ring(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1192]) ).

fof(f1192,axiom,
    class_Rings_Odivision__ring(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odivision__ring) ).

fof(f6114,plain,
    spl50_13,
    inference(avatar_split_clause,[],[f3888,f6111]) ).

fof(f3888,plain,
    class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1115]) ).

fof(f1115,axiom,
    class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero) ).

fof(f6109,plain,
    spl50_12,
    inference(avatar_split_clause,[],[f3887,f6106]) ).

fof(f3887,plain,
    class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1176]) ).

fof(f1176,axiom,
    class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero) ).

fof(f6104,plain,
    spl50_11,
    inference(avatar_split_clause,[],[f3886,f6101]) ).

fof(f6101,plain,
    ( spl50_11
  <=> class_Fields_Ofield(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_11])]) ).

fof(f3886,plain,
    class_Fields_Ofield(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1167]) ).

fof(f1167,axiom,
    class_Fields_Ofield(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Ofield) ).

fof(f6099,plain,
    spl50_10,
    inference(avatar_split_clause,[],[f3885,f6096]) ).

fof(f6096,plain,
    ( spl50_10
  <=> class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_10])]) ).

fof(f3885,plain,
    class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1113]) ).

fof(f1113,axiom,
    class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra) ).

fof(f6094,plain,
    spl50_9,
    inference(avatar_split_clause,[],[f3884,f6091]) ).

fof(f3884,plain,
    class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1175]) ).

fof(f1175,axiom,
    class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) ).

fof(f6089,plain,
    spl50_8,
    inference(avatar_split_clause,[],[f3883,f6086]) ).

fof(f6086,plain,
    ( spl50_8
  <=> class_Fields_Ofield(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_8])]) ).

fof(f3883,plain,
    class_Fields_Ofield(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1208]) ).

fof(f1208,axiom,
    class_Fields_Ofield(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Fields_Ofield) ).

fof(f6084,plain,
    spl50_7,
    inference(avatar_split_clause,[],[f3882,f6081]) ).

fof(f3882,plain,
    class_Lattices_Oboolean__algebra(tc_HOL_Obool),
    inference(cnf_transformation,[],[f1101]) ).

fof(f1101,axiom,
    class_Lattices_Oboolean__algebra(tc_HOL_Obool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Oboolean__algebra) ).

fof(f6079,plain,
    spl50_6,
    inference(avatar_split_clause,[],[f3881,f6076]) ).

fof(f3881,plain,
    class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1116]) ).

fof(f1116,axiom,
    class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1) ).

fof(f6074,plain,
    spl50_5,
    inference(avatar_split_clause,[],[f3880,f6071]) ).

fof(f6071,plain,
    ( spl50_5
  <=> class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_5])]) ).

fof(f3880,plain,
    class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1132]) ).

fof(f1132,axiom,
    class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Ofield__inverse__zero) ).

fof(f6069,plain,
    spl50_4,
    inference(avatar_split_clause,[],[f3879,f6066]) ).

fof(f3879,plain,
    class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1177]) ).

fof(f1177,axiom,
    class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) ).

fof(f6064,plain,
    spl50_3,
    inference(avatar_split_clause,[],[f3878,f6061]) ).

fof(f3878,plain,
    class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1184]) ).

fof(f1184,axiom,
    class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Fields_Ofield__inverse__zero) ).

fof(f6059,plain,
    spl50_2,
    inference(avatar_split_clause,[],[f3877,f6056]) ).

fof(f6056,plain,
    ( spl50_2
  <=> class_Fields_Olinordered__field(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_2])]) ).

fof(f3877,plain,
    class_Fields_Olinordered__field(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1137]) ).

fof(f1137,axiom,
    class_Fields_Olinordered__field(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Olinordered__field) ).

fof(f6054,plain,
    spl50_1,
    inference(avatar_split_clause,[],[f3876,f6051]) ).

fof(f3876,plain,
    class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1111]) ).

fof(f1111,axiom,
    class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SWW258+1 : TPTP v8.2.0. Released v5.2.0.
% 0.13/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35  % Computer : n017.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Sat May 18 19:04:38 EDT 2024
% 0.15/0.35  % CPUTime    : 
% 0.22/0.36  % (20134)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.42  % (20137)WARNING: value z3 for option sas not known
% 0.22/0.42  % (20136)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.42  % (20137)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)
% 0.22/0.42  % (20139)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)
% 0.22/0.42  % (20141)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)
% 0.22/0.42  % (20135)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.42  % (20138)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.42  % (20140)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)
% 1.96/0.66  TRYING [1]
% 1.96/0.71  TRYING [2]
% 6.50/1.32  % (20139)First to succeed.
% 6.94/1.41  % (20139)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-20134"
% 6.94/1.42  % (20139)Refutation found. Thanks to Tanya!
% 6.94/1.42  % SZS status Theorem for theBenchmark
% 6.94/1.42  % SZS output start Proof for theBenchmark
% See solution above
% 7.34/1.47  % (20139)------------------------------
% 7.34/1.47  % (20139)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 7.34/1.47  % (20139)Termination reason: Refutation
% 7.34/1.47  
% 7.34/1.47  % (20139)Memory used [KB]: 13251
% 7.34/1.47  % (20139)Time elapsed: 0.993 s
% 7.34/1.47  % (20139)Instructions burned: 1717 (million)
% 7.34/1.47  % (20134)Success in time 1.08 s
%------------------------------------------------------------------------------