TSTP Solution File: SWW209+1 by Vampire-SAT---4.8

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SWW209+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n010.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Apr 30 17:28:32 EDT 2024

% Result   : Theorem 1.38s 0.60s
% Output   : Refutation 1.46s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :  948
% Syntax   : Number of formulae    : 2628 (1083 unt;   0 def)
%            Number of atoms       : 5652 (1379 equ)
%            Maximal formula atoms :   13 (   2 avg)
%            Number of connectives : 4613 (1589   ~;1529   |; 497   &)
%                                         ( 685 <=>; 313  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   3 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :  588 ( 586 usr; 500 prp; 0-4 aty)
%            Number of functors    :   56 (  56 usr;  10 con; 0-5 aty)
%            Number of variables   : 3135 (3028   !; 107   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f9758,plain,
    $false,
    inference(avatar_sat_refutation,[],[f5859,f5864,f5869,f5874,f5879,f5884,f5889,f5894,f5899,f5904,f5909,f5914,f5919,f5924,f5929,f5934,f5939,f5944,f5949,f5954,f5959,f5964,f5969,f5974,f5979,f5984,f5989,f5994,f5999,f6004,f6009,f6014,f6019,f6024,f6029,f6034,f6039,f6044,f6049,f6054,f6059,f6064,f6069,f6074,f6079,f6084,f6089,f6094,f6099,f6104,f6109,f6114,f6119,f6124,f6129,f6134,f6139,f6144,f6149,f6154,f6159,f6164,f6169,f6174,f6179,f6184,f6189,f6194,f6199,f6204,f6209,f6214,f6219,f6224,f6229,f6234,f6239,f6244,f6249,f6254,f6259,f6264,f6269,f6274,f6279,f6284,f6289,f6294,f6299,f6304,f6309,f6314,f6319,f6324,f6329,f6334,f6339,f6344,f6349,f6354,f6359,f6364,f6369,f6374,f6379,f6384,f6389,f6394,f6399,f6404,f6409,f6414,f6419,f6424,f6429,f6434,f6439,f6444,f6449,f6454,f6459,f6464,f6469,f6474,f6479,f6484,f6489,f6494,f6499,f6504,f6509,f6514,f6519,f6524,f6529,f6534,f6539,f6544,f6549,f6554,f6559,f6564,f6569,f6574,f6579,f6584,f6589,f6594,f6599,f6604,f6609,f6614,f6619,f6624,f6629,f6634,f6639,f6644,f6649,f6654,f6659,f6663,f6667,f6671,f6675,f6680,f6687,f6692,f6697,f6702,f6706,f6710,f6714,f6718,f6723,f6728,f6733,f6738,f6743,f6748,f6753,f6758,f6763,f6768,f6773,f6778,f6782,f6786,f6790,f6794,f6798,f6802,f6806,f6810,f6814,f6818,f6822,f6826,f6830,f6834,f6839,f6844,f6849,f6854,f6859,f6863,f6867,f6871,f6875,f6879,f6883,f6887,f6891,f6895,f6899,f6903,f6907,f6911,f6915,f6919,f6923,f6927,f6937,f6946,f6952,f6957,f6962,f6967,f6972,f6976,f6980,f6984,f6988,f6992,f6996,f7000,f7004,f7008,f7012,f7016,f7020,f7024,f7028,f7032,f7036,f7040,f7044,f7048,f7052,f7056,f7060,f7065,f7088,f7095,f7099,f7103,f7108,f7112,f7116,f7120,f7124,f7128,f7132,f7136,f7140,f7144,f7148,f7152,f7156,f7160,f7164,f7168,f7172,f7176,f7180,f7184,f7188,f7192,f7196,f7200,f7204,f7208,f7212,f7216,f7220,f7224,f7228,f7232,f7236,f7240,f7244,f7248,f7252,f7256,f7260,f7264,f7269,f7409,f7433,f7437,f7441,f7445,f7449,f7453,f7457,f7461,f7465,f7469,f7473,f7477,f7481,f7485,f7489,f7493,f7497,f7501,f7505,f7509,f7513,f7517,f7521,f7525,f7529,f7533,f7537,f7541,f7545,f7549,f7553,f7557,f7561,f7565,f7569,f7573,f7577,f7581,f7633,f7688,f7754,f7758,f7762,f7766,f7770,f7774,f7778,f7782,f7786,f7790,f7794,f7798,f7802,f7806,f7810,f7814,f7818,f7822,f7826,f7830,f7835,f7839,f7843,f7847,f7851,f7855,f7859,f7863,f7867,f7871,f7876,f7880,f7884,f7888,f7892,f7896,f7900,f7904,f7908,f7912,f7917,f7921,f7925,f7929,f7933,f7937,f7941,f7945,f7949,f7953,f7957,f7962,f7966,f7970,f7974,f7978,f7982,f7986,f7990,f7994,f7998,f8002,f8007,f8011,f8015,f8019,f8023,f8027,f8031,f8035,f8039,f8043,f8047,f8052,f8056,f8060,f8064,f8103,f8221,f8252,f8321,f8573,f8648,f8662,f8666,f8671,f8675,f8679,f8708,f8712,f8716,f8720,f8724,f8728,f8732,f8736,f8740,f8744,f8749,f8753,f8757,f8761,f8765,f8769,f8773,f8777,f8781,f8785,f8789,f8794,f8798,f8802,f8806,f8810,f8814,f8818,f8822,f8826,f8830,f8834,f8838,f8842,f8846,f8850,f8854,f8858,f8862,f8866,f8870,f8874,f8878,f8882,f8886,f8890,f8894,f8898,f8902,f8906,f8910,f8914,f8923,f8927,f8931,f8935,f8939,f8943,f8947,f8953,f8957,f8962,f8966,f8970,f8974,f8978,f8982,f8990,f9233,f9489,f9711,f9757]) ).

fof(f9757,plain,
    ( ~ spl77_1
    | ~ spl77_459
    | spl77_498 ),
    inference(avatar_split_clause,[],[f9620,f9486,f8836,f5856]) ).

fof(f5856,plain,
    ( spl77_1
  <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK23,sK24) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_1])]) ).

fof(f8836,plain,
    ( spl77_459
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_ga____,X0),hAPP(v_ga____,X1))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_459])]) ).

fof(f9486,plain,
    ( spl77_498
  <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_ga____,sK23),hAPP(v_ga____,sK24)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_498])]) ).

fof(f9620,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK23,sK24)
    | ~ spl77_459
    | spl77_498 ),
    inference(resolution,[],[f9488,f8837]) ).

fof(f8837,plain,
    ( ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_ga____,X0),hAPP(v_ga____,X1))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) )
    | ~ spl77_459 ),
    inference(avatar_component_clause,[],[f8836]) ).

fof(f9488,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_ga____,sK23),hAPP(v_ga____,sK24))
    | spl77_498 ),
    inference(avatar_component_clause,[],[f9486]) ).

fof(f9711,plain,
    ( spl77_499
    | ~ spl77_137
    | ~ spl77_377
    | ~ spl77_486 ),
    inference(avatar_split_clause,[],[f8949,f8945,f7906,f6536,f9709]) ).

fof(f9709,plain,
    ( spl77_499
  <=> ! [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,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_499])]) ).

fof(f6536,plain,
    ( spl77_137
  <=> class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_137])]) ).

fof(f7906,plain,
    ( spl77_377
  <=> ! [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,[spl77_377])]) ).

fof(f8945,plain,
    ( spl77_486
  <=> ! [X0] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(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,[spl77_486])]) ).

fof(f8949,plain,
    ( ! [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,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0)))
    | ~ spl77_137
    | ~ spl77_377
    | ~ spl77_486 ),
    inference(forward_demodulation,[],[f8948,f8322]) ).

fof(f8322,plain,
    ( ! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1)
    | ~ spl77_137
    | ~ spl77_377 ),
    inference(resolution,[],[f7907,f6538]) ).

fof(f6538,plain,
    ( class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)
    | ~ spl77_137 ),
    inference(avatar_component_clause,[],[f6536]) ).

fof(f7907,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) )
    | ~ spl77_377 ),
    inference(avatar_component_clause,[],[f7906]) ).

fof(f8948,plain,
    ( ! [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,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
    | ~ spl77_486 ),
    inference(forward_demodulation,[],[f8946,f5321]) ).

fof(f5321,plain,
    ! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
    inference(definition_unfolding,[],[f3910,f3879]) ).

fof(f3879,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,[],[f1199]) ).

fof(f1199,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,[],[f264]) ).

fof(f264,axiom,
    ! [X21] : c_Nat_OSuc(X21) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).

fof(f3910,plain,
    ! [X0] : hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(X0)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
    inference(cnf_transformation,[],[f1230]) ).

fof(f1230,plain,
    ! [X0] : hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(X0)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
    inference(rectify,[],[f682]) ).

fof(f682,axiom,
    ! [X21] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X21),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(X21)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__Suc) ).

fof(f8946,plain,
    ( ! [X0] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | ~ spl77_486 ),
    inference(avatar_component_clause,[],[f8945]) ).

fof(f9489,plain,
    ( ~ spl77_498
    | spl77_167
    | ~ spl77_458 ),
    inference(avatar_split_clause,[],[f9404,f8832,f6684,f9486]) ).

fof(f6684,plain,
    ( spl77_167
  <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_f____,hAPP(v_ga____,sK23)),hAPP(v_f____,hAPP(v_ga____,sK24))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_167])]) ).

fof(f8832,plain,
    ( spl77_458
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_f____,X0),hAPP(v_f____,X1))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_458])]) ).

fof(f9404,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_ga____,sK23),hAPP(v_ga____,sK24))
    | spl77_167
    | ~ spl77_458 ),
    inference(resolution,[],[f8833,f6686]) ).

fof(f6686,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_f____,hAPP(v_ga____,sK23)),hAPP(v_f____,hAPP(v_ga____,sK24)))
    | spl77_167 ),
    inference(avatar_component_clause,[],[f6684]) ).

fof(f8833,plain,
    ( ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_f____,X0),hAPP(v_f____,X1))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) )
    | ~ spl77_458 ),
    inference(avatar_component_clause,[],[f8832]) ).

fof(f9233,plain,
    ( spl77_496
    | ~ spl77_497
    | ~ spl77_227
    | ~ spl77_420 ),
    inference(avatar_split_clause,[],[f8702,f8571,f6959,f9230,f9226]) ).

fof(f9226,plain,
    ( spl77_496
  <=> sP14(c_RealDef_Oreal(tc_Nat_Onat),sK23,sK24) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_496])]) ).

fof(f9230,plain,
    ( spl77_497
  <=> hBOOL(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_497])]) ).

fof(f6959,plain,
    ( spl77_227
  <=> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_227])]) ).

fof(f8571,plain,
    ( spl77_420
  <=> ! [X0] :
        ( ~ hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | sP14(X0,sK23,sK24) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_420])]) ).

fof(f8702,plain,
    ( ~ hBOOL(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    | sP14(c_RealDef_Oreal(tc_Nat_Onat),sK23,sK24)
    | ~ spl77_227
    | ~ spl77_420 ),
    inference(superposition,[],[f8572,f6961]) ).

fof(f6961,plain,
    ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ spl77_227 ),
    inference(avatar_component_clause,[],[f6959]) ).

fof(f8572,plain,
    ( ! [X0] :
        ( ~ hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | sP14(X0,sK23,sK24) )
    | ~ spl77_420 ),
    inference(avatar_component_clause,[],[f8571]) ).

fof(f8990,plain,
    ( spl77_495
    | ~ spl77_137
    | ~ spl77_377
    | ~ spl77_423 ),
    inference(avatar_split_clause,[],[f8667,f8664,f7906,f6536,f8988]) ).

fof(f8988,plain,
    ( spl77_495
  <=> ! [X0] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(X0)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_495])]) ).

fof(f8664,plain,
    ( spl77_423
  <=> ! [X0] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(X0)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_423])]) ).

fof(f8667,plain,
    ( ! [X0] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(X0))))
    | ~ spl77_137
    | ~ spl77_377
    | ~ spl77_423 ),
    inference(forward_demodulation,[],[f8665,f8322]) ).

fof(f8665,plain,
    ( ! [X0] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(X0)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
    | ~ spl77_423 ),
    inference(avatar_component_clause,[],[f8664]) ).

fof(f8982,plain,
    spl77_494,
    inference(avatar_split_clause,[],[f5712,f8980]) ).

fof(f8980,plain,
    ( spl77_494
  <=> ! [X0] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(c_Int_Onat,X0))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_494])]) ).

fof(f5712,plain,
    ! [X0] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(c_Int_Onat,X0))
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0) ),
    inference(forward_demodulation,[],[f5711,f3871]) ).

fof(f3871,plain,
    ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
    inference(cnf_transformation,[],[f1191]) ).

fof(f1191,plain,
    ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
    inference(rectify,[],[f282]) ).

fof(f282,axiom,
    ! [X26] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X26,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X26,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).

fof(f5711,plain,
    ! [X0] :
      ( ~ 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(c_Int_Onat,X0))
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0) ),
    inference(forward_demodulation,[],[f5337,f5313]) ).

fof(f5313,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,[],[f3880,f3879]) ).

fof(f3880,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,[],[f1200]) ).

fof(f1200,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,[],[f263]) ).

fof(f263,axiom,
    ! [X21] : c_Nat_OSuc(X21) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X21),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).

fof(f5337,plain,
    ! [X0] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),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)),hAPP(c_Int_Onat,X0)) ),
    inference(definition_unfolding,[],[f3997,f3879]) ).

fof(f3997,plain,
    ! [X0] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,X0)) ),
    inference(cnf_transformation,[],[f3207]) ).

fof(f3207,plain,
    ! [X0] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,X0))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,X0)) ) ),
    inference(nnf_transformation,[],[f1293]) ).

fof(f1293,plain,
    ! [X0] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,X0))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0) ),
    inference(rectify,[],[f658]) ).

fof(f658,axiom,
    ! [X50] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,X50))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X50) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__less__nat__eq) ).

fof(f8978,plain,
    spl77_493,
    inference(avatar_split_clause,[],[f5710,f8976]) ).

fof(f8976,plain,
    ( spl77_493
  <=> ! [X0] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(c_Int_Onat,X0))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_493])]) ).

fof(f5710,plain,
    ! [X0] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(c_Int_Onat,X0))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0) ),
    inference(forward_demodulation,[],[f5709,f3871]) ).

fof(f5709,plain,
    ! [X0] :
      ( 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(c_Int_Onat,X0))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0) ),
    inference(forward_demodulation,[],[f5336,f5313]) ).

fof(f5336,plain,
    ! [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)),hAPP(c_Int_Onat,X0))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0) ),
    inference(definition_unfolding,[],[f3998,f3879]) ).

fof(f3998,plain,
    ! [X0] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,X0))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0) ),
    inference(cnf_transformation,[],[f3207]) ).

fof(f8974,plain,
    spl77_492,
    inference(avatar_split_clause,[],[f5582,f8972]) ).

fof(f8972,plain,
    ( spl77_492
  <=> ! [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,[spl77_492])]) ).

fof(f5582,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,[],[f4618]) ).

fof(f4618,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,[],[f3443]) ).

fof(f3443,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,[],[f3442]) ).

fof(f3442,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,[],[f2490]) ).

fof(f2490,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,[],[f1688]) ).

fof(f1688,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,[],[f212]) ).

fof(f212,axiom,
    ! [X17,X18,X7] :
      ( class_Rings_Oring__no__zero__divisors(X7)
     => ( c_Groups_Ozero__class_Ozero(X7) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X18),X17)
      <=> ( c_Groups_Ozero__class_Ozero(X7) = X17
          | c_Groups_Ozero__class_Ozero(X7) = X18 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__0__iff) ).

fof(f8970,plain,
    spl77_491,
    inference(avatar_split_clause,[],[f5581,f8968]) ).

fof(f8968,plain,
    ( spl77_491
  <=> ! [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,[spl77_491])]) ).

fof(f5581,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,[],[f4619]) ).

fof(f4619,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,[],[f3443]) ).

fof(f8966,plain,
    spl77_490,
    inference(avatar_split_clause,[],[f5540,f8964]) ).

fof(f8964,plain,
    ( spl77_490
  <=> ! [X2,X1] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_490])]) ).

fof(f5540,plain,
    ! [X2,X1] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))),
    inference(equality_resolution,[],[f4449]) ).

fof(f4449,plain,
    ! [X2,X0,X1] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X0))
      | c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)) != X0 ),
    inference(cnf_transformation,[],[f3362]) ).

fof(f3362,plain,
    ! [X0,X1] :
      ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X0))
        | ! [X2] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)) != X0 )
      & ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK59(X0,X1))) = X0
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X0)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK59])],[f3360,f3361]) ).

fof(f3361,plain,
    ! [X0,X1] :
      ( ? [X3] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3)) = X0
     => c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK59(X0,X1))) = X0 ),
    introduced(choice_axiom,[]) ).

fof(f3360,plain,
    ! [X0,X1] :
      ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X0))
        | ! [X2] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)) != X0 )
      & ( ? [X3] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3)) = X0
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X0)) ) ),
    inference(rectify,[],[f3359]) ).

fof(f3359,plain,
    ! [X0,X1] :
      ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X0))
        | ! [X2] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)) != X0 )
      & ( ? [X2] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)) = X0
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X0)) ) ),
    inference(nnf_transformation,[],[f1605]) ).

fof(f1605,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X0))
    <=> ? [X2] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)) = X0 ),
    inference(rectify,[],[f518]) ).

fof(f518,axiom,
    ! [X50,X51] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X51),X50))
    <=> ? [X4] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X51,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4)) = X50 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__iff__zadd) ).

fof(f8962,plain,
    ~ spl77_489,
    inference(avatar_split_clause,[],[f5480,f8959]) ).

fof(f8959,plain,
    ( spl77_489
  <=> 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,[spl77_489])]) ).

fof(f5480,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,[],[f4000]) ).

fof(f4000,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,[],[f3208]) ).

fof(f3208,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,[],[f1294]) ).

fof(f1294,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,[],[f609]) ).

fof(f609,axiom,
    ! [X10] :
      ( ~ 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),X10),X10))
    <=> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X10 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__real__square__gt__zero) ).

fof(f8957,plain,
    spl77_488,
    inference(avatar_split_clause,[],[f5386,f8955]) ).

fof(f8955,plain,
    ( spl77_488
  <=> ! [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,[spl77_488])]) ).

fof(f5386,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,[],[f4382,f3879]) ).

fof(f4382,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,[],[f3313]) ).

fof(f3313,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,[],[f1585]) ).

fof(f1585,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,[],[f78]) ).

fof(f78,axiom,
    ! [X22,X23] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X23,X22)
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,c_Nat_OSuc(X23)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__eq) ).

fof(f8953,plain,
    spl77_487,
    inference(avatar_split_clause,[],[f5385,f8951]) ).

fof(f8951,plain,
    ( spl77_487
  <=> ! [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,[spl77_487])]) ).

fof(f5385,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,[],[f4383,f3879]) ).

fof(f4383,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,[],[f3313]) ).

fof(f8947,plain,
    spl77_486,
    inference(avatar_split_clause,[],[f5316,f8945]) ).

fof(f5316,plain,
    ! [X0] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
    inference(definition_unfolding,[],[f3892,f3879]) ).

fof(f3892,plain,
    ! [X0] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(X0))),
    inference(cnf_transformation,[],[f1212]) ).

fof(f1212,plain,
    ! [X0] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(X0))),
    inference(rectify,[],[f680]) ).

fof(f680,axiom,
    ! [X21] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(X21))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__Suc__gt__zero) ).

fof(f8943,plain,
    spl77_485,
    inference(avatar_split_clause,[],[f5006,f8941]) ).

fof(f8941,plain,
    ( spl77_485
  <=> ! [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,[spl77_485])]) ).

fof(f5006,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,[],[f3574]) ).

fof(f3574,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,[],[f1928]) ).

fof(f1928,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,[],[f269]) ).

fof(f269,axiom,
    ! [X22,X23,X60] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X60,X23) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X60,X22)
    <=> X22 = X23 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel) ).

fof(f8939,plain,
    spl77_484,
    inference(avatar_split_clause,[],[f5004,f8937]) ).

fof(f8937,plain,
    ( spl77_484
  <=> ! [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,[spl77_484])]) ).

fof(f5004,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,[],[f3573]) ).

fof(f3573,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,[],[f1927]) ).

fof(f1927,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,[],[f268]) ).

fof(f268,axiom,
    ! [X22,X60,X23] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X23,X60) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X60)
    <=> X22 = X23 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__right__cancel) ).

fof(f8935,plain,
    spl77_483,
    inference(avatar_split_clause,[],[f4846,f8933]) ).

fof(f8933,plain,
    ( spl77_483
  <=> ! [X2,X0,X1] :
        ( hBOOL(hAPP(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,[spl77_483])]) ).

fof(f4846,plain,
    ! [X2,X0,X1] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,X1),X0))
      | ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
      | ~ class_Orderings_Oorder(X2) ),
    inference(cnf_transformation,[],[f3505]) ).

fof(f3505,plain,
    ! [X0,X1,X2] :
      ( ( ( c_Orderings_Oord__class_Oless(X2,X1,X0)
          | X0 = X1
          | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,X1),X0)) )
        & ( ( X0 != X1
            & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,X1),X0)) )
          | ~ c_Orderings_Oord__class_Oless(X2,X1,X0) ) )
      | ~ class_Orderings_Oorder(X2) ),
    inference(flattening,[],[f3504]) ).

fof(f3504,plain,
    ! [X0,X1,X2] :
      ( ( ( c_Orderings_Oord__class_Oless(X2,X1,X0)
          | X0 = X1
          | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,X1),X0)) )
        & ( ( X0 != X1
            & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,X1),X0)) )
          | ~ c_Orderings_Oord__class_Oless(X2,X1,X0) ) )
      | ~ class_Orderings_Oorder(X2) ),
    inference(nnf_transformation,[],[f2729]) ).

fof(f2729,plain,
    ! [X0,X1,X2] :
      ( ( c_Orderings_Oord__class_Oless(X2,X1,X0)
      <=> ( X0 != X1
          & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,X1),X0)) ) )
      | ~ class_Orderings_Oorder(X2) ),
    inference(ennf_transformation,[],[f1846]) ).

fof(f1846,plain,
    ! [X0,X1,X2] :
      ( class_Orderings_Oorder(X2)
     => ( c_Orderings_Oord__class_Oless(X2,X1,X0)
      <=> ( X0 != X1
          & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,X1),X0)) ) ) ),
    inference(rectify,[],[f414]) ).

fof(f414,axiom,
    ! [X34,X10,X7] :
      ( class_Orderings_Oorder(X7)
     => ( c_Orderings_Oord__class_Oless(X7,X10,X34)
      <=> ( X10 != X34
          & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X7,X10),X34)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__le) ).

fof(f8931,plain,
    spl77_482,
    inference(avatar_split_clause,[],[f4828,f8929]) ).

fof(f8929,plain,
    ( spl77_482
  <=> ! [X2,X0,X1] :
        ( ~ hBOOL(hAPP(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,[spl77_482])]) ).

fof(f4828,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,X0),X1))
      | ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
      | ~ class_Orderings_Opreorder(X2) ),
    inference(cnf_transformation,[],[f3500]) ).

fof(f3500,plain,
    ! [X0,X1,X2] :
      ( ( ( c_Orderings_Oord__class_Oless(X2,X1,X0)
          | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,X0),X1))
          | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,X1),X0)) )
        & ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,X0),X1))
            & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,X1),X0)) )
          | ~ c_Orderings_Oord__class_Oless(X2,X1,X0) ) )
      | ~ class_Orderings_Opreorder(X2) ),
    inference(flattening,[],[f3499]) ).

fof(f3499,plain,
    ! [X0,X1,X2] :
      ( ( ( c_Orderings_Oord__class_Oless(X2,X1,X0)
          | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,X0),X1))
          | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,X1),X0)) )
        & ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,X0),X1))
            & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,X1),X0)) )
          | ~ c_Orderings_Oord__class_Oless(X2,X1,X0) ) )
      | ~ class_Orderings_Opreorder(X2) ),
    inference(nnf_transformation,[],[f2703]) ).

fof(f2703,plain,
    ! [X0,X1,X2] :
      ( ( c_Orderings_Oord__class_Oless(X2,X1,X0)
      <=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,X0),X1))
          & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,X1),X0)) ) )
      | ~ class_Orderings_Opreorder(X2) ),
    inference(ennf_transformation,[],[f1832]) ).

fof(f1832,plain,
    ! [X0,X1,X2] :
      ( class_Orderings_Opreorder(X2)
     => ( c_Orderings_Oord__class_Oless(X2,X1,X0)
      <=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,X0),X1))
          & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,X1),X0)) ) ) ),
    inference(rectify,[],[f413]) ).

fof(f413,axiom,
    ! [X34,X10,X7] :
      ( class_Orderings_Opreorder(X7)
     => ( c_Orderings_Oord__class_Oless(X7,X10,X34)
      <=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X7,X34),X10))
          & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X7,X10),X34)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__le__not__le) ).

fof(f8927,plain,
    spl77_481,
    inference(avatar_split_clause,[],[f4826,f8925]) ).

fof(f8925,plain,
    ( spl77_481
  <=> ! [X2,X0,X1] :
        ( hBOOL(hAPP(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,[spl77_481])]) ).

fof(f4826,plain,
    ! [X2,X0,X1] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,X1),X0))
      | ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
      | ~ class_Orderings_Opreorder(X2) ),
    inference(cnf_transformation,[],[f2702]) ).

fof(f2702,plain,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,X1),X0))
      | ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
      | ~ class_Orderings_Opreorder(X2) ),
    inference(flattening,[],[f2701]) ).

fof(f2701,plain,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,X1),X0))
      | ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
      | ~ class_Orderings_Opreorder(X2) ),
    inference(ennf_transformation,[],[f1831]) ).

fof(f1831,plain,
    ! [X0,X1,X2] :
      ( class_Orderings_Opreorder(X2)
     => ( c_Orderings_Oord__class_Oless(X2,X1,X0)
       => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,X1),X0)) ) ),
    inference(rectify,[],[f405]) ).

fof(f405,axiom,
    ! [X24,X25,X7] :
      ( class_Orderings_Opreorder(X7)
     => ( c_Orderings_Oord__class_Oless(X7,X25,X24)
       => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X7,X25),X24)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__le) ).

fof(f8923,plain,
    ( spl77_479
    | ~ spl77_480
    | ~ spl77_228
    | ~ spl77_420 ),
    inference(avatar_split_clause,[],[f8701,f8571,f6964,f8920,f8916]) ).

fof(f8916,plain,
    ( spl77_479
  <=> sP14(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK23,sK24) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_479])]) ).

fof(f8920,plain,
    ( spl77_480
  <=> hBOOL(c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_480])]) ).

fof(f6964,plain,
    ( spl77_228
  <=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_228])]) ).

fof(f8701,plain,
    ( ~ hBOOL(c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | sP14(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK23,sK24)
    | ~ spl77_228
    | ~ spl77_420 ),
    inference(superposition,[],[f8572,f6966]) ).

fof(f6966,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ spl77_228 ),
    inference(avatar_component_clause,[],[f6964]) ).

fof(f8914,plain,
    spl77_478,
    inference(avatar_split_clause,[],[f4784,f8912]) ).

fof(f8912,plain,
    ( spl77_478
  <=> ! [X2,X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,X1),X0))
        | ~ class_Orderings_Olinorder(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_478])]) ).

fof(f4784,plain,
    ! [X2,X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,X1),X0))
      | ~ class_Orderings_Olinorder(X2) ),
    inference(cnf_transformation,[],[f2649]) ).

fof(f2649,plain,
    ! [X0,X1,X2] :
      ( ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,X1),X0))
      | ~ class_Orderings_Olinorder(X2) ),
    inference(flattening,[],[f2648]) ).

fof(f2648,plain,
    ! [X0,X1,X2] :
      ( ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,X1),X0))
      | ~ class_Orderings_Olinorder(X2) ),
    inference(ennf_transformation,[],[f1798]) ).

fof(f1798,plain,
    ! [X0,X1,X2] :
      ( class_Orderings_Olinorder(X2)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,X1),X0))
       => ~ c_Orderings_Oord__class_Oless(X2,X0,X1) ) ),
    inference(rectify,[],[f406]) ).

fof(f406,axiom,
    ! [X25,X24,X7] :
      ( class_Orderings_Olinorder(X7)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X7,X24),X25))
       => ~ c_Orderings_Oord__class_Oless(X7,X25,X24) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_leD) ).

fof(f8910,plain,
    spl77_477,
    inference(avatar_split_clause,[],[f4773,f8908]) ).

fof(f8908,plain,
    ( spl77_477
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless(X2,X0,X1)
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,X1),X0))
        | ~ class_Orderings_Olinorder(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_477])]) ).

fof(f4773,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless(X2,X0,X1)
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,X1),X0))
      | ~ class_Orderings_Olinorder(X2) ),
    inference(cnf_transformation,[],[f2631]) ).

fof(f2631,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(X2,X0,X1)
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,X1),X0))
      | ~ class_Orderings_Olinorder(X2) ),
    inference(flattening,[],[f2630]) ).

fof(f2630,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(X2,X0,X1)
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,X1),X0))
      | ~ class_Orderings_Olinorder(X2) ),
    inference(ennf_transformation,[],[f1789]) ).

fof(f1789,plain,
    ! [X0,X1,X2] :
      ( class_Orderings_Olinorder(X2)
     => ( c_Orderings_Oord__class_Oless(X2,X0,X1)
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,X1),X0)) ) ),
    inference(rectify,[],[f415]) ).

fof(f415,axiom,
    ! [X24,X25,X7] :
      ( class_Orderings_Olinorder(X7)
     => ( c_Orderings_Oord__class_Oless(X7,X24,X25)
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X7,X25),X24)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__le__less__linear) ).

fof(f8906,plain,
    spl77_476,
    inference(avatar_split_clause,[],[f4737,f8904]) ).

fof(f8904,plain,
    ( spl77_476
  <=> ! [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,[spl77_476])]) ).

fof(f4737,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,[],[f3485]) ).

fof(f3485,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,[],[f2577]) ).

fof(f2577,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,[],[f1758]) ).

fof(f1758,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,[],[f352]) ).

fof(f352,axiom,
    ! [X18,X17,X7] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X7)
     => ( c_Groups_Oplus__class_Oplus(X7,X17,X18) = X17
      <=> c_Groups_Ozero__class_Ozero(X7) = X18 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__iff) ).

fof(f8902,plain,
    spl77_475,
    inference(avatar_split_clause,[],[f4731,f8900]) ).

fof(f8900,plain,
    ( spl77_475
  <=> ! [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,[spl77_475])]) ).

fof(f4731,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,[],[f3483]) ).

fof(f3483,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,[],[f2571]) ).

fof(f2571,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,[],[f1754]) ).

fof(f1754,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,[],[f165]) ).

fof(f165,axiom,
    ! [X17,X18,X7] :
      ( class_Groups_Ogroup__add(X7)
     => ( c_Groups_Ouminus__class_Ouminus(X7,X17) = c_Groups_Ouminus__class_Ouminus(X7,X18)
      <=> X17 = X18 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__equal__iff__equal) ).

fof(f8898,plain,
    spl77_474,
    inference(avatar_split_clause,[],[f4727,f8896]) ).

fof(f8896,plain,
    ( spl77_474
  <=> ! [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,[spl77_474])]) ).

fof(f4727,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,[],[f3481]) ).

fof(f3481,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,[],[f2569]) ).

fof(f2569,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,[],[f1752]) ).

fof(f1752,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,[],[f860]) ).

fof(f860,axiom,
    ! [X17,X18,X7] :
      ( class_Groups_Ogroup__add(X7)
     => ( c_Groups_Ozero__class_Ozero(X7) = c_Groups_Ominus__class_Ominus(X7,X18,X17)
      <=> X17 = X18 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__minus__eq) ).

fof(f8894,plain,
    spl77_473,
    inference(avatar_split_clause,[],[f4650,f8892]) ).

fof(f8892,plain,
    ( spl77_473
  <=> ! [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,[spl77_473])]) ).

fof(f4650,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,[],[f3451]) ).

fof(f3451,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,[],[f2516]) ).

fof(f2516,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,[],[f1710]) ).

fof(f1710,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,[],[f861]) ).

fof(f861,axiom,
    ! [X17,X18,X7] :
      ( class_Groups_Oab__group__add(X7)
     => ( X17 = X18
      <=> c_Groups_Ozero__class_Ozero(X7) = c_Groups_Ominus__class_Ominus(X7,X18,X17) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__iff__diff__eq__0) ).

fof(f8890,plain,
    spl77_472,
    inference(avatar_split_clause,[],[f4634,f8888]) ).

fof(f8888,plain,
    ( spl77_472
  <=> ! [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,[spl77_472])]) ).

fof(f4634,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,[],[f3449]) ).

fof(f3449,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,[],[f2502]) ).

fof(f2502,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,[],[f1698]) ).

fof(f1698,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,[],[f607]) ).

fof(f607,axiom,
    ! [X34,X10,X7] :
      ( class_Lattices_Oboolean__algebra(X7)
     => ( c_Groups_Ouminus__class_Ouminus(X7,X10) = c_Groups_Ouminus__class_Ouminus(X7,X34)
      <=> X10 = X34 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__eq__compl__iff) ).

fof(f8886,plain,
    spl77_471,
    inference(avatar_split_clause,[],[f4629,f8884]) ).

fof(f8884,plain,
    ( spl77_471
  <=> ! [X2,X0,X1] :
        ( X0 = X1
        | c_Int_Oring__1__class_Oof__int(X2,X0) != c_Int_Oring__1__class_Oof__int(X2,X1)
        | ~ class_Int_Oring__char__0(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_471])]) ).

fof(f4629,plain,
    ! [X2,X0,X1] :
      ( X0 = X1
      | c_Int_Oring__1__class_Oof__int(X2,X0) != c_Int_Oring__1__class_Oof__int(X2,X1)
      | ~ class_Int_Oring__char__0(X2) ),
    inference(cnf_transformation,[],[f3448]) ).

fof(f3448,plain,
    ! [X0,X1,X2] :
      ( ( ( c_Int_Oring__1__class_Oof__int(X2,X0) = c_Int_Oring__1__class_Oof__int(X2,X1)
          | X0 != X1 )
        & ( X0 = X1
          | c_Int_Oring__1__class_Oof__int(X2,X0) != c_Int_Oring__1__class_Oof__int(X2,X1) ) )
      | ~ class_Int_Oring__char__0(X2) ),
    inference(nnf_transformation,[],[f2497]) ).

fof(f2497,plain,
    ! [X0,X1,X2] :
      ( ( c_Int_Oring__1__class_Oof__int(X2,X0) = c_Int_Oring__1__class_Oof__int(X2,X1)
      <=> X0 = X1 )
      | ~ class_Int_Oring__char__0(X2) ),
    inference(ennf_transformation,[],[f1694]) ).

fof(f1694,plain,
    ! [X0,X1,X2] :
      ( class_Int_Oring__char__0(X2)
     => ( c_Int_Oring__1__class_Oof__int(X2,X0) = c_Int_Oring__1__class_Oof__int(X2,X1)
      <=> X0 = X1 ) ),
    inference(rectify,[],[f715]) ).

fof(f715,axiom,
    ! [X50,X51,X7] :
      ( class_Int_Oring__char__0(X7)
     => ( c_Int_Oring__1__class_Oof__int(X7,X50) = c_Int_Oring__1__class_Oof__int(X7,X51)
      <=> X50 = X51 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__eq__iff) ).

fof(f8882,plain,
    spl77_470,
    inference(avatar_split_clause,[],[f4532,f8880]) ).

fof(f8880,plain,
    ( spl77_470
  <=> ! [X0,X1] :
        ( X0 = X1
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_470])]) ).

fof(f4532,plain,
    ! [X0,X1] :
      ( X0 = X1
      | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) ),
    inference(cnf_transformation,[],[f3412]) ).

fof(f3412,plain,
    ! [X0,X1] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)
        | X0 != X1 )
      & ( X0 = X1
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) ) ),
    inference(nnf_transformation,[],[f1633]) ).

fof(f1633,plain,
    ! [X0,X1] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)
    <=> X0 = X1 ),
    inference(rectify,[],[f91]) ).

fof(f91,axiom,
    ! [X34,X10] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X10) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X34)
    <=> X10 = X34 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__relations_I1_J) ).

fof(f8878,plain,
    spl77_469,
    inference(avatar_split_clause,[],[f4530,f8876]) ).

fof(f8876,plain,
    ( spl77_469
  <=> ! [X0,X1] :
        ( X0 = X1
        | hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0) != hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_469])]) ).

fof(f4530,plain,
    ! [X0,X1] :
      ( X0 = X1
      | hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0) != hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1) ),
    inference(cnf_transformation,[],[f3411]) ).

fof(f3411,plain,
    ! [X0,X1] :
      ( ( hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1)
        | X0 != X1 )
      & ( X0 = X1
        | hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0) != hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1) ) ),
    inference(nnf_transformation,[],[f1632]) ).

fof(f1632,plain,
    ! [X0,X1] :
      ( hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1)
    <=> X0 = X1 ),
    inference(rectify,[],[f669]) ).

fof(f669,axiom,
    ! [X23,X22] :
      ( hAPP(c_RealDef_Oreal(tc_Nat_Onat),X22) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),X23)
    <=> X22 = X23 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__inject) ).

fof(f8874,plain,
    spl77_468,
    inference(avatar_split_clause,[],[f4525,f8872]) ).

fof(f8872,plain,
    ( spl77_468
  <=> ! [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,[spl77_468])]) ).

fof(f4525,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,[],[f3408]) ).

fof(f3408,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,[],[f1630]) ).

fof(f1630,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,[],[f588]) ).

fof(f588,axiom,
    ! [X18,X10] :
      ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X10,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X18))
    <=> X10 = X18 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__minus__iff) ).

fof(f8870,plain,
    spl77_467,
    inference(avatar_split_clause,[],[f4517,f8868]) ).

fof(f8868,plain,
    ( spl77_467
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Int_Onat,X1),hAPP(c_Int_Onat,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_467])]) ).

fof(f4517,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Int_Onat,X1),hAPP(c_Int_Onat,X0)) ),
    inference(cnf_transformation,[],[f3403]) ).

fof(f3403,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Int_Onat,X1),hAPP(c_Int_Onat,X0))
        | ~ 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),X0) )
      & ( ( 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),X0) )
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Int_Onat,X1),hAPP(c_Int_Onat,X0)) ) ),
    inference(flattening,[],[f3402]) ).

fof(f3402,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Int_Onat,X1),hAPP(c_Int_Onat,X0))
        | ~ 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),X0) )
      & ( ( 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),X0) )
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Int_Onat,X1),hAPP(c_Int_Onat,X0)) ) ),
    inference(nnf_transformation,[],[f1627]) ).

fof(f1627,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Int_Onat,X1),hAPP(c_Int_Onat,X0))
    <=> ( 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),X0) ) ),
    inference(rectify,[],[f637]) ).

fof(f637,axiom,
    ! [X50,X51] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Int_Onat,X51),hAPP(c_Int_Onat,X50))
    <=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X51,X50)
        & c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X50) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__nat__conj) ).

fof(f8866,plain,
    spl77_466,
    inference(avatar_split_clause,[],[f4512,f8864]) ).

fof(f8864,plain,
    ( spl77_466
  <=> ! [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,[spl77_466])]) ).

fof(f4512,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,[],[f3399]) ).

fof(f3399,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,[],[f1625]) ).

fof(f1625,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,[],[f811]) ).

fof(f811,axiom,
    ! [X23,X22] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X22,X23))
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X23,X22) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__diff) ).

fof(f8862,plain,
    spl77_465,
    inference(avatar_split_clause,[],[f4511,f8860]) ).

fof(f8860,plain,
    ( spl77_465
  <=> ! [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,[spl77_465])]) ).

fof(f4511,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,[],[f3399]) ).

fof(f8858,plain,
    spl77_464,
    inference(avatar_split_clause,[],[f4509,f8856]) ).

fof(f8856,plain,
    ( spl77_464
  <=> ! [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,[spl77_464])]) ).

fof(f4509,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,[],[f3398]) ).

fof(f3398,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,[],[f3397]) ).

fof(f3397,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,[],[f1624]) ).

fof(f1624,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,[],[f146]) ).

fof(f146,axiom,
    ! [X50,X51] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X51,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X50,c_Groups_Oone__class_Oone(tc_Int_Oint)))
    <=> ( X50 = X51
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X51,X50) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__add1__eq) ).

fof(f8854,plain,
    spl77_463,
    inference(avatar_split_clause,[],[f4463,f8852]) ).

fof(f8852,plain,
    ( spl77_463
  <=> ! [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,[spl77_463])]) ).

fof(f4463,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,[],[f3376]) ).

fof(f3376,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,[],[f1612]) ).

fof(f1612,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,[],[f587]) ).

fof(f587,axiom,
    ! [X34,X10] :
      ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X10,X34)
    <=> c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X10) = X34 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__eq__0__iff) ).

fof(f8850,plain,
    spl77_462,
    inference(avatar_split_clause,[],[f4388,f8848]) ).

fof(f8848,plain,
    ( spl77_462
  <=> ! [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,[spl77_462])]) ).

fof(f4388,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,[],[f3316]) ).

fof(f3316,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,[],[f1587]) ).

fof(f1587,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,[],[f915]) ).

fof(f915,axiom,
    ! [X77,X60] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X60,X77)
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X60,X77),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__bin__lemma) ).

fof(f8846,plain,
    spl77_461,
    inference(avatar_split_clause,[],[f4387,f8844]) ).

fof(f8844,plain,
    ( spl77_461
  <=> ! [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,[spl77_461])]) ).

fof(f4387,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,[],[f3316]) ).

fof(f8842,plain,
    spl77_460,
    inference(avatar_split_clause,[],[f4251,f8840]) ).

fof(f8840,plain,
    ( spl77_460
  <=> ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK50(X0,X1))
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_460])]) ).

fof(f4251,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK50(X0,X1))
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
    inference(cnf_transformation,[],[f3282]) ).

fof(f3282,plain,
    ! [X0,X1] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),sK50(X0,X1)),c_Nat_OSuc(X0)) = X1
        & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK50(X0,X1)) )
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK50])],[f2337,f3281]) ).

fof(f3281,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X2),c_Nat_OSuc(X0)) = X1
          & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) )
     => ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),sK50(X0,X1)),c_Nat_OSuc(X0)) = X1
        & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK50(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f2337,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X2),c_Nat_OSuc(X0)) = X1
          & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) )
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
    inference(ennf_transformation,[],[f1487]) ).

fof(f1487,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
     => ? [X2] :
          ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X2),c_Nat_OSuc(X0)) = X1
          & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ) ),
    inference(rectify,[],[f808]) ).

fof(f808,axiom,
    ! [X21,X32] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X32)
     => ? [X84] :
          ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X84),c_Nat_OSuc(X21)) = X32
          & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X84) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__pos__nth2) ).

fof(f8838,plain,
    spl77_459,
    inference(avatar_split_clause,[],[f4232,f8836]) ).

fof(f4232,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_ga____,X0),hAPP(v_ga____,X1))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
    inference(cnf_transformation,[],[f2316]) ).

fof(f2316,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_ga____,X0),hAPP(v_ga____,X1))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
    inference(ennf_transformation,[],[f1475]) ).

fof(f1475,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_ga____,X0),hAPP(v_ga____,X1)) ),
    inference(rectify,[],[f3]) ).

fof(f3,axiom,
    ! [X3,X4] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_ga____,X3),hAPP(v_ga____,X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096ALL_Am_An_O_Am_A_060_An_A_N_N_062_Ag_Am_A_060_Ag_An_096) ).

fof(f8834,plain,
    spl77_458,
    inference(avatar_split_clause,[],[f4231,f8832]) ).

fof(f4231,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_f____,X0),hAPP(v_f____,X1))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
    inference(cnf_transformation,[],[f2315]) ).

fof(f2315,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_f____,X0),hAPP(v_f____,X1))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
    inference(ennf_transformation,[],[f1474]) ).

fof(f1474,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_f____,X0),hAPP(v_f____,X1)) ),
    inference(rectify,[],[f2]) ).

fof(f2,axiom,
    ! [X3,X4] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_f____,X3),hAPP(v_f____,X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096ALL_Am_An_O_Am_A_060_An_A_N_N_062_Af_Am_A_060_Af_An_096) ).

fof(f8830,plain,
    spl77_457,
    inference(avatar_split_clause,[],[f4198,f8828]) ).

fof(f8828,plain,
    ( spl77_457
  <=> ! [X0,X1] :
        ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X0)))
        | ~ class_Rings_Olinordered__semidom(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_457])]) ).

fof(f4198,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X0)))
      | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(cnf_transformation,[],[f2286]) ).

fof(f2286,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X0)))
      | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(ennf_transformation,[],[f1447]) ).

fof(f1447,plain,
    ! [X0,X1] :
      ( class_Rings_Olinordered__semidom(X1)
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X0))) ),
    inference(rectify,[],[f500]) ).

fof(f500,axiom,
    ! [X26,X7] :
      ( class_Rings_Olinordered__semidom(X7)
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X7),X26))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__imp__of__nat) ).

fof(f8826,plain,
    spl77_456,
    inference(avatar_split_clause,[],[f4194,f8824]) ).

fof(f8824,plain,
    ( spl77_456
  <=> ! [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,[spl77_456])]) ).

fof(f4194,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,[],[f2282]) ).

fof(f2282,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,[],[f1443]) ).

fof(f1443,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,[],[f351]) ).

fof(f351,axiom,
    ! [X32,X7] :
      ( class_Rings_Ocomm__semiring__1(X7)
     => c_Groups_Ozero__class_Ozero(X7) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),c_Groups_Ozero__class_Ozero(X7)),X32) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).

fof(f8822,plain,
    spl77_455,
    inference(avatar_split_clause,[],[f4193,f8820]) ).

fof(f8820,plain,
    ( spl77_455
  <=> ! [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,[spl77_455])]) ).

fof(f4193,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,[],[f2281]) ).

fof(f2281,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,[],[f1442]) ).

fof(f1442,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,[],[f348]) ).

fof(f348,axiom,
    ! [X32,X7] :
      ( class_Rings_Ocomm__semiring__1(X7)
     => c_Groups_Ozero__class_Ozero(X7) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X32),c_Groups_Ozero__class_Ozero(X7)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).

fof(f8818,plain,
    spl77_454,
    inference(avatar_split_clause,[],[f4192,f8816]) ).

fof(f8816,plain,
    ( spl77_454
  <=> ! [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,[spl77_454])]) ).

fof(f4192,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,[],[f2280]) ).

fof(f2280,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,[],[f1441]) ).

fof(f1441,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,[],[f711]) ).

fof(f711,axiom,
    ! [X25,X7] :
      ( class_Rings_Ocomm__semiring__1(X7)
     => c_Groups_Oone__class_Oone(X7) = hAPP(hAPP(c_Power_Opower__class_Opower(X7),X25),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).

fof(f8814,plain,
    spl77_453,
    inference(avatar_split_clause,[],[f4186,f8812]) ).

fof(f8812,plain,
    ( spl77_453
  <=> ! [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,[spl77_453])]) ).

fof(f4186,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,[],[f2274]) ).

fof(f2274,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,[],[f1435]) ).

fof(f1435,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,[],[f751]) ).

fof(f751,axiom,
    ! [X21,X7] :
      ( class_Groups_Omonoid__mult(X7)
     => c_Groups_Oone__class_Oone(X7) = hAPP(hAPP(c_Power_Opower__class_Opower(X7),c_Groups_Oone__class_Oone(X7)),X21) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__one) ).

fof(f8810,plain,
    spl77_452,
    inference(avatar_split_clause,[],[f4181,f8808]) ).

fof(f8808,plain,
    ( spl77_452
  <=> ! [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,[spl77_452])]) ).

fof(f4181,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,[],[f2269]) ).

fof(f2269,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,[],[f1430]) ).

fof(f1430,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,[],[f764]) ).

fof(f764,axiom,
    ! [X32,X7] :
      ( class_Power_Opower(X7)
     => c_Groups_Oone__class_Oone(X7) = hAPP(hAPP(c_Power_Opower__class_Opower(X7),X32),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__0) ).

fof(f8806,plain,
    spl77_451,
    inference(avatar_split_clause,[],[f4180,f8804]) ).

fof(f8804,plain,
    ( spl77_451
  <=> ! [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,[spl77_451])]) ).

fof(f4180,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,[],[f2268]) ).

fof(f2268,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,[],[f1429]) ).

fof(f1429,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,[],[f214]) ).

fof(f214,axiom,
    ! [X32,X7] :
      ( class_Rings_Omult__zero(X7)
     => c_Groups_Ozero__class_Ozero(X7) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),c_Groups_Ozero__class_Ozero(X7)),X32) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__zero__left) ).

fof(f8802,plain,
    spl77_450,
    inference(avatar_split_clause,[],[f4179,f8800]) ).

fof(f8800,plain,
    ( spl77_450
  <=> ! [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,[spl77_450])]) ).

fof(f4179,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,[],[f2267]) ).

fof(f2267,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,[],[f1428]) ).

fof(f1428,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,[],[f213]) ).

fof(f213,axiom,
    ! [X32,X7] :
      ( class_Rings_Omult__zero(X7)
     => c_Groups_Ozero__class_Ozero(X7) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X32),c_Groups_Ozero__class_Ozero(X7)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__zero__right) ).

fof(f8798,plain,
    spl77_449,
    inference(avatar_split_clause,[],[f4165,f8796]) ).

fof(f8796,plain,
    ( spl77_449
  <=> ! [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,[spl77_449])]) ).

fof(f4165,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,[],[f3258]) ).

fof(f3258,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,[],[f2257]) ).

fof(f2257,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,[],[f1418]) ).

fof(f1418,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,[],[f185]) ).

fof(f185,axiom,
    ! [X18,X7] :
      ( class_Groups_Ogroup__add(X7)
     => ( c_Groups_Ozero__class_Ozero(X7) = c_Groups_Ouminus__class_Ouminus(X7,X18)
      <=> c_Groups_Ozero__class_Ozero(X7) = X18 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__equal__0__iff__equal) ).

fof(f8794,plain,
    ( spl77_448
    | ~ spl77_188
    | ~ spl77_420 ),
    inference(avatar_split_clause,[],[f8681,f8571,f6784,f8791]) ).

fof(f8791,plain,
    ( spl77_448
  <=> sP14(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK23,sK24) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_448])]) ).

fof(f6784,plain,
    ( spl77_188
  <=> ! [X0] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_188])]) ).

fof(f8681,plain,
    ( sP14(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK23,sK24)
    | ~ spl77_188
    | ~ spl77_420 ),
    inference(resolution,[],[f8572,f6785]) ).

fof(f6785,plain,
    ( ! [X0] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0),X0))
    | ~ spl77_188 ),
    inference(avatar_component_clause,[],[f6784]) ).

fof(f8789,plain,
    spl77_447,
    inference(avatar_split_clause,[],[f4102,f8787]) ).

fof(f8787,plain,
    ( spl77_447
  <=> ! [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,[spl77_447])]) ).

fof(f4102,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,[],[f2214]) ).

fof(f2214,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,[],[f1377]) ).

fof(f1377,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,[],[f245]) ).

fof(f245,axiom,
    ! [X32,X7] :
      ( class_Rings_Olinordered__ring(X7)
     => ~ c_Orderings_Oord__class_Oless(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X32),X32),c_Groups_Ozero__class_Ozero(X7)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__square__less__zero) ).

fof(f8785,plain,
    spl77_446,
    inference(avatar_split_clause,[],[f4097,f8783]) ).

fof(f8783,plain,
    ( spl77_446
  <=> ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0
        | c_Groups_Ozero__class_Ozero(X1) != c_Int_Oring__1__class_Oof__int(X1,X0)
        | ~ class_Int_Oring__char__0(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_446])]) ).

fof(f4097,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0
      | c_Groups_Ozero__class_Ozero(X1) != c_Int_Oring__1__class_Oof__int(X1,X0)
      | ~ class_Int_Oring__char__0(X1) ),
    inference(cnf_transformation,[],[f3235]) ).

fof(f3235,plain,
    ! [X0,X1] :
      ( ( ( c_Groups_Ozero__class_Ozero(X1) = c_Int_Oring__1__class_Oof__int(X1,X0)
          | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 )
        & ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0
          | c_Groups_Ozero__class_Ozero(X1) != c_Int_Oring__1__class_Oof__int(X1,X0) ) )
      | ~ class_Int_Oring__char__0(X1) ),
    inference(nnf_transformation,[],[f2211]) ).

fof(f2211,plain,
    ! [X0,X1] :
      ( ( c_Groups_Ozero__class_Ozero(X1) = c_Int_Oring__1__class_Oof__int(X1,X0)
      <=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 )
      | ~ class_Int_Oring__char__0(X1) ),
    inference(ennf_transformation,[],[f1374]) ).

fof(f1374,plain,
    ! [X0,X1] :
      ( class_Int_Oring__char__0(X1)
     => ( c_Groups_Ozero__class_Ozero(X1) = c_Int_Oring__1__class_Oof__int(X1,X0)
      <=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 ) ),
    inference(rectify,[],[f700]) ).

fof(f700,axiom,
    ! [X50,X7] :
      ( class_Int_Oring__char__0(X7)
     => ( c_Groups_Ozero__class_Ozero(X7) = c_Int_Oring__1__class_Oof__int(X7,X50)
      <=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X50 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__eq__0__iff) ).

fof(f8781,plain,
    spl77_445,
    inference(avatar_split_clause,[],[f4091,f8779]) ).

fof(f8779,plain,
    ( spl77_445
  <=> ! [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,[spl77_445])]) ).

fof(f4091,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,[],[f2207]) ).

fof(f2207,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,[],[f1370]) ).

fof(f1370,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,[],[f349]) ).

fof(f349,axiom,
    ! [X24,X7] :
      ( class_RealVector_Oreal__normed__algebra(X7)
     => c_Groups_Ozero__class_Ozero(X7) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),c_Groups_Ozero__class_Ozero(X7)),X24) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Ozero) ).

fof(f8777,plain,
    spl77_444,
    inference(avatar_split_clause,[],[f4089,f8775]) ).

fof(f8775,plain,
    ( spl77_444
  <=> ! [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,[spl77_444])]) ).

fof(f4089,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,[],[f2205]) ).

fof(f2205,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,[],[f1368]) ).

fof(f1368,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,[],[f346]) ).

fof(f346,axiom,
    ! [X25,X7] :
      ( class_RealVector_Oreal__normed__algebra(X7)
     => c_Groups_Ozero__class_Ozero(X7) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),c_Groups_Ozero__class_Ozero(X7)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Ozero) ).

fof(f8773,plain,
    spl77_443,
    inference(avatar_split_clause,[],[f4084,f8771]) ).

fof(f8771,plain,
    ( spl77_443
  <=> ! [X0,X1] :
        ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),X1))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_443])]) ).

fof(f4084,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),X1))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X0)) ),
    inference(cnf_transformation,[],[f1362]) ).

fof(f1362,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),X1))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X0)) ),
    inference(rectify,[],[f579]) ).

fof(f579,axiom,
    ! [X21,X26] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21),X26))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26),X21)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__linear) ).

fof(f8769,plain,
    spl77_442,
    inference(avatar_split_clause,[],[f4083,f8767]) ).

fof(f8767,plain,
    ( spl77_442
  <=> ! [X0,X1] :
        ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0),X1))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_442])]) ).

fof(f4083,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0),X1))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X0)) ),
    inference(cnf_transformation,[],[f1361]) ).

fof(f1361,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0),X1))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X0)) ),
    inference(rectify,[],[f573]) ).

fof(f573,axiom,
    ! [X52,X30] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X52),X30))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X30),X52)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__linear) ).

fof(f8765,plain,
    spl77_441,
    inference(avatar_split_clause,[],[f4082,f8763]) ).

fof(f8763,plain,
    ( spl77_441
  <=> ! [X0,X1] :
        ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X1))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_441])]) ).

fof(f4082,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X1))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X0)) ),
    inference(cnf_transformation,[],[f1360]) ).

fof(f1360,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X1))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X0)) ),
    inference(rectify,[],[f567]) ).

fof(f567,axiom,
    ! [X52,X30] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X52),X30))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X30),X52)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__linear) ).

fof(f8761,plain,
    spl77_440,
    inference(avatar_split_clause,[],[f4078,f8759]) ).

fof(f8759,plain,
    ( spl77_440
  <=> ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Nat__Transfer_Otsub(X0,X1)
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_440])]) ).

fof(f4078,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Nat__Transfer_Otsub(X0,X1)
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X0)) ),
    inference(cnf_transformation,[],[f2198]) ).

fof(f2198,plain,
    ! [X0,X1] :
      ( ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Nat__Transfer_Otsub(X0,X1)
        | hBOOL(hAPP(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)
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X0)) ) ),
    inference(ennf_transformation,[],[f1357]) ).

fof(f1357,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP(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) )
      & ( hBOOL(hAPP(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,[],[f920]) ).

fof(f920,axiom,
    ! [X25,X24] :
      ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X24),X25))
       => c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Nat__Transfer_Otsub(X25,X24) )
      & ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X24),X25))
       => c_Nat__Transfer_Otsub(X25,X24) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X25,X24) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tsub__def) ).

fof(f8757,plain,
    spl77_439,
    inference(avatar_split_clause,[],[f4042,f8755]) ).

fof(f8755,plain,
    ( spl77_439
  <=> ! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_439])]) ).

fof(f4042,plain,
    ! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))),
    inference(cnf_transformation,[],[f1325]) ).

fof(f1325,plain,
    ! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))),
    inference(rectify,[],[f249]) ).

fof(f249,axiom,
    ! [X26,X21] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X21),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X26))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__int__zless__negative) ).

fof(f8753,plain,
    spl77_438,
    inference(avatar_split_clause,[],[f4018,f8751]) ).

fof(f8751,plain,
    ( spl77_438
  <=> ! [X2,X0] :
        ( hBOOL(hAPP(X0,sK41(X0)))
        | ~ hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_438])]) ).

fof(f4018,plain,
    ! [X2,X0] :
      ( hBOOL(hAPP(X0,sK41(X0)))
      | ~ hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ),
    inference(cnf_transformation,[],[f3231]) ).

fof(f3231,plain,
    ! [X0] :
      ( ( ( hBOOL(hAPP(X0,sK41(X0)))
          & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK41(X0))) )
        | ! [X2] : ~ hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) )
      & ( hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK42(X0))))
        | ! [X4] :
            ( ~ hBOOL(hAPP(X0,X4))
            | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4)) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK41,sK42])],[f3228,f3230,f3229]) ).

fof(f3229,plain,
    ! [X0] :
      ( ? [X1] :
          ( hBOOL(hAPP(X0,X1))
          & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) )
     => ( hBOOL(hAPP(X0,sK41(X0)))
        & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK41(X0))) ) ),
    introduced(choice_axiom,[]) ).

fof(f3230,plain,
    ! [X0] :
      ( ? [X3] : hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3)))
     => hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK42(X0)))) ),
    introduced(choice_axiom,[]) ).

fof(f3228,plain,
    ! [X0] :
      ( ( ? [X1] :
            ( hBOOL(hAPP(X0,X1))
            & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) )
        | ! [X2] : ~ hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) )
      & ( ? [X3] : hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3)))
        | ! [X4] :
            ( ~ hBOOL(hAPP(X0,X4))
            | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4)) ) ) ),
    inference(rectify,[],[f3227]) ).

fof(f3227,plain,
    ! [X0] :
      ( ( ? [X1] :
            ( hBOOL(hAPP(X0,X1))
            & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) )
        | ! [X2] : ~ hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) )
      & ( ? [X2] : hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))
        | ! [X1] :
            ( ~ hBOOL(hAPP(X0,X1))
            | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ) ) ),
    inference(nnf_transformation,[],[f1301]) ).

fof(f1301,plain,
    ! [X0] :
      ( ? [X1] :
          ( hBOOL(hAPP(X0,X1))
          & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) )
    <=> ? [X2] : hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ),
    inference(rectify,[],[f514]) ).

fof(f514,axiom,
    ! [X29] :
      ( ? [X2] :
          ( hBOOL(hAPP(X29,X2))
          & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) )
    <=> ? [X2] : hBOOL(hAPP(X29,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__quantifiers_I2_J) ).

fof(f8749,plain,
    ( spl77_437
    | ~ spl77_187
    | ~ spl77_420 ),
    inference(avatar_split_clause,[],[f8680,f8571,f6780,f8746]) ).

fof(f8746,plain,
    ( spl77_437
  <=> sP14(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK23,sK24) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_437])]) ).

fof(f6780,plain,
    ( spl77_187
  <=> ! [X0] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_187])]) ).

fof(f8680,plain,
    ( sP14(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK23,sK24)
    | ~ spl77_187
    | ~ spl77_420 ),
    inference(resolution,[],[f8572,f6781]) ).

fof(f6781,plain,
    ( ! [X0] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X0))
    | ~ spl77_187 ),
    inference(avatar_component_clause,[],[f6780]) ).

fof(f8744,plain,
    spl77_436,
    inference(avatar_split_clause,[],[f4013,f8742]) ).

fof(f8742,plain,
    ( spl77_436
  <=> ! [X4,X0] :
        ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK40(X0)))
        | ~ hBOOL(hAPP(X0,X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_436])]) ).

fof(f4013,plain,
    ! [X0,X4] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK40(X0)))
      | ~ hBOOL(hAPP(X0,X4)) ),
    inference(cnf_transformation,[],[f3226]) ).

fof(f3226,plain,
    ! [X0] :
      ( ( hBOOL(hAPP(X0,sK39(X0)))
        | ! [X2] :
            ( ~ hBOOL(hAPP(X0,hAPP(c_Int_Onat,X2)))
            | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ) )
      & ( ( hBOOL(hAPP(X0,hAPP(c_Int_Onat,sK40(X0))))
          & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK40(X0))) )
        | ! [X4] : ~ hBOOL(hAPP(X0,X4)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK39,sK40])],[f3223,f3225,f3224]) ).

fof(f3224,plain,
    ! [X0] :
      ( ? [X1] : hBOOL(hAPP(X0,X1))
     => hBOOL(hAPP(X0,sK39(X0))) ),
    introduced(choice_axiom,[]) ).

fof(f3225,plain,
    ! [X0] :
      ( ? [X3] :
          ( hBOOL(hAPP(X0,hAPP(c_Int_Onat,X3)))
          & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) )
     => ( hBOOL(hAPP(X0,hAPP(c_Int_Onat,sK40(X0))))
        & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK40(X0))) ) ),
    introduced(choice_axiom,[]) ).

fof(f3223,plain,
    ! [X0] :
      ( ( ? [X1] : hBOOL(hAPP(X0,X1))
        | ! [X2] :
            ( ~ hBOOL(hAPP(X0,hAPP(c_Int_Onat,X2)))
            | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ) )
      & ( ? [X3] :
            ( hBOOL(hAPP(X0,hAPP(c_Int_Onat,X3)))
            & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) )
        | ! [X4] : ~ hBOOL(hAPP(X0,X4)) ) ),
    inference(rectify,[],[f3222]) ).

fof(f3222,plain,
    ! [X0] :
      ( ( ? [X1] : hBOOL(hAPP(X0,X1))
        | ! [X2] :
            ( ~ hBOOL(hAPP(X0,hAPP(c_Int_Onat,X2)))
            | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ) )
      & ( ? [X2] :
            ( hBOOL(hAPP(X0,hAPP(c_Int_Onat,X2)))
            & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) )
        | ! [X1] : ~ hBOOL(hAPP(X0,X1)) ) ),
    inference(nnf_transformation,[],[f1300]) ).

fof(f1300,plain,
    ! [X0] :
      ( ? [X1] : hBOOL(hAPP(X0,X1))
    <=> ? [X2] :
          ( hBOOL(hAPP(X0,hAPP(c_Int_Onat,X2)))
          & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ) ),
    inference(rectify,[],[f629]) ).

fof(f629,axiom,
    ! [X29] :
      ( ? [X81] : hBOOL(hAPP(X29,X81))
    <=> ? [X2] :
          ( hBOOL(hAPP(X29,hAPP(c_Int_Onat,X2)))
          & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ex__nat) ).

fof(f8740,plain,
    spl77_435,
    inference(avatar_split_clause,[],[f4011,f8738]) ).

fof(f8738,plain,
    ( spl77_435
  <=> ! [X0,X3] :
        ( hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3)))
        | ~ hBOOL(hAPP(X0,sK38(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_435])]) ).

fof(f4011,plain,
    ! [X3,X0] :
      ( hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3)))
      | ~ hBOOL(hAPP(X0,sK38(X0))) ),
    inference(cnf_transformation,[],[f3221]) ).

fof(f3221,plain,
    ! [X0] :
      ( ( ! [X1] :
            ( hBOOL(hAPP(X0,X1))
            | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) )
        | ~ hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK37(X0)))) )
      & ( ! [X3] : hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3)))
        | ( ~ hBOOL(hAPP(X0,sK38(X0)))
          & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK38(X0))) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK37,sK38])],[f3218,f3220,f3219]) ).

fof(f3219,plain,
    ! [X0] :
      ( ? [X2] : ~ hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))
     => ~ hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK37(X0)))) ),
    introduced(choice_axiom,[]) ).

fof(f3220,plain,
    ! [X0] :
      ( ? [X4] :
          ( ~ hBOOL(hAPP(X0,X4))
          & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4)) )
     => ( ~ hBOOL(hAPP(X0,sK38(X0)))
        & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK38(X0))) ) ),
    introduced(choice_axiom,[]) ).

fof(f3218,plain,
    ! [X0] :
      ( ( ! [X1] :
            ( hBOOL(hAPP(X0,X1))
            | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) )
        | ? [X2] : ~ hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) )
      & ( ! [X3] : hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3)))
        | ? [X4] :
            ( ~ hBOOL(hAPP(X0,X4))
            & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4)) ) ) ),
    inference(rectify,[],[f3217]) ).

fof(f3217,plain,
    ! [X0] :
      ( ( ! [X1] :
            ( hBOOL(hAPP(X0,X1))
            | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) )
        | ? [X2] : ~ hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) )
      & ( ! [X2] : hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))
        | ? [X1] :
            ( ~ hBOOL(hAPP(X0,X1))
            & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ) ) ),
    inference(nnf_transformation,[],[f2194]) ).

fof(f2194,plain,
    ! [X0] :
      ( ! [X1] :
          ( hBOOL(hAPP(X0,X1))
          | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) )
    <=> ! [X2] : hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ),
    inference(ennf_transformation,[],[f1299]) ).

fof(f1299,plain,
    ! [X0] :
      ( ! [X1] :
          ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
         => hBOOL(hAPP(X0,X1)) )
    <=> ! [X2] : hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ),
    inference(rectify,[],[f513]) ).

fof(f513,axiom,
    ! [X29] :
      ( ! [X2] :
          ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
         => hBOOL(hAPP(X29,X2)) )
    <=> ! [X2] : hBOOL(hAPP(X29,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__quantifiers_I1_J) ).

fof(f8736,plain,
    spl77_434,
    inference(avatar_split_clause,[],[f4008,f8734]) ).

fof(f8734,plain,
    ( spl77_434
  <=> ! [X0,X1] :
        ( hBOOL(hAPP(X0,X1))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK35(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_434])]) ).

fof(f4008,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP(X0,X1))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK35(X0))) ),
    inference(cnf_transformation,[],[f3216]) ).

fof(f3216,plain,
    ! [X0] :
      ( ( ! [X1] : hBOOL(hAPP(X0,X1))
        | ( ~ hBOOL(hAPP(X0,hAPP(c_Int_Onat,sK35(X0))))
          & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK35(X0))) ) )
      & ( ! [X3] :
            ( hBOOL(hAPP(X0,hAPP(c_Int_Onat,X3)))
            | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) )
        | ~ hBOOL(hAPP(X0,sK36(X0))) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK35,sK36])],[f3213,f3215,f3214]) ).

fof(f3214,plain,
    ! [X0] :
      ( ? [X2] :
          ( ~ hBOOL(hAPP(X0,hAPP(c_Int_Onat,X2)))
          & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) )
     => ( ~ hBOOL(hAPP(X0,hAPP(c_Int_Onat,sK35(X0))))
        & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK35(X0))) ) ),
    introduced(choice_axiom,[]) ).

fof(f3215,plain,
    ! [X0] :
      ( ? [X4] : ~ hBOOL(hAPP(X0,X4))
     => ~ hBOOL(hAPP(X0,sK36(X0))) ),
    introduced(choice_axiom,[]) ).

fof(f3213,plain,
    ! [X0] :
      ( ( ! [X1] : hBOOL(hAPP(X0,X1))
        | ? [X2] :
            ( ~ hBOOL(hAPP(X0,hAPP(c_Int_Onat,X2)))
            & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ) )
      & ( ! [X3] :
            ( hBOOL(hAPP(X0,hAPP(c_Int_Onat,X3)))
            | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) )
        | ? [X4] : ~ hBOOL(hAPP(X0,X4)) ) ),
    inference(rectify,[],[f3212]) ).

fof(f3212,plain,
    ! [X0] :
      ( ( ! [X1] : hBOOL(hAPP(X0,X1))
        | ? [X2] :
            ( ~ hBOOL(hAPP(X0,hAPP(c_Int_Onat,X2)))
            & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ) )
      & ( ! [X2] :
            ( hBOOL(hAPP(X0,hAPP(c_Int_Onat,X2)))
            | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) )
        | ? [X1] : ~ hBOOL(hAPP(X0,X1)) ) ),
    inference(nnf_transformation,[],[f2193]) ).

fof(f2193,plain,
    ! [X0] :
      ( ! [X1] : hBOOL(hAPP(X0,X1))
    <=> ! [X2] :
          ( hBOOL(hAPP(X0,hAPP(c_Int_Onat,X2)))
          | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ) ),
    inference(ennf_transformation,[],[f1298]) ).

fof(f1298,plain,
    ! [X0] :
      ( ! [X1] : hBOOL(hAPP(X0,X1))
    <=> ! [X2] :
          ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
         => hBOOL(hAPP(X0,hAPP(c_Int_Onat,X2))) ) ),
    inference(rectify,[],[f628]) ).

fof(f628,axiom,
    ! [X29] :
      ( ! [X81] : hBOOL(hAPP(X29,X81))
    <=> ! [X2] :
          ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
         => hBOOL(hAPP(X29,hAPP(c_Int_Onat,X2))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_all__nat) ).

fof(f8732,plain,
    spl77_433,
    inference(avatar_split_clause,[],[f3988,f8730]) ).

fof(f8730,plain,
    ( spl77_433
  <=> ! [X0] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Int_Onat,X0))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_433])]) ).

fof(f3988,plain,
    ! [X0] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Int_Onat,X0))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
    inference(cnf_transformation,[],[f3202]) ).

fof(f3202,plain,
    ! [X0] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Int_Onat,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(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Int_Onat,X0)) ) ),
    inference(nnf_transformation,[],[f1288]) ).

fof(f1288,plain,
    ! [X0] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Int_Onat,X0))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
    inference(rectify,[],[f646]) ).

fof(f646,axiom,
    ! [X50] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Int_Onat,X50))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X50) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__nat__eq) ).

fof(f8728,plain,
    spl77_432,
    inference(avatar_split_clause,[],[f3987,f8726]) ).

fof(f8726,plain,
    ( spl77_432
  <=> ! [X0] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Int_Onat,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_432])]) ).

fof(f3987,plain,
    ! [X0] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Int_Onat,X0)) ),
    inference(cnf_transformation,[],[f3202]) ).

fof(f8724,plain,
    spl77_431,
    inference(avatar_split_clause,[],[f3986,f8722]) ).

fof(f8722,plain,
    ( spl77_431
  <=> ! [X0] :
        ( hBOOL(hAPP(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,[spl77_431])]) ).

fof(f3986,plain,
    ! [X0] :
      ( hBOOL(hAPP(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,[],[f3201]) ).

fof(f3201,plain,
    ! [X0] :
      ( ( hBOOL(hAPP(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)
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),X0)) ) ),
    inference(nnf_transformation,[],[f1287]) ).

fof(f1287,plain,
    ! [X0] :
      ( hBOOL(hAPP(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,[],[f545]) ).

fof(f545,axiom,
    ! [X50] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),X50))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X50) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__one__le__iff__zero__less) ).

fof(f8720,plain,
    spl77_430,
    inference(avatar_split_clause,[],[f3985,f8718]) ).

fof(f8718,plain,
    ( spl77_430
  <=> ! [X0] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_430])]) ).

fof(f3985,plain,
    ! [X0] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),X0)) ),
    inference(cnf_transformation,[],[f3201]) ).

fof(f8716,plain,
    spl77_429,
    inference(avatar_split_clause,[],[f3970,f8714]) ).

fof(f8714,plain,
    ( spl77_429
  <=> ! [X0] :
        ( c_SEQ_Osubseq(X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X0,sK32(X0)),hAPP(X0,sK33(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_429])]) ).

fof(f3970,plain,
    ! [X0] :
      ( c_SEQ_Osubseq(X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X0,sK32(X0)),hAPP(X0,sK33(X0))) ),
    inference(cnf_transformation,[],[f3190]) ).

fof(f3190,plain,
    ! [X0] :
      ( ( c_SEQ_Osubseq(X0)
        | ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X0,sK32(X0)),hAPP(X0,sK33(X0)))
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK32(X0),sK33(X0)) ) )
      & ( ! [X3,X4] :
            ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X0,X3),hAPP(X0,X4))
            | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4) )
        | ~ c_SEQ_Osubseq(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK32,sK33])],[f3188,f3189]) ).

fof(f3189,plain,
    ! [X0] :
      ( ? [X1,X2] :
          ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X0,X1),hAPP(X0,X2))
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) )
     => ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X0,sK32(X0)),hAPP(X0,sK33(X0)))
        & c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK32(X0),sK33(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f3188,plain,
    ! [X0] :
      ( ( c_SEQ_Osubseq(X0)
        | ? [X1,X2] :
            ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X0,X1),hAPP(X0,X2))
            & c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ) )
      & ( ! [X3,X4] :
            ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X0,X3),hAPP(X0,X4))
            | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4) )
        | ~ c_SEQ_Osubseq(X0) ) ),
    inference(rectify,[],[f3187]) ).

fof(f3187,plain,
    ! [X0] :
      ( ( c_SEQ_Osubseq(X0)
        | ? [X1,X2] :
            ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X0,X1),hAPP(X0,X2))
            & c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ) )
      & ( ! [X1,X2] :
            ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X0,X1),hAPP(X0,X2))
            | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) )
        | ~ c_SEQ_Osubseq(X0) ) ),
    inference(nnf_transformation,[],[f2192]) ).

fof(f2192,plain,
    ! [X0] :
      ( c_SEQ_Osubseq(X0)
    <=> ! [X1,X2] :
          ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X0,X1),hAPP(X0,X2))
          | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ) ),
    inference(ennf_transformation,[],[f1279]) ).

fof(f1279,plain,
    ! [X0] :
      ( c_SEQ_Osubseq(X0)
    <=> ! [X1,X2] :
          ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
         => c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X0,X1),hAPP(X0,X2)) ) ),
    inference(rectify,[],[f19]) ).

fof(f19,axiom,
    ! [X1] :
      ( c_SEQ_Osubseq(X1)
    <=> ! [X3,X4] :
          ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4)
         => c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X1,X3),hAPP(X1,X4)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subseq__def) ).

fof(f8712,plain,
    spl77_428,
    inference(avatar_split_clause,[],[f3950,f8710]) ).

fof(f8710,plain,
    ( spl77_428
  <=> ! [X0] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_RComplete_Onatfloor(X0)
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_428])]) ).

fof(f3950,plain,
    ! [X0] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_RComplete_Onatfloor(X0)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
    inference(cnf_transformation,[],[f2176]) ).

fof(f2176,plain,
    ! [X0] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_RComplete_Onatfloor(X0)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
    inference(ennf_transformation,[],[f1264]) ).

fof(f1264,plain,
    ! [X0] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
     => c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_RComplete_Onatfloor(X0) ),
    inference(rectify,[],[f631]) ).

fof(f631,axiom,
    ! [X25] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X25),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
     => c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_RComplete_Onatfloor(X25) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__neg) ).

fof(f8708,plain,
    spl77_427,
    inference(avatar_split_clause,[],[f3949,f8706]) ).

fof(f8706,plain,
    ( spl77_427
  <=> ! [X0] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_RComplete_Onatceiling(X0)
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_427])]) ).

fof(f3949,plain,
    ! [X0] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_RComplete_Onatceiling(X0)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
    inference(cnf_transformation,[],[f2175]) ).

fof(f2175,plain,
    ! [X0] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_RComplete_Onatceiling(X0)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
    inference(ennf_transformation,[],[f1263]) ).

fof(f1263,plain,
    ! [X0] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
     => c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_RComplete_Onatceiling(X0) ),
    inference(rectify,[],[f632]) ).

fof(f632,axiom,
    ! [X25] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X25),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
     => c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_RComplete_Onatceiling(X25) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__neg) ).

fof(f8679,plain,
    spl77_426,
    inference(avatar_split_clause,[],[f3943,f8677]) ).

fof(f8677,plain,
    ( spl77_426
  <=> ! [X0] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK27(X0)) = X0
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_426])]) ).

fof(f3943,plain,
    ! [X0] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK27(X0)) = X0
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
    inference(cnf_transformation,[],[f3176]) ).

fof(f3176,plain,
    ! [X0] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK27(X0)) = X0
        & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),sK27(X0)) )
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK27])],[f2168,f3175]) ).

fof(f3175,plain,
    ! [X0] :
      ( ? [X1] :
          ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) = X0
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) )
     => ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK27(X0)) = X0
        & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),sK27(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f2168,plain,
    ! [X0] :
      ( ? [X1] :
          ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) = X0
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) )
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
    inference(ennf_transformation,[],[f1257]) ).

fof(f1257,plain,
    ! [X0] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
     => ? [X1] :
          ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) = X0
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ) ),
    inference(rectify,[],[f372]) ).

fof(f372,axiom,
    ! [X40] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X40)
     => ? [X4] :
          ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4) = X40
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__imp__eq__int) ).

fof(f8675,plain,
    spl77_425,
    inference(avatar_split_clause,[],[f3926,f8673]) ).

fof(f8673,plain,
    ( spl77_425
  <=> ! [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,[spl77_425])]) ).

fof(f3926,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,[],[f2155]) ).

fof(f2155,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,[],[f1245]) ).

fof(f1245,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,[],[f206]) ).

fof(f206,axiom,
    ! [X7] :
      ( class_Rings_Olinordered__semidom(X7)
     => c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),c_Groups_Oplus__class_Oplus(X7,c_Groups_Oone__class_Oone(X7),c_Groups_Oone__class_Oone(X7))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__two) ).

fof(f8671,plain,
    spl77_424,
    inference(avatar_split_clause,[],[f3907,f8669]) ).

fof(f8669,plain,
    ( spl77_424
  <=> ! [X0] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_424])]) ).

fof(f3907,plain,
    ! [X0] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(X0))),
    inference(cnf_transformation,[],[f1227]) ).

fof(f1227,plain,
    ! [X0] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(X0))),
    inference(rectify,[],[f929]) ).

fof(f929,axiom,
    ! [X25] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X25,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(X25))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__natfloor__gt__diff__one) ).

fof(f8666,plain,
    spl77_423,
    inference(avatar_split_clause,[],[f3906,f8664]) ).

fof(f3906,plain,
    ! [X0] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(X0)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
    inference(cnf_transformation,[],[f1226]) ).

fof(f1226,plain,
    ! [X0] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(X0)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
    inference(rectify,[],[f691]) ).

fof(f691,axiom,
    ! [X25] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X25,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(X25)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__natfloor__add__one__gt) ).

fof(f8662,plain,
    spl77_422,
    inference(avatar_split_clause,[],[f3905,f8660]) ).

fof(f8660,plain,
    ( spl77_422
  <=> ! [X0] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_422])]) ).

fof(f3905,plain,
    ! [X0] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(cnf_transformation,[],[f1225]) ).

fof(f1225,plain,
    ! [X0] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(rectify,[],[f550]) ).

fof(f550,axiom,
    ! [X21] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X21))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negative__zle__0) ).

fof(f8648,plain,
    ( spl77_421
    | ~ spl77_394
    | ~ spl77_419 ),
    inference(avatar_split_clause,[],[f8483,f8318,f7976,f8646]) ).

fof(f8646,plain,
    ( spl77_421
  <=> ! [X0] :
        ( hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ sP15(X0,sK24,sK23) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_421])]) ).

fof(f7976,plain,
    ( spl77_394
  <=> ! [X2,X0,X1] :
        ( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0)))
        | ~ sP15(X2,X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_394])]) ).

fof(f8318,plain,
    ( spl77_419
  <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,sK23,sK24) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_419])]) ).

fof(f8483,plain,
    ( ! [X0] :
        ( hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ sP15(X0,sK24,sK23) )
    | ~ spl77_394
    | ~ spl77_419 ),
    inference(superposition,[],[f7977,f8320]) ).

fof(f8320,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,sK23,sK24)
    | ~ spl77_419 ),
    inference(avatar_component_clause,[],[f8318]) ).

fof(f7977,plain,
    ( ! [X2,X0,X1] :
        ( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0)))
        | ~ sP15(X2,X0,X1) )
    | ~ spl77_394 ),
    inference(avatar_component_clause,[],[f7976]) ).

fof(f8573,plain,
    ( spl77_420
    | ~ spl77_392
    | ~ spl77_419 ),
    inference(avatar_split_clause,[],[f8465,f8318,f7968,f8571]) ).

fof(f7968,plain,
    ( spl77_392
  <=> ! [X2,X0,X1] :
        ( sP14(X2,X1,X0)
        | ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_392])]) ).

fof(f8465,plain,
    ( ! [X0] :
        ( ~ hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | sP14(X0,sK23,sK24) )
    | ~ spl77_392
    | ~ spl77_419 ),
    inference(superposition,[],[f7969,f8320]) ).

fof(f7969,plain,
    ( ! [X2,X0,X1] :
        ( ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0)))
        | sP14(X2,X1,X0) )
    | ~ spl77_392 ),
    inference(avatar_component_clause,[],[f7968]) ).

fof(f8321,plain,
    ( spl77_419
    | ~ spl77_1
    | ~ spl77_370 ),
    inference(avatar_split_clause,[],[f8297,f7878,f5856,f8318]) ).

fof(f7878,plain,
    ( spl77_370
  <=> ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_370])]) ).

fof(f8297,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,sK23,sK24)
    | ~ spl77_1
    | ~ spl77_370 ),
    inference(resolution,[],[f7879,f5858]) ).

fof(f5858,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK23,sK24)
    | ~ spl77_1 ),
    inference(avatar_component_clause,[],[f5856]) ).

fof(f7879,plain,
    ( ! [X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0) )
    | ~ spl77_370 ),
    inference(avatar_component_clause,[],[f7878]) ).

fof(f8252,plain,
    ( spl77_418
    | ~ spl77_23
    | ~ spl77_274 ),
    inference(avatar_split_clause,[],[f7347,f7174,f5966,f8250]) ).

fof(f8250,plain,
    ( spl77_418
  <=> ! [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,[spl77_418])]) ).

fof(f5966,plain,
    ( spl77_23
  <=> class_Lattices_Oboolean__algebra(tc_HOL_Obool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_23])]) ).

fof(f7174,plain,
    ( spl77_274
  <=> ! [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,[spl77_274])]) ).

fof(f7347,plain,
    ( ! [X0] : c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool,c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool,X0)) = X0
    | ~ spl77_23
    | ~ spl77_274 ),
    inference(resolution,[],[f7175,f5968]) ).

fof(f5968,plain,
    ( class_Lattices_Oboolean__algebra(tc_HOL_Obool)
    | ~ spl77_23 ),
    inference(avatar_component_clause,[],[f5966]) ).

fof(f7175,plain,
    ( ! [X0,X1] :
        ( ~ class_Lattices_Oboolean__algebra(X1)
        | c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0)) = X0 )
    | ~ spl77_274 ),
    inference(avatar_component_clause,[],[f7174]) ).

fof(f8221,plain,
    ( spl77_417
    | ~ spl77_221
    | ~ spl77_266 ),
    inference(avatar_split_clause,[],[f7309,f7142,f6921,f8219]) ).

fof(f8219,plain,
    ( spl77_417
  <=> ! [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,[spl77_417])]) ).

fof(f6921,plain,
    ( spl77_221
  <=> ! [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,[spl77_221])]) ).

fof(f7142,plain,
    ( spl77_266
  <=> ! [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,[spl77_266])]) ).

fof(f7309,plain,
    ( ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) != X0
    | ~ spl77_221
    | ~ spl77_266 ),
    inference(superposition,[],[f6922,f7143]) ).

fof(f7143,plain,
    ( ! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)
    | ~ spl77_266 ),
    inference(avatar_component_clause,[],[f7142]) ).

fof(f6922,plain,
    ( ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X0
    | ~ spl77_221 ),
    inference(avatar_component_clause,[],[f6921]) ).

fof(f8103,plain,
    ( spl77_416
    | ~ spl77_42
    | ~ spl77_263 ),
    inference(avatar_split_clause,[],[f7279,f7130,f6061,f8100]) ).

fof(f8100,plain,
    ( spl77_416
  <=> 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,[spl77_416])]) ).

fof(f6061,plain,
    ( spl77_42
  <=> class_Groups_Ogroup__add(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_42])]) ).

fof(f7130,plain,
    ( spl77_263
  <=> ! [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,[spl77_263])]) ).

fof(f7279,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))
    | ~ spl77_42
    | ~ spl77_263 ),
    inference(resolution,[],[f7131,f6063]) ).

fof(f6063,plain,
    ( class_Groups_Ogroup__add(tc_RealDef_Oreal)
    | ~ spl77_42 ),
    inference(avatar_component_clause,[],[f6061]) ).

fof(f7131,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)) )
    | ~ spl77_263 ),
    inference(avatar_component_clause,[],[f7130]) ).

fof(f8064,plain,
    spl77_415,
    inference(avatar_split_clause,[],[f5783,f8062]) ).

fof(f8062,plain,
    ( spl77_415
  <=> ! [X0,X1] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
        | ~ sP5(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_415])]) ).

fof(f5783,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
      | ~ sP5(X0,X1) ),
    inference(forward_demodulation,[],[f5782,f3871]) ).

fof(f5782,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
      | ~ sP5(X0,X1) ),
    inference(forward_demodulation,[],[f5424,f4025]) ).

fof(f4025,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,[],[f1308]) ).

fof(f1308,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,[],[f277]) ).

fof(f277,axiom,
    ! [X21,X26] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X26,X21) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X26),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__commute) ).

fof(f5424,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
      | ~ sP5(X0,X1) ),
    inference(definition_unfolding,[],[f4492,f3879]) ).

fof(f4492,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
      | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
      | ~ sP5(X0,X1) ),
    inference(cnf_transformation,[],[f3391]) ).

fof(f3391,plain,
    ! [X0,X1] :
      ( ( sP5(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 )
        | ~ sP5(X0,X1) ) ),
    inference(flattening,[],[f3390]) ).

fof(f3390,plain,
    ! [X0,X1] :
      ( ( sP5(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 )
        | ~ sP5(X0,X1) ) ),
    inference(nnf_transformation,[],[f3135]) ).

fof(f3135,plain,
    ! [X0,X1] :
      ( sP5(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,[sP5])]) ).

fof(f8060,plain,
    spl77_414,
    inference(avatar_split_clause,[],[f5781,f8058]) ).

fof(f8058,plain,
    ( spl77_414
  <=> ! [X0,X1] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
        | ~ sP5(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_414])]) ).

fof(f5781,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
      | c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
      | ~ sP5(X0,X1) ),
    inference(forward_demodulation,[],[f5780,f3871]) ).

fof(f5780,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
      | ~ sP5(X0,X1) ),
    inference(forward_demodulation,[],[f5779,f4025]) ).

fof(f5779,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
      | ~ sP5(X0,X1) ),
    inference(forward_demodulation,[],[f5778,f3871]) ).

fof(f5778,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
      | ~ sP5(X0,X1) ),
    inference(forward_demodulation,[],[f5423,f4025]) ).

fof(f5423,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
      | ~ sP5(X0,X1) ),
    inference(definition_unfolding,[],[f4494,f3879,f3879]) ).

fof(f4494,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
      | ~ sP5(X0,X1) ),
    inference(cnf_transformation,[],[f3391]) ).

fof(f8056,plain,
    spl77_413,
    inference(avatar_split_clause,[],[f5777,f8054]) ).

fof(f8054,plain,
    ( spl77_413
  <=> ! [X0,X1] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
        | ~ sP5(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_413])]) ).

fof(f5777,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
      | ~ sP5(X0,X1) ),
    inference(forward_demodulation,[],[f5776,f3871]) ).

fof(f5776,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
      | ~ sP5(X0,X1) ),
    inference(forward_demodulation,[],[f5422,f4025]) ).

fof(f5422,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
      | ~ sP5(X0,X1) ),
    inference(definition_unfolding,[],[f4495,f3879]) ).

fof(f4495,plain,
    ! [X0,X1] :
      ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
      | ~ sP5(X0,X1) ),
    inference(cnf_transformation,[],[f3391]) ).

fof(f8052,plain,
    ( spl77_412
    | ~ spl77_35
    | ~ spl77_262 ),
    inference(avatar_split_clause,[],[f7278,f7126,f6026,f8049]) ).

fof(f8049,plain,
    ( spl77_412
  <=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_Oring__1__class_Oof__int(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_412])]) ).

fof(f6026,plain,
    ( spl77_35
  <=> class_Rings_Oring__1(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_35])]) ).

fof(f7126,plain,
    ( spl77_262
  <=> ! [X0] :
        ( c_Groups_Ozero__class_Ozero(X0) = c_Int_Oring__1__class_Oof__int(X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ class_Rings_Oring__1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_262])]) ).

fof(f7278,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_Oring__1__class_Oof__int(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl77_35
    | ~ spl77_262 ),
    inference(resolution,[],[f7127,f6028]) ).

fof(f6028,plain,
    ( class_Rings_Oring__1(tc_Int_Oint)
    | ~ spl77_35 ),
    inference(avatar_component_clause,[],[f6026]) ).

fof(f7127,plain,
    ( ! [X0] :
        ( ~ class_Rings_Oring__1(X0)
        | c_Groups_Ozero__class_Ozero(X0) = c_Int_Oring__1__class_Oof__int(X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
    | ~ spl77_262 ),
    inference(avatar_component_clause,[],[f7126]) ).

fof(f8047,plain,
    spl77_411,
    inference(avatar_split_clause,[],[f5767,f8045]) ).

fof(f8045,plain,
    ( spl77_411
  <=> ! [X0,X1] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
        | ~ sP4(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_411])]) ).

fof(f5767,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
      | ~ sP4(X0,X1) ),
    inference(forward_demodulation,[],[f5766,f3871]) ).

fof(f5766,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
      | ~ sP4(X0,X1) ),
    inference(forward_demodulation,[],[f5417,f4025]) ).

fof(f5417,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
      | ~ sP4(X0,X1) ),
    inference(definition_unfolding,[],[f4484,f3879]) ).

fof(f4484,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
      | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
      | ~ sP4(X0,X1) ),
    inference(cnf_transformation,[],[f3388]) ).

fof(f3388,plain,
    ! [X0,X1] :
      ( ( sP4(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 )
        | ~ sP4(X0,X1) ) ),
    inference(flattening,[],[f3387]) ).

fof(f3387,plain,
    ! [X0,X1] :
      ( ( sP4(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 )
        | ~ sP4(X0,X1) ) ),
    inference(nnf_transformation,[],[f3133]) ).

fof(f3133,plain,
    ! [X0,X1] :
      ( sP4(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,[sP4])]) ).

fof(f8043,plain,
    spl77_410,
    inference(avatar_split_clause,[],[f5765,f8041]) ).

fof(f8041,plain,
    ( spl77_410
  <=> ! [X0,X1] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
        | ~ sP4(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_410])]) ).

fof(f5765,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
      | c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
      | ~ sP4(X0,X1) ),
    inference(forward_demodulation,[],[f5764,f3871]) ).

fof(f5764,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
      | ~ sP4(X0,X1) ),
    inference(forward_demodulation,[],[f5763,f4025]) ).

fof(f5763,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
      | ~ sP4(X0,X1) ),
    inference(forward_demodulation,[],[f5762,f3871]) ).

fof(f5762,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
      | ~ sP4(X0,X1) ),
    inference(forward_demodulation,[],[f5416,f4025]) ).

fof(f5416,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
      | ~ sP4(X0,X1) ),
    inference(definition_unfolding,[],[f4486,f3879,f3879]) ).

fof(f4486,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
      | ~ sP4(X0,X1) ),
    inference(cnf_transformation,[],[f3388]) ).

fof(f8039,plain,
    spl77_409,
    inference(avatar_split_clause,[],[f5761,f8037]) ).

fof(f8037,plain,
    ( spl77_409
  <=> ! [X0,X1] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
        | ~ sP4(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_409])]) ).

fof(f5761,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
      | ~ sP4(X0,X1) ),
    inference(forward_demodulation,[],[f5760,f3871]) ).

fof(f5760,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
      | ~ sP4(X0,X1) ),
    inference(forward_demodulation,[],[f5415,f4025]) ).

fof(f5415,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
      | ~ sP4(X0,X1) ),
    inference(definition_unfolding,[],[f4487,f3879]) ).

fof(f4487,plain,
    ! [X0,X1] :
      ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
      | ~ sP4(X0,X1) ),
    inference(cnf_transformation,[],[f3388]) ).

fof(f8035,plain,
    spl77_408,
    inference(avatar_split_clause,[],[f5716,f8033]) ).

fof(f8033,plain,
    ( spl77_408
  <=> ! [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,[spl77_408])]) ).

fof(f5716,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,[],[f5339,f5313]) ).

fof(f5339,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,[],[f4022,f3879]) ).

fof(f4022,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,[],[f1305]) ).

fof(f1305,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,[],[f311]) ).

fof(f311,axiom,
    ! [X26,X42] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X42,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X42,X26))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__Suc1) ).

fof(f8031,plain,
    spl77_407,
    inference(avatar_split_clause,[],[f5715,f8029]) ).

fof(f8029,plain,
    ( spl77_407
  <=> ! [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,[spl77_407])]) ).

fof(f5715,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,[],[f5338,f5313]) ).

fof(f5338,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,[],[f4021,f3879]) ).

fof(f4021,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,[],[f1304]) ).

fof(f1304,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,[],[f310]) ).

fof(f310,axiom,
    ! [X26,X42] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X42,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X26,X42))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__Suc2) ).

fof(f8027,plain,
    spl77_406,
    inference(avatar_split_clause,[],[f5642,f8025]) ).

fof(f8025,plain,
    ( spl77_406
  <=> ! [X4,X0,X2] :
        ( hBOOL(hAPP(X0,X4))
        | ~ sP17(X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X4),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_406])]) ).

fof(f5642,plain,
    ! [X2,X0,X4] :
      ( hBOOL(hAPP(X0,X4))
      | ~ sP17(X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X4),X2) ),
    inference(equality_resolution,[],[f4995]) ).

fof(f4995,plain,
    ! [X2,X0,X1,X4] :
      ( hBOOL(hAPP(X0,X4))
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X4) != X1
      | ~ sP17(X0,X1,X2) ),
    inference(cnf_transformation,[],[f3570]) ).

fof(f3570,plain,
    ! [X0,X1,X2] :
      ( ( sP17(X0,X1,X2)
        | ( ~ hBOOL(hAPP(X0,sK73(X0,X1,X2)))
          & c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,sK73(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) ) )
        | ~ sP17(X0,X1,X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK73])],[f3568,f3569]) ).

fof(f3569,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ~ hBOOL(hAPP(X0,X3))
          & c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3) = X1 )
     => ( ~ hBOOL(hAPP(X0,sK73(X0,X1,X2)))
        & c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,sK73(X0,X1,X2)) = X1 ) ),
    introduced(choice_axiom,[]) ).

fof(f3568,plain,
    ! [X0,X1,X2] :
      ( ( sP17(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) ) )
        | ~ sP17(X0,X1,X2) ) ),
    inference(rectify,[],[f3567]) ).

fof(f3567,plain,
    ! [X2,X1,X0] :
      ( ( sP17(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) ) )
        | ~ sP17(X2,X1,X0) ) ),
    inference(flattening,[],[f3566]) ).

fof(f3566,plain,
    ! [X2,X1,X0] :
      ( ( sP17(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) ) )
        | ~ sP17(X2,X1,X0) ) ),
    inference(nnf_transformation,[],[f3155]) ).

fof(f3155,plain,
    ! [X2,X1,X0] :
      ( sP17(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,[sP17])]) ).

fof(f8023,plain,
    spl77_405,
    inference(avatar_split_clause,[],[f5641,f8021]) ).

fof(f8021,plain,
    ( spl77_405
  <=> ! [X4,X0,X2] :
        ( hBOOL(hAPP(X0,X4))
        | ~ sP16(X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X4),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_405])]) ).

fof(f5641,plain,
    ! [X2,X0,X4] :
      ( hBOOL(hAPP(X0,X4))
      | ~ sP16(X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X4),X2) ),
    inference(equality_resolution,[],[f4987]) ).

fof(f4987,plain,
    ! [X2,X0,X1,X4] :
      ( hBOOL(hAPP(X0,X4))
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X4) != X1
      | ~ sP16(X0,X1,X2) ),
    inference(cnf_transformation,[],[f3564]) ).

fof(f3564,plain,
    ! [X0,X1,X2] :
      ( ( sP16(X0,X1,X2)
        | ( ~ hBOOL(hAPP(X0,sK72(X0,X1,X2)))
          & c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,sK72(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) ) )
        | ~ sP16(X0,X1,X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK72])],[f3562,f3563]) ).

fof(f3563,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ~ hBOOL(hAPP(X0,X3))
          & c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3) = X1 )
     => ( ~ hBOOL(hAPP(X0,sK72(X0,X1,X2)))
        & c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,sK72(X0,X1,X2)) = X1 ) ),
    introduced(choice_axiom,[]) ).

fof(f3562,plain,
    ! [X0,X1,X2] :
      ( ( sP16(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) ) )
        | ~ sP16(X0,X1,X2) ) ),
    inference(rectify,[],[f3561]) ).

fof(f3561,plain,
    ! [X2,X1,X0] :
      ( ( sP16(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) ) )
        | ~ sP16(X2,X1,X0) ) ),
    inference(flattening,[],[f3560]) ).

fof(f3560,plain,
    ! [X2,X1,X0] :
      ( ( sP16(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) ) )
        | ~ sP16(X2,X1,X0) ) ),
    inference(nnf_transformation,[],[f3153]) ).

fof(f3153,plain,
    ! [X2,X1,X0] :
      ( sP16(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,[sP16])]) ).

fof(f8019,plain,
    spl77_404,
    inference(avatar_split_clause,[],[f5529,f8017]) ).

fof(f8017,plain,
    ( spl77_404
  <=> ! [X1] :
        ( sP1(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_404])]) ).

fof(f5529,plain,
    ! [X1] :
      ( sP1(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(equality_resolution,[],[f4417]) ).

fof(f4417,plain,
    ! [X0,X1] :
      ( sP1(X0,X1)
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(cnf_transformation,[],[f3337]) ).

fof(f3337,plain,
    ! [X0,X1] :
      ( ( sP1(X0,X1)
        | ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
          & ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) )
        | ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) != X1
          & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ) )
      & ( ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
            | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) )
          & ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) = X1
            | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ) )
        | ~ sP1(X0,X1) ) ),
    inference(rectify,[],[f3336]) ).

fof(f3336,plain,
    ! [X1,X0] :
      ( ( sP1(X1,X0)
        | ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
          & ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) )
        | ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) != X0
          & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) ) )
      & ( ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
            | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) )
          & ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) = X0
            | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) ) )
        | ~ sP1(X1,X0) ) ),
    inference(flattening,[],[f3335]) ).

fof(f3335,plain,
    ! [X1,X0] :
      ( ( sP1(X1,X0)
        | ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
          & ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) )
        | ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) != X0
          & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) ) )
      & ( ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
            | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) )
          & ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) = X0
            | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) ) )
        | ~ sP1(X1,X0) ) ),
    inference(nnf_transformation,[],[f3127]) ).

fof(f3127,plain,
    ! [X1,X0] :
      ( sP1(X1,X0)
    <=> ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
          | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) )
        & ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) = X0
          | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

fof(f8015,plain,
    spl77_403,
    inference(avatar_split_clause,[],[f5524,f8013]) ).

fof(f8013,plain,
    ( spl77_403
  <=> ! [X1] :
        ( sP0(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_403])]) ).

fof(f5524,plain,
    ! [X1] :
      ( sP0(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(equality_resolution,[],[f4409]) ).

fof(f4409,plain,
    ! [X0,X1] :
      ( sP0(X0,X1)
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(cnf_transformation,[],[f3333]) ).

fof(f3333,plain,
    ! [X0,X1] :
      ( ( sP0(X0,X1)
        | ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
          & ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) )
        | ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) != X1
          & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ) )
      & ( ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
            | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) )
          & ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) = X1
            | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ) )
        | ~ sP0(X0,X1) ) ),
    inference(flattening,[],[f3332]) ).

fof(f3332,plain,
    ! [X0,X1] :
      ( ( sP0(X0,X1)
        | ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
          & ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) )
        | ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) != X1
          & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ) )
      & ( ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
            | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) )
          & ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) = X1
            | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ) )
        | ~ sP0(X0,X1) ) ),
    inference(nnf_transformation,[],[f3125]) ).

fof(f3125,plain,
    ! [X0,X1] :
      ( sP0(X0,X1)
    <=> ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
          | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) )
        & ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) = X1
          | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f8011,plain,
    spl77_402,
    inference(avatar_split_clause,[],[f5492,f8009]) ).

fof(f8009,plain,
    ( spl77_402
  <=> ! [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,[spl77_402])]) ).

fof(f5492,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,[],[f4116]) ).

fof(f4116,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,[],[f3241]) ).

fof(f3241,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,[],[f2223]) ).

fof(f2223,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,[],[f1386]) ).

fof(f1386,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,[],[f209]) ).

fof(f209,axiom,
    ! [X18,X7] :
      ( class_Groups_Olinordered__ab__group__add(X7)
     => ( c_Groups_Ozero__class_Ozero(X7) = c_Groups_Oplus__class_Oplus(X7,X18,X18)
      <=> c_Groups_Ozero__class_Ozero(X7) = X18 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__eq__0__iff) ).

fof(f8007,plain,
    ( spl77_401
    | ~ spl77_34
    | ~ spl77_262 ),
    inference(avatar_split_clause,[],[f7277,f7126,f6021,f8004]) ).

fof(f8004,plain,
    ( spl77_401
  <=> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Int_Oring__1__class_Oof__int(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_401])]) ).

fof(f6021,plain,
    ( spl77_34
  <=> class_Rings_Oring__1(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_34])]) ).

fof(f7277,plain,
    ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Int_Oring__1__class_Oof__int(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl77_34
    | ~ spl77_262 ),
    inference(resolution,[],[f7127,f6023]) ).

fof(f6023,plain,
    ( class_Rings_Oring__1(tc_RealDef_Oreal)
    | ~ spl77_34 ),
    inference(avatar_component_clause,[],[f6021]) ).

fof(f8002,plain,
    spl77_400,
    inference(avatar_split_clause,[],[f5340,f8000]) ).

fof(f8000,plain,
    ( spl77_400
  <=> ! [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,[spl77_400])]) ).

fof(f5340,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,[],[f4023,f3879]) ).

fof(f4023,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,[],[f1306]) ).

fof(f1306,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,[],[f813]) ).

fof(f813,axiom,
    ! [X21,X26] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X26,X21),c_Nat_OSuc(X26)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less__Suc) ).

fof(f7998,plain,
    spl77_399,
    inference(avatar_split_clause,[],[f5050,f7996]) ).

fof(f7996,plain,
    ( spl77_399
  <=> ! [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,[spl77_399])]) ).

fof(f5050,plain,
    ! [X2,X3,X0,X1] : hAPP(hAPP(c_Power_Opower_Opower(X3,X2,X1),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X2,
    inference(cnf_transformation,[],[f1944]) ).

fof(f1944,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,[],[f786]) ).

fof(f786,axiom,
    ! [X18,X85,X86,X7] : hAPP(hAPP(c_Power_Opower_Opower(X7,X86,X85),X18),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X86,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power_Opower_Opower__0) ).

fof(f7994,plain,
    spl77_398,
    inference(avatar_split_clause,[],[f5001,f7992]) ).

fof(f7992,plain,
    ( spl77_398
  <=> ! [X2,X0,X1] :
        ( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
        | ~ sP17(X2,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_398])]) ).

fof(f5001,plain,
    ! [X2,X0,X1] :
      ( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
      | ~ sP17(X2,X1,X0) ),
    inference(cnf_transformation,[],[f3571]) ).

fof(f3571,plain,
    ! [X0,X1,X2] :
      ( ( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
        | ~ sP17(X2,X1,X0) )
      & ( sP17(X2,X1,X0)
        | ~ hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ) ),
    inference(nnf_transformation,[],[f3156]) ).

fof(f3156,plain,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
    <=> sP17(X2,X1,X0) ),
    inference(definition_folding,[],[f2837,f3155]) ).

fof(f2837,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,[],[f1925]) ).

fof(f1925,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,[],[f893]) ).

fof(f893,axiom,
    ! [X17,X18,X29] :
      ( hBOOL(hAPP(X29,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,X17)))
    <=> ~ ( ? [X90] :
              ( ~ hBOOL(hAPP(X29,X90))
              & c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X90) = X18 )
          | ( ~ hBOOL(hAPP(X29,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            & c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X17) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__split__asm) ).

fof(f7990,plain,
    spl77_397,
    inference(avatar_split_clause,[],[f5000,f7988]) ).

fof(f7988,plain,
    ( spl77_397
  <=> ! [X2,X0,X1] :
        ( sP17(X2,X1,X0)
        | ~ hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_397])]) ).

fof(f5000,plain,
    ! [X2,X0,X1] :
      ( sP17(X2,X1,X0)
      | ~ hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ),
    inference(cnf_transformation,[],[f3571]) ).

fof(f7986,plain,
    spl77_396,
    inference(avatar_split_clause,[],[f4993,f7984]) ).

fof(f7984,plain,
    ( spl77_396
  <=> ! [X2,X0,X1] :
        ( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
        | ~ sP16(X2,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_396])]) ).

fof(f4993,plain,
    ! [X2,X0,X1] :
      ( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
      | ~ sP16(X2,X1,X0) ),
    inference(cnf_transformation,[],[f3565]) ).

fof(f3565,plain,
    ! [X0,X1,X2] :
      ( ( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
        | ~ sP16(X2,X1,X0) )
      & ( sP16(X2,X1,X0)
        | ~ hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ) ),
    inference(nnf_transformation,[],[f3154]) ).

fof(f3154,plain,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
    <=> sP16(X2,X1,X0) ),
    inference(definition_folding,[],[f2836,f3153]) ).

fof(f2836,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,[],[f1924]) ).

fof(f1924,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,[],[f892]) ).

fof(f892,axiom,
    ! [X17,X18,X29] :
      ( hBOOL(hAPP(X29,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,X17)))
    <=> ( ! [X90] :
            ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X90) = X18
           => hBOOL(hAPP(X29,X90)) )
        & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X17)
         => hBOOL(hAPP(X29,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__split) ).

fof(f7982,plain,
    spl77_395,
    inference(avatar_split_clause,[],[f4992,f7980]) ).

fof(f7980,plain,
    ( spl77_395
  <=> ! [X2,X0,X1] :
        ( sP16(X2,X1,X0)
        | ~ hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_395])]) ).

fof(f4992,plain,
    ! [X2,X0,X1] :
      ( sP16(X2,X1,X0)
      | ~ hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ),
    inference(cnf_transformation,[],[f3565]) ).

fof(f7978,plain,
    spl77_394,
    inference(avatar_split_clause,[],[f4985,f7976]) ).

fof(f4985,plain,
    ! [X2,X0,X1] :
      ( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0)))
      | ~ sP15(X2,X0,X1) ),
    inference(cnf_transformation,[],[f3559]) ).

fof(f3559,plain,
    ! [X0,X1,X2] :
      ( ( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0)))
        | ( ~ sP15(X2,X0,X1)
          & ( ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) ) )
      & ( sP15(X2,X0,X1)
        | ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
        | ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0))) ) ),
    inference(flattening,[],[f3558]) ).

fof(f3558,plain,
    ! [X0,X1,X2] :
      ( ( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0)))
        | ( ~ sP15(X2,X0,X1)
          & ( ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) ) )
      & ( sP15(X2,X0,X1)
        | ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
        | ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0))) ) ),
    inference(nnf_transformation,[],[f3152]) ).

fof(f3152,plain,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0)))
    <=> ( sP15(X2,X0,X1)
        | ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) ) ),
    inference(definition_folding,[],[f1923,f3151]) ).

fof(f3151,plain,
    ! [X2,X0,X1] :
      ( sP15(X2,X0,X1)
    <=> ? [X3] :
          ( hBOOL(hAPP(X2,X3))
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),c_Nat_OSuc(X3)))
          & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3)),X1)) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP15])]) ).

fof(f1923,plain,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0)))
    <=> ( ? [X3] :
            ( hBOOL(hAPP(X2,X3))
            & c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),c_Nat_OSuc(X3)))
            & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3)),X1)) )
        | ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) ) ),
    inference(rectify,[],[f996]) ).

fof(f996,axiom,
    ! [X22,X23,X29] :
      ( hBOOL(hAPP(X29,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X23,X22)))
    <=> ( ? [X96] :
            ( hBOOL(hAPP(X29,X96))
            & c_Orderings_Oord__class_Oless(tc_Nat_Onat,X23,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22),c_Nat_OSuc(X96)))
            & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22),X96)),X23)) )
        | ( hBOOL(hAPP(X29,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X22 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__div_H) ).

fof(f7974,plain,
    spl77_393,
    inference(avatar_split_clause,[],[f4980,f7972]) ).

fof(f7972,plain,
    ( spl77_393
  <=> ! [X2,X0,X1] :
        ( hBOOL(hAPP(X0,sK71(X0,X1,X2)))
        | ~ sP15(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_393])]) ).

fof(f4980,plain,
    ! [X2,X0,X1] :
      ( hBOOL(hAPP(X0,sK71(X0,X1,X2)))
      | ~ sP15(X0,X1,X2) ),
    inference(cnf_transformation,[],[f3557]) ).

fof(f3557,plain,
    ! [X0,X1,X2] :
      ( ( sP15(X0,X1,X2)
        | ! [X3] :
            ( ~ hBOOL(hAPP(X0,X3))
            | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Nat_OSuc(X3)))
            | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),X2)) ) )
      & ( ( hBOOL(hAPP(X0,sK71(X0,X1,X2)))
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Nat_OSuc(sK71(X0,X1,X2))))
          & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),sK71(X0,X1,X2))),X2)) )
        | ~ sP15(X0,X1,X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK71])],[f3555,f3556]) ).

fof(f3556,plain,
    ! [X0,X1,X2] :
      ( ? [X4] :
          ( hBOOL(hAPP(X0,X4))
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Nat_OSuc(X4)))
          & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X4)),X2)) )
     => ( hBOOL(hAPP(X0,sK71(X0,X1,X2)))
        & c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Nat_OSuc(sK71(X0,X1,X2))))
        & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),sK71(X0,X1,X2))),X2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f3555,plain,
    ! [X0,X1,X2] :
      ( ( sP15(X0,X1,X2)
        | ! [X3] :
            ( ~ hBOOL(hAPP(X0,X3))
            | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Nat_OSuc(X3)))
            | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),X2)) ) )
      & ( ? [X4] :
            ( hBOOL(hAPP(X0,X4))
            & c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Nat_OSuc(X4)))
            & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X4)),X2)) )
        | ~ sP15(X0,X1,X2) ) ),
    inference(rectify,[],[f3554]) ).

fof(f3554,plain,
    ! [X2,X0,X1] :
      ( ( sP15(X2,X0,X1)
        | ! [X3] :
            ( ~ hBOOL(hAPP(X2,X3))
            | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),c_Nat_OSuc(X3)))
            | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3)),X1)) ) )
      & ( ? [X3] :
            ( hBOOL(hAPP(X2,X3))
            & c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),c_Nat_OSuc(X3)))
            & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3)),X1)) )
        | ~ sP15(X2,X0,X1) ) ),
    inference(nnf_transformation,[],[f3151]) ).

fof(f7970,plain,
    spl77_392,
    inference(avatar_split_clause,[],[f4975,f7968]) ).

fof(f4975,plain,
    ! [X2,X0,X1] :
      ( sP14(X2,X1,X0)
      | ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0))) ),
    inference(cnf_transformation,[],[f3553]) ).

fof(f3553,plain,
    ! [X0,X1,X2] :
      ( ( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0)))
        | ~ sP14(X2,X1,X0)
        | ( ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) )
      & ( ( sP14(X2,X1,X0)
          & ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) )
        | ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0))) ) ),
    inference(flattening,[],[f3552]) ).

fof(f3552,plain,
    ! [X0,X1,X2] :
      ( ( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0)))
        | ~ sP14(X2,X1,X0)
        | ( ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) )
      & ( ( sP14(X2,X1,X0)
          & ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) )
        | ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0))) ) ),
    inference(nnf_transformation,[],[f3150]) ).

fof(f3150,plain,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0)))
    <=> ( sP14(X2,X1,X0)
        & ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) ) ),
    inference(definition_folding,[],[f2835,f3149]) ).

fof(f3149,plain,
    ! [X2,X1,X0] :
      ( sP14(X2,X1,X0)
    <=> ( ! [X3,X4] :
            ( hBOOL(hAPP(X2,X3))
            | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3),X4) != X1
            | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X0) )
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP14])]) ).

fof(f2835,plain,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0)))
    <=> ( ( ! [X3,X4] :
              ( hBOOL(hAPP(X2,X3))
              | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3),X4) != X1
              | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X0) )
          | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
        & ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) ) ),
    inference(flattening,[],[f2834]) ).

fof(f2834,plain,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0)))
    <=> ( ( ! [X3,X4] :
              ( hBOOL(hAPP(X2,X3))
              | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3),X4) != X1
              | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X0) )
          | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
        & ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) ) ),
    inference(ennf_transformation,[],[f1922]) ).

fof(f1922,plain,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0)))
    <=> ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
         => ! [X3,X4] :
              ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X0)
             => ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3),X4) = X1
               => hBOOL(hAPP(X2,X3)) ) ) )
        & ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
         => hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
    inference(rectify,[],[f992]) ).

fof(f992,axiom,
    ! [X60,X22,X29] :
      ( hBOOL(hAPP(X29,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X22,X60)))
    <=> ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X60
         => ! [X79,X47] :
              ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X47,X60)
             => ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X60),X79),X47) = X22
               => hBOOL(hAPP(X29,X79)) ) ) )
        & ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X60
         => hBOOL(hAPP(X29,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__div) ).

fof(f7966,plain,
    spl77_391,
    inference(avatar_split_clause,[],[f4973,f7964]) ).

fof(f7964,plain,
    ( spl77_391
  <=> ! [X2,X0,X1] :
        ( sP14(X0,X1,X2)
        | ~ hBOOL(hAPP(X0,sK69(X0,X1,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_391])]) ).

fof(f4973,plain,
    ! [X2,X0,X1] :
      ( sP14(X0,X1,X2)
      | ~ hBOOL(hAPP(X0,sK69(X0,X1,X2))) ),
    inference(cnf_transformation,[],[f3551]) ).

fof(f3551,plain,
    ! [X0,X1,X2] :
      ( ( sP14(X0,X1,X2)
        | ( ~ hBOOL(hAPP(X0,sK69(X0,X1,X2)))
          & c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),sK69(X0,X1,X2)),sK70(X0,X1,X2)) = X1
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK70(X0,X1,X2),X2)
          & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2 ) )
      & ( ! [X5,X6] :
            ( hBOOL(hAPP(X0,X5))
            | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X5),X6) != X1
            | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,X2) )
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2
        | ~ sP14(X0,X1,X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK69,sK70])],[f3549,f3550]) ).

fof(f3550,plain,
    ! [X0,X1,X2] :
      ( ? [X3,X4] :
          ( ~ hBOOL(hAPP(X0,X3))
          & c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X4) = X1
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X2) )
     => ( ~ hBOOL(hAPP(X0,sK69(X0,X1,X2)))
        & c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),sK69(X0,X1,X2)),sK70(X0,X1,X2)) = X1
        & c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK70(X0,X1,X2),X2) ) ),
    introduced(choice_axiom,[]) ).

fof(f3549,plain,
    ! [X0,X1,X2] :
      ( ( sP14(X0,X1,X2)
        | ( ? [X3,X4] :
              ( ~ hBOOL(hAPP(X0,X3))
              & c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X4) = X1
              & c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X2) )
          & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2 ) )
      & ( ! [X5,X6] :
            ( hBOOL(hAPP(X0,X5))
            | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X5),X6) != X1
            | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,X2) )
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2
        | ~ sP14(X0,X1,X2) ) ),
    inference(rectify,[],[f3548]) ).

fof(f3548,plain,
    ! [X2,X1,X0] :
      ( ( sP14(X2,X1,X0)
        | ( ? [X3,X4] :
              ( ~ hBOOL(hAPP(X2,X3))
              & c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3),X4) = X1
              & c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X0) )
          & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) )
      & ( ! [X3,X4] :
            ( hBOOL(hAPP(X2,X3))
            | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3),X4) != X1
            | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X0) )
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
        | ~ sP14(X2,X1,X0) ) ),
    inference(flattening,[],[f3547]) ).

fof(f3547,plain,
    ! [X2,X1,X0] :
      ( ( sP14(X2,X1,X0)
        | ( ? [X3,X4] :
              ( ~ hBOOL(hAPP(X2,X3))
              & c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3),X4) = X1
              & c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X0) )
          & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) )
      & ( ! [X3,X4] :
            ( hBOOL(hAPP(X2,X3))
            | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3),X4) != X1
            | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X0) )
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
        | ~ sP14(X2,X1,X0) ) ),
    inference(nnf_transformation,[],[f3149]) ).

fof(f7962,plain,
    ( spl77_390
    | ~ spl77_35
    | ~ spl77_261 ),
    inference(avatar_split_clause,[],[f7276,f7122,f6026,f7959]) ).

fof(f7959,plain,
    ( spl77_390
  <=> c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Int_Oring__1__class_Oof__int(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_390])]) ).

fof(f7122,plain,
    ( spl77_261
  <=> ! [X0] :
        ( c_Groups_Oone__class_Oone(X0) = c_Int_Oring__1__class_Oof__int(X0,c_Groups_Oone__class_Oone(tc_Int_Oint))
        | ~ class_Rings_Oring__1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_261])]) ).

fof(f7276,plain,
    ( c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Int_Oring__1__class_Oof__int(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ spl77_35
    | ~ spl77_261 ),
    inference(resolution,[],[f7123,f6028]) ).

fof(f7123,plain,
    ( ! [X0] :
        ( ~ class_Rings_Oring__1(X0)
        | c_Groups_Oone__class_Oone(X0) = c_Int_Oring__1__class_Oof__int(X0,c_Groups_Oone__class_Oone(tc_Int_Oint)) )
    | ~ spl77_261 ),
    inference(avatar_component_clause,[],[f7122]) ).

fof(f7957,plain,
    spl77_389,
    inference(avatar_split_clause,[],[f4971,f7955]) ).

fof(f7955,plain,
    ( spl77_389
  <=> ! [X2,X0,X1] :
        ( sP14(X0,X1,X2)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK70(X0,X1,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_389])]) ).

fof(f4971,plain,
    ! [X2,X0,X1] :
      ( sP14(X0,X1,X2)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK70(X0,X1,X2),X2) ),
    inference(cnf_transformation,[],[f3551]) ).

fof(f7953,plain,
    spl77_388,
    inference(avatar_split_clause,[],[f4968,f7951]) ).

fof(f7951,plain,
    ( spl77_388
  <=> ! [X2,X0,X1] :
        ( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0)))
        | ~ sP13(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_388])]) ).

fof(f4968,plain,
    ! [X2,X0,X1] :
      ( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0)))
      | ~ sP13(X0,X1,X2) ),
    inference(cnf_transformation,[],[f3546]) ).

fof(f3546,plain,
    ! [X0,X1,X2] :
      ( ( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0)))
        | ~ sP13(X0,X1,X2) )
      & ( sP13(X0,X1,X2)
        | ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0))) ) ),
    inference(nnf_transformation,[],[f3148]) ).

fof(f3148,plain,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0)))
    <=> sP13(X0,X1,X2) ),
    inference(definition_folding,[],[f2833,f3147,f3146,f3145]) ).

fof(f3145,plain,
    ! [X2,X1,X0] :
      ( sP11(X2,X1,X0)
    <=> ( ! [X5] :
            ( hBOOL(hAPP(X2,X5))
            | ! [X6] :
                ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X5),X6) != X1
                | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X0)
                | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6)) ) )
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP11])]) ).

fof(f3146,plain,
    ! [X2,X1,X0] :
      ( sP12(X2,X1,X0)
    <=> ( ! [X3] :
            ( hBOOL(hAPP(X2,X3))
            | ! [X4] :
                ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3),X4) != X1
                | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X4) ) )
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP12])]) ).

fof(f3147,plain,
    ! [X0,X1,X2] :
      ( sP13(X0,X1,X2)
    <=> ( sP12(X2,X1,X0)
        & sP11(X2,X1,X0)
        & ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP13])]) ).

fof(f2833,plain,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0)))
    <=> ( ( ! [X3] :
              ( hBOOL(hAPP(X2,X3))
              | ! [X4] :
                  ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3),X4) != X1
                  | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                  | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X4) ) )
          | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
        & ( ! [X5] :
              ( hBOOL(hAPP(X2,X5))
              | ! [X6] :
                  ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X5),X6) != X1
                  | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X0)
                  | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6)) ) )
          | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) )
        & ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ) ) ),
    inference(ennf_transformation,[],[f1921]) ).

fof(f1921,plain,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0)))
    <=> ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
         => ! [X3] :
              ( ? [X4] :
                  ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3),X4) = X1
                  & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                  & c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X4) )
             => hBOOL(hAPP(X2,X3)) ) )
        & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
         => ! [X5] :
              ( ? [X6] :
                  ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X5),X6) = X1
                  & c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X0)
                  & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6)) )
             => hBOOL(hAPP(X2,X5)) ) )
        & ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0
         => hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ),
    inference(rectify,[],[f973]) ).

fof(f973,axiom,
    ! [X60,X22,X29] :
      ( hBOOL(hAPP(X29,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X22,X60)))
    <=> ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X60,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
         => ! [X79] :
              ( ? [X47] :
                  ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X60),X79),X47) = X22
                  & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X47),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                  & c_Orderings_Oord__class_Oless(tc_Int_Oint,X60,X47) )
             => hBOOL(hAPP(X29,X79)) ) )
        & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X60)
         => ! [X79] :
              ( ? [X47] :
                  ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X60),X79),X47) = X22
                  & c_Orderings_Oord__class_Oless(tc_Int_Oint,X47,X60)
                  & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X47)) )
             => hBOOL(hAPP(X29,X79)) ) )
        & ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X60
         => hBOOL(hAPP(X29,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__zdiv) ).

fof(f7949,plain,
    spl77_387,
    inference(avatar_split_clause,[],[f4967,f7947]) ).

fof(f7947,plain,
    ( spl77_387
  <=> ! [X2,X0,X1] :
        ( sP13(X0,X1,X2)
        | ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_387])]) ).

fof(f4967,plain,
    ! [X2,X0,X1] :
      ( sP13(X0,X1,X2)
      | ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0))) ),
    inference(cnf_transformation,[],[f3546]) ).

fof(f7945,plain,
    spl77_386,
    inference(avatar_split_clause,[],[f4966,f7943]) ).

fof(f7943,plain,
    ( spl77_386
  <=> ! [X2,X0,X1] :
        ( sP11(X0,X1,X2)
        | ~ hBOOL(hAPP(X0,sK67(X0,X1,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_386])]) ).

fof(f4966,plain,
    ! [X2,X0,X1] :
      ( sP11(X0,X1,X2)
      | ~ hBOOL(hAPP(X0,sK67(X0,X1,X2))) ),
    inference(cnf_transformation,[],[f3545]) ).

fof(f3545,plain,
    ! [X0,X1,X2] :
      ( ( sP11(X0,X1,X2)
        | ( ~ hBOOL(hAPP(X0,sK67(X0,X1,X2)))
          & c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sK67(X0,X1,X2)),sK68(X0,X1,X2)) = X1
          & c_Orderings_Oord__class_Oless(tc_Int_Oint,sK68(X0,X1,X2),X2)
          & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK68(X0,X1,X2)))
          & c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ) )
      & ( ! [X5] :
            ( hBOOL(hAPP(X0,X5))
            | ! [X6] :
                ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X5),X6) != X1
                | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X2)
                | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6)) ) )
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
        | ~ sP11(X0,X1,X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK67,sK68])],[f3542,f3544,f3543]) ).

fof(f3543,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ~ hBOOL(hAPP(X0,X3))
          & ? [X4] :
              ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3),X4) = X1
              & c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X2)
              & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4)) ) )
     => ( ~ hBOOL(hAPP(X0,sK67(X0,X1,X2)))
        & ? [X4] :
            ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sK67(X0,X1,X2)),X4) = X1
            & c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X2)
            & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4)) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f3544,plain,
    ! [X0,X1,X2] :
      ( ? [X4] :
          ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sK67(X0,X1,X2)),X4) = X1
          & c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X2)
          & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4)) )
     => ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sK67(X0,X1,X2)),sK68(X0,X1,X2)) = X1
        & c_Orderings_Oord__class_Oless(tc_Int_Oint,sK68(X0,X1,X2),X2)
        & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK68(X0,X1,X2))) ) ),
    introduced(choice_axiom,[]) ).

fof(f3542,plain,
    ! [X0,X1,X2] :
      ( ( sP11(X0,X1,X2)
        | ( ? [X3] :
              ( ~ hBOOL(hAPP(X0,X3))
              & ? [X4] :
                  ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3),X4) = X1
                  & c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X2)
                  & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4)) ) )
          & c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ) )
      & ( ! [X5] :
            ( hBOOL(hAPP(X0,X5))
            | ! [X6] :
                ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X5),X6) != X1
                | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X2)
                | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6)) ) )
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
        | ~ sP11(X0,X1,X2) ) ),
    inference(rectify,[],[f3541]) ).

fof(f3541,plain,
    ! [X2,X1,X0] :
      ( ( sP11(X2,X1,X0)
        | ( ? [X5] :
              ( ~ hBOOL(hAPP(X2,X5))
              & ? [X6] :
                  ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X5),X6) = X1
                  & c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X0)
                  & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6)) ) )
          & c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ) )
      & ( ! [X5] :
            ( hBOOL(hAPP(X2,X5))
            | ! [X6] :
                ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X5),X6) != X1
                | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X0)
                | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6)) ) )
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
        | ~ sP11(X2,X1,X0) ) ),
    inference(flattening,[],[f3540]) ).

fof(f3540,plain,
    ! [X2,X1,X0] :
      ( ( sP11(X2,X1,X0)
        | ( ? [X5] :
              ( ~ hBOOL(hAPP(X2,X5))
              & ? [X6] :
                  ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X5),X6) = X1
                  & c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X0)
                  & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6)) ) )
          & c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ) )
      & ( ! [X5] :
            ( hBOOL(hAPP(X2,X5))
            | ! [X6] :
                ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X5),X6) != X1
                | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X0)
                | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6)) ) )
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
        | ~ sP11(X2,X1,X0) ) ),
    inference(nnf_transformation,[],[f3145]) ).

fof(f7941,plain,
    spl77_385,
    inference(avatar_split_clause,[],[f4964,f7939]) ).

fof(f7939,plain,
    ( spl77_385
  <=> ! [X2,X0,X1] :
        ( sP11(X0,X1,X2)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,sK68(X0,X1,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_385])]) ).

fof(f4964,plain,
    ! [X2,X0,X1] :
      ( sP11(X0,X1,X2)
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,sK68(X0,X1,X2),X2) ),
    inference(cnf_transformation,[],[f3545]) ).

fof(f7937,plain,
    spl77_384,
    inference(avatar_split_clause,[],[f4960,f7935]) ).

fof(f7935,plain,
    ( spl77_384
  <=> ! [X2,X0,X1] :
        ( sP12(X0,X1,X2)
        | ~ hBOOL(hAPP(X0,sK65(X0,X1,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_384])]) ).

fof(f4960,plain,
    ! [X2,X0,X1] :
      ( sP12(X0,X1,X2)
      | ~ hBOOL(hAPP(X0,sK65(X0,X1,X2))) ),
    inference(cnf_transformation,[],[f3539]) ).

fof(f3539,plain,
    ! [X0,X1,X2] :
      ( ( sP12(X0,X1,X2)
        | ( ~ hBOOL(hAPP(X0,sK65(X0,X1,X2)))
          & c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sK65(X0,X1,X2)),sK66(X0,X1,X2)) = X1
          & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK66(X0,X1,X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,sK66(X0,X1,X2))
          & c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) )
      & ( ! [X5] :
            ( hBOOL(hAPP(X0,X5))
            | ! [X6] :
                ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X5),X6) != X1
                | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X6),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X6) ) )
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ sP12(X0,X1,X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK65,sK66])],[f3536,f3538,f3537]) ).

fof(f3537,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ~ hBOOL(hAPP(X0,X3))
          & ? [X4] :
              ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3),X4) = X1
              & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X4) ) )
     => ( ~ hBOOL(hAPP(X0,sK65(X0,X1,X2)))
        & ? [X4] :
            ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sK65(X0,X1,X2)),X4) = X1
            & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            & c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X4) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f3538,plain,
    ! [X0,X1,X2] :
      ( ? [X4] :
          ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sK65(X0,X1,X2)),X4) = X1
          & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X4) )
     => ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sK65(X0,X1,X2)),sK66(X0,X1,X2)) = X1
        & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK66(X0,X1,X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        & c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,sK66(X0,X1,X2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f3536,plain,
    ! [X0,X1,X2] :
      ( ( sP12(X0,X1,X2)
        | ( ? [X3] :
              ( ~ hBOOL(hAPP(X0,X3))
              & ? [X4] :
                  ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3),X4) = X1
                  & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                  & c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X4) ) )
          & c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) )
      & ( ! [X5] :
            ( hBOOL(hAPP(X0,X5))
            | ! [X6] :
                ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X5),X6) != X1
                | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X6),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X6) ) )
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ sP12(X0,X1,X2) ) ),
    inference(rectify,[],[f3535]) ).

fof(f3535,plain,
    ! [X2,X1,X0] :
      ( ( sP12(X2,X1,X0)
        | ( ? [X3] :
              ( ~ hBOOL(hAPP(X2,X3))
              & ? [X4] :
                  ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3),X4) = X1
                  & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                  & c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X4) ) )
          & c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) )
      & ( ! [X3] :
            ( hBOOL(hAPP(X2,X3))
            | ! [X4] :
                ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3),X4) != X1
                | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X4) ) )
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ sP12(X2,X1,X0) ) ),
    inference(flattening,[],[f3534]) ).

fof(f3534,plain,
    ! [X2,X1,X0] :
      ( ( sP12(X2,X1,X0)
        | ( ? [X3] :
              ( ~ hBOOL(hAPP(X2,X3))
              & ? [X4] :
                  ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3),X4) = X1
                  & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                  & c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X4) ) )
          & c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) )
      & ( ! [X3] :
            ( hBOOL(hAPP(X2,X3))
            | ! [X4] :
                ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3),X4) != X1
                | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X4) ) )
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ sP12(X2,X1,X0) ) ),
    inference(nnf_transformation,[],[f3146]) ).

fof(f7933,plain,
    spl77_383,
    inference(avatar_split_clause,[],[f4957,f7931]) ).

fof(f7931,plain,
    ( spl77_383
  <=> ! [X2,X0,X1] :
        ( sP12(X0,X1,X2)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,sK66(X0,X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_383])]) ).

fof(f4957,plain,
    ! [X2,X0,X1] :
      ( sP12(X0,X1,X2)
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,sK66(X0,X1,X2)) ),
    inference(cnf_transformation,[],[f3539]) ).

fof(f7929,plain,
    spl77_382,
    inference(avatar_split_clause,[],[f4932,f7927]) ).

fof(f7927,plain,
    ( spl77_382
  <=> ! [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,[spl77_382])]) ).

fof(f4932,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,[],[f2819]) ).

fof(f2819,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,[],[f1912]) ).

fof(f1912,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,[],[f303]) ).

fof(f303,axiom,
    ! [X40,X41,X42] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X42,X41),X40)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X42,X40) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__lessD1) ).

fof(f7925,plain,
    spl77_381,
    inference(avatar_split_clause,[],[f4863,f7923]) ).

fof(f7923,plain,
    ( spl77_381
  <=> ! [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,[spl77_381])]) ).

fof(f4863,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,[],[f2742]) ).

fof(f2742,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,[],[f1857]) ).

fof(f1857,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,[],[f835]) ).

fof(f835,axiom,
    ! [X21,X40,X41] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X41,X40)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X41,X21),X40) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__diff__less) ).

fof(f7921,plain,
    spl77_380,
    inference(avatar_split_clause,[],[f4860,f7919]) ).

fof(f7919,plain,
    ( spl77_380
  <=> ! [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,[spl77_380])]) ).

fof(f4860,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,[],[f2739]) ).

fof(f2739,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,[],[f1854]) ).

fof(f1854,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,[],[f298]) ).

fof(f298,axiom,
    ! [X30,X24,X25] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X25,X24)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X25,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X24,X30)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I1_J) ).

fof(f7917,plain,
    ( spl77_379
    | ~ spl77_34
    | ~ spl77_261 ),
    inference(avatar_split_clause,[],[f7275,f7122,f6021,f7914]) ).

fof(f7914,plain,
    ( spl77_379
  <=> c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Int_Oring__1__class_Oof__int(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_379])]) ).

fof(f7275,plain,
    ( c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Int_Oring__1__class_Oof__int(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ spl77_34
    | ~ spl77_261 ),
    inference(resolution,[],[f7123,f6023]) ).

fof(f7912,plain,
    spl77_378,
    inference(avatar_split_clause,[],[f4859,f7910]) ).

fof(f7910,plain,
    ( spl77_378
  <=> ! [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,[spl77_378])]) ).

fof(f4859,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,[],[f2738]) ).

fof(f2738,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,[],[f1853]) ).

fof(f1853,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,[],[f299]) ).

fof(f299,axiom,
    ! [X24,X30,X25] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X25,X30)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X25,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X24,X30)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I2_J) ).

fof(f7908,plain,
    spl77_377,
    inference(avatar_split_clause,[],[f4797,f7906]) ).

fof(f4797,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,[],[f2656]) ).

fof(f2656,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,[],[f1804]) ).

fof(f1804,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,[],[f345]) ).

fof(f345,axiom,
    ! [X31,X32,X7] :
      ( class_Rings_Ocomm__semiring__1(X7)
     => c_Groups_Oplus__class_Oplus(X7,X32,X31) = c_Groups_Oplus__class_Oplus(X7,X31,X32) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).

fof(f7904,plain,
    spl77_376,
    inference(avatar_split_clause,[],[f4714,f7902]) ).

fof(f7902,plain,
    ( spl77_376
  <=> ! [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,[spl77_376])]) ).

fof(f4714,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,[],[f2558]) ).

fof(f2558,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,[],[f1742]) ).

fof(f1742,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,[],[f846]) ).

fof(f846,axiom,
    ! [X33,X32,X7] :
      ( class_Groups_Ogroup__add(X7)
     => c_Groups_Oplus__class_Oplus(X7,c_Groups_Ominus__class_Ominus(X7,X32,X33),X33) = X32 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__cancel) ).

fof(f7900,plain,
    spl77_375,
    inference(avatar_split_clause,[],[f4713,f7898]) ).

fof(f7898,plain,
    ( spl77_375
  <=> ! [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,[spl77_375])]) ).

fof(f4713,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,[],[f2557]) ).

fof(f2557,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,[],[f1741]) ).

fof(f1741,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,[],[f845]) ).

fof(f845,axiom,
    ! [X33,X32,X7] :
      ( class_Groups_Ogroup__add(X7)
     => c_Groups_Ominus__class_Ominus(X7,c_Groups_Oplus__class_Oplus(X7,X32,X33),X33) = X32 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__cancel) ).

fof(f7896,plain,
    spl77_374,
    inference(avatar_split_clause,[],[f4493,f7894]) ).

fof(f7894,plain,
    ( spl77_374
  <=> ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
        | ~ sP5(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_374])]) ).

fof(f4493,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
      | ~ sP5(X0,X1) ),
    inference(cnf_transformation,[],[f3391]) ).

fof(f7892,plain,
    spl77_373,
    inference(avatar_split_clause,[],[f4485,f7890]) ).

fof(f7890,plain,
    ( spl77_373
  <=> ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
        | ~ sP4(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_373])]) ).

fof(f4485,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
      | ~ sP4(X0,X1) ),
    inference(cnf_transformation,[],[f3388]) ).

fof(f7888,plain,
    spl77_372,
    inference(avatar_split_clause,[],[f4477,f7886]) ).

fof(f7886,plain,
    ( spl77_372
  <=> ! [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,[spl77_372])]) ).

fof(f4477,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,[],[f3383]) ).

fof(f3383,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,[],[f3382]) ).

fof(f3382,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,[],[f1615]) ).

fof(f1615,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,[],[f283]) ).

fof(f283,axiom,
    ! [X22,X23] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X23,X22)
    <=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X22
        & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X23 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__is__0) ).

fof(f7884,plain,
    spl77_371,
    inference(avatar_split_clause,[],[f4476,f7882]) ).

fof(f7882,plain,
    ( spl77_371
  <=> ! [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,[spl77_371])]) ).

fof(f4476,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,[],[f3383]) ).

fof(f7880,plain,
    spl77_370,
    inference(avatar_split_clause,[],[f4229,f7878]) ).

fof(f4229,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
    inference(cnf_transformation,[],[f2313]) ).

fof(f2313,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
    inference(ennf_transformation,[],[f1472]) ).

fof(f1472,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
     => c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0) ),
    inference(rectify,[],[f978]) ).

fof(f978,axiom,
    ! [X21,X26] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X26,X21)
     => c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X26,X21) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__less) ).

fof(f7876,plain,
    spl77_369,
    inference(avatar_split_clause,[],[f4215,f7874]) ).

fof(f7874,plain,
    ( spl77_369
  <=> ! [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,[spl77_369])]) ).

fof(f4215,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,[],[f2299]) ).

fof(f2299,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,[],[f2298]) ).

fof(f2298,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,[],[f1459]) ).

fof(f1459,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,[],[f14]) ).

fof(f14,axiom,
    ! [X24,X25] :
      ( X24 != X25
     => ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X25,X24)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X24,X25) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE__nat) ).

fof(f7871,plain,
    spl77_368,
    inference(avatar_split_clause,[],[f4191,f7869]) ).

fof(f7869,plain,
    ( spl77_368
  <=> ! [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,[spl77_368])]) ).

fof(f4191,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,[],[f2279]) ).

fof(f2279,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,[],[f1440]) ).

fof(f1440,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,[],[f365]) ).

fof(f365,axiom,
    ! [X32,X7] :
      ( class_Rings_Ocomm__semiring__1(X7)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),c_Groups_Oone__class_Oone(X7)),X32) = X32 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).

fof(f7867,plain,
    spl77_367,
    inference(avatar_split_clause,[],[f4190,f7865]) ).

fof(f7865,plain,
    ( spl77_367
  <=> ! [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,[spl77_367])]) ).

fof(f4190,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,[],[f2278]) ).

fof(f2278,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,[],[f1439]) ).

fof(f1439,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,[],[f364]) ).

fof(f364,axiom,
    ! [X32,X7] :
      ( class_Rings_Ocomm__semiring__1(X7)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X32),c_Groups_Oone__class_Oone(X7)) = X32 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).

fof(f7863,plain,
    spl77_366,
    inference(avatar_split_clause,[],[f4189,f7861]) ).

fof(f7861,plain,
    ( spl77_366
  <=> ! [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,[spl77_366])]) ).

fof(f4189,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,[],[f2277]) ).

fof(f2277,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,[],[f1438]) ).

fof(f1438,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,[],[f719]) ).

fof(f719,axiom,
    ! [X25,X7] :
      ( class_Rings_Ocomm__semiring__1(X7)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X7),X25),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X25 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).

fof(f7859,plain,
    spl77_365,
    inference(avatar_split_clause,[],[f4185,f7857]) ).

fof(f7857,plain,
    ( spl77_365
  <=> ! [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,[spl77_365])]) ).

fof(f4185,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,[],[f2273]) ).

fof(f2273,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,[],[f1434]) ).

fof(f1434,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,[],[f157]) ).

fof(f157,axiom,
    ! [X32,X7] :
      ( class_Groups_Omonoid__mult(X7)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),c_Groups_Oone__class_Oone(X7)),X32) = X32 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1__left) ).

fof(f7855,plain,
    spl77_364,
    inference(avatar_split_clause,[],[f4184,f7853]) ).

fof(f7853,plain,
    ( spl77_364
  <=> ! [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,[spl77_364])]) ).

fof(f4184,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,[],[f2272]) ).

fof(f2272,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,[],[f1433]) ).

fof(f1433,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,[],[f160]) ).

fof(f160,axiom,
    ! [X32,X7] :
      ( class_Groups_Omonoid__mult(X7)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X32),c_Groups_Oone__class_Oone(X7)) = X32 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1__right) ).

fof(f7851,plain,
    spl77_363,
    inference(avatar_split_clause,[],[f4183,f7849]) ).

fof(f7849,plain,
    ( spl77_363
  <=> ! [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,[spl77_363])]) ).

fof(f4183,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,[],[f2271]) ).

fof(f2271,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,[],[f1432]) ).

fof(f1432,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,[],[f754]) ).

fof(f754,axiom,
    ! [X32,X7] :
      ( class_Groups_Omonoid__mult(X7)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X7),X32),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X32 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__one__right) ).

fof(f7847,plain,
    spl77_362,
    inference(avatar_split_clause,[],[f4178,f7845]) ).

fof(f7845,plain,
    ( spl77_362
  <=> ! [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,[spl77_362])]) ).

fof(f4178,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,[],[f2266]) ).

fof(f2266,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,[],[f1427]) ).

fof(f1427,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,[],[f158]) ).

fof(f158,axiom,
    ! [X32,X7] :
      ( class_Groups_Ocomm__monoid__mult(X7)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),c_Groups_Oone__class_Oone(X7)),X32) = X32 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1) ).

fof(f7843,plain,
    spl77_361,
    inference(avatar_split_clause,[],[f4177,f7841]) ).

fof(f7841,plain,
    ( spl77_361
  <=> ! [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,[spl77_361])]) ).

fof(f4177,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,[],[f2265]) ).

fof(f2265,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,[],[f1426]) ).

fof(f1426,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,[],[f161]) ).

fof(f161,axiom,
    ! [X32,X7] :
      ( class_Groups_Ocomm__monoid__mult(X7)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X32),c_Groups_Oone__class_Oone(X7)) = X32 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ocomm__neutral) ).

fof(f7839,plain,
    spl77_360,
    inference(avatar_split_clause,[],[f4164,f7837]) ).

fof(f7837,plain,
    ( spl77_360
  <=> ! [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,[spl77_360])]) ).

fof(f4164,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,[],[f2256]) ).

fof(f2256,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,[],[f1417]) ).

fof(f1417,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,[],[f877]) ).

fof(f877,axiom,
    ! [X32,X7] :
      ( class_Groups_Ogroup__add(X7)
     => c_Groups_Ouminus__class_Ouminus(X7,X32) = c_Groups_Ominus__class_Ominus(X7,c_Groups_Ozero__class_Ozero(X7),X32) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__0) ).

fof(f7835,plain,
    spl77_359,
    inference(avatar_split_clause,[],[f4163,f7833]) ).

fof(f7833,plain,
    ( spl77_359
  <=> ! [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,[spl77_359])]) ).

fof(f4163,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,[],[f2255]) ).

fof(f2255,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,[],[f1416]) ).

fof(f1416,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,[],[f130]) ).

fof(f130,axiom,
    ! [X32,X7] :
      ( class_Groups_Ogroup__add(X7)
     => c_Groups_Ozero__class_Ozero(X7) = c_Groups_Oplus__class_Oplus(X7,c_Groups_Ouminus__class_Ouminus(X7,X32),X32) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__minus) ).

fof(f7830,plain,
    spl77_358,
    inference(avatar_split_clause,[],[f4162,f7828]) ).

fof(f7828,plain,
    ( spl77_358
  <=> ! [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,[spl77_358])]) ).

fof(f4162,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,[],[f2254]) ).

fof(f2254,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,[],[f1415]) ).

fof(f1415,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,[],[f134]) ).

fof(f134,axiom,
    ! [X32,X7] :
      ( class_Groups_Ogroup__add(X7)
     => c_Groups_Ozero__class_Ozero(X7) = c_Groups_Oplus__class_Oplus(X7,X32,c_Groups_Ouminus__class_Ouminus(X7,X32)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__minus) ).

fof(f7826,plain,
    spl77_357,
    inference(avatar_split_clause,[],[f4107,f7824]) ).

fof(f7824,plain,
    ( spl77_357
  <=> ! [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,[spl77_357])]) ).

fof(f4107,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,[],[f3237]) ).

fof(f3237,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,[],[f2219]) ).

fof(f2219,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,[],[f1382]) ).

fof(f1382,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,[],[f186]) ).

fof(f186,axiom,
    ! [X18,X7] :
      ( class_Groups_Olinordered__ab__group__add(X7)
     => ( c_Groups_Ouminus__class_Ouminus(X7,X18) = X18
      <=> c_Groups_Ozero__class_Ozero(X7) = X18 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__equal__zero) ).

fof(f7822,plain,
    spl77_356,
    inference(avatar_split_clause,[],[f4106,f7820]) ).

fof(f7820,plain,
    ( spl77_356
  <=> ! [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,[spl77_356])]) ).

fof(f4106,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,[],[f2218]) ).

fof(f2218,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,[],[f1381]) ).

fof(f1381,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,[],[f129]) ).

fof(f129,axiom,
    ! [X32,X7] :
      ( class_Groups_Oab__group__add(X7)
     => c_Groups_Ozero__class_Ozero(X7) = c_Groups_Oplus__class_Oplus(X7,c_Groups_Ouminus__class_Ouminus(X7,X32),X32) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__left__minus) ).

fof(f7818,plain,
    spl77_355,
    inference(avatar_split_clause,[],[f4081,f7816]) ).

fof(f7816,plain,
    ( spl77_355
  <=> ! [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,[spl77_355])]) ).

fof(f4081,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,[],[f1359]) ).

fof(f1359,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,[],[f94]) ).

fof(f94,axiom,
    ! [X24,X25] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X24,X25)
      | X24 = X25
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,X25,X24) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__linear) ).

fof(f7814,plain,
    spl77_354,
    inference(avatar_split_clause,[],[f4040,f7812]) ).

fof(f7812,plain,
    ( spl77_354
  <=> ! [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,[spl77_354])]) ).

fof(f4040,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,[],[f1323]) ).

fof(f1323,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,[],[f917]) ).

fof(f917,axiom,
    ! [X52,X30] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X30,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X52)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X30,X52),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__int__def) ).

fof(f7810,plain,
    spl77_353,
    inference(avatar_split_clause,[],[f4034,f7808]) ).

fof(f7808,plain,
    ( spl77_353
  <=> ! [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,[spl77_353])]) ).

fof(f4034,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,[],[f1317]) ).

fof(f1317,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,[],[f922]) ).

fof(f922,axiom,
    ! [X28,X58] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X58,X28) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X58,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X28)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__diff__def) ).

fof(f7806,plain,
    spl77_352,
    inference(avatar_split_clause,[],[f4014,f7804]) ).

fof(f7804,plain,
    ( spl77_352
  <=> ! [X4,X0] :
        ( hBOOL(hAPP(X0,hAPP(c_Int_Onat,sK40(X0))))
        | ~ hBOOL(hAPP(X0,X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_352])]) ).

fof(f4014,plain,
    ! [X0,X4] :
      ( hBOOL(hAPP(X0,hAPP(c_Int_Onat,sK40(X0))))
      | ~ hBOOL(hAPP(X0,X4)) ),
    inference(cnf_transformation,[],[f3226]) ).

fof(f7802,plain,
    spl77_351,
    inference(avatar_split_clause,[],[f4009,f7800]) ).

fof(f7800,plain,
    ( spl77_351
  <=> ! [X0,X1] :
        ( hBOOL(hAPP(X0,X1))
        | ~ hBOOL(hAPP(X0,hAPP(c_Int_Onat,sK35(X0)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_351])]) ).

fof(f4009,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,hAPP(c_Int_Onat,sK35(X0)))) ),
    inference(cnf_transformation,[],[f3216]) ).

fof(f7798,plain,
    spl77_350,
    inference(avatar_split_clause,[],[f3983,f7796]) ).

fof(f7796,plain,
    ( spl77_350
  <=> ! [X0] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_350])]) ).

fof(f3983,plain,
    ! [X0] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(cnf_transformation,[],[f3200]) ).

fof(f3200,plain,
    ! [X0] :
      ( ( hBOOL(hAPP(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
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
    inference(nnf_transformation,[],[f1286]) ).

fof(f1286,plain,
    ! [X0] :
      ( hBOOL(hAPP(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,[],[f429]) ).

fof(f429,axiom,
    ! [X22] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X22 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__0__eq) ).

fof(f7794,plain,
    spl77_349,
    inference(avatar_split_clause,[],[f3981,f7792]) ).

fof(f7792,plain,
    ( spl77_349
  <=> ! [X0] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
        | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_349])]) ).

fof(f3981,plain,
    ! [X0] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
      | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) ),
    inference(cnf_transformation,[],[f3199]) ).

fof(f3199,plain,
    ! [X0] :
      ( ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 )
      & ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
        | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) ) ),
    inference(nnf_transformation,[],[f1285]) ).

fof(f1285,plain,
    ! [X0] :
      ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)
    <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
    inference(rectify,[],[f250]) ).

fof(f250,axiom,
    ! [X22] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X22 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__eq__0__conv) ).

fof(f7790,plain,
    ( spl77_348
    | ~ spl77_232
    | ~ spl77_320 ),
    inference(avatar_split_clause,[],[f7655,f7515,f6982,f7788]) ).

fof(f7788,plain,
    ( spl77_348
  <=> ! [X0] : sP3(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_348])]) ).

fof(f6982,plain,
    ( spl77_232
  <=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_232])]) ).

fof(f7515,plain,
    ( spl77_320
  <=> ! [X0,X1] :
        ( sP3(X1,X0)
        | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_320])]) ).

fof(f7655,plain,
    ( ! [X0] : sP3(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
    | ~ spl77_232
    | ~ spl77_320 ),
    inference(trivial_inequality_removal,[],[f7654]) ).

fof(f7654,plain,
    ( ! [X0] :
        ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | sP3(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) )
    | ~ spl77_232
    | ~ spl77_320 ),
    inference(superposition,[],[f7516,f6983]) ).

fof(f6983,plain,
    ( ! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
    | ~ spl77_232 ),
    inference(avatar_component_clause,[],[f6982]) ).

fof(f7516,plain,
    ( ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0)
        | sP3(X1,X0) )
    | ~ spl77_320 ),
    inference(avatar_component_clause,[],[f7515]) ).

fof(f7786,plain,
    spl77_347,
    inference(avatar_split_clause,[],[f3979,f7784]) ).

fof(f7784,plain,
    ( spl77_347
  <=> ! [X0] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
        | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_347])]) ).

fof(f3979,plain,
    ! [X0] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
      | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0) ),
    inference(cnf_transformation,[],[f3198]) ).

fof(f3198,plain,
    ! [X0] :
      ( ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0)
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 )
      & ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
        | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0) ) ),
    inference(nnf_transformation,[],[f1284]) ).

fof(f1284,plain,
    ! [X0] :
      ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0)
    <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
    inference(rectify,[],[f671]) ).

fof(f671,axiom,
    ! [X22] :
      ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),X22)
    <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X22 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__zero__iff) ).

fof(f7782,plain,
    spl77_346,
    inference(avatar_split_clause,[],[f3942,f7780]) ).

fof(f7780,plain,
    ( spl77_346
  <=> ! [X0] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),sK27(X0))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_346])]) ).

fof(f3942,plain,
    ! [X0] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),sK27(X0))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
    inference(cnf_transformation,[],[f3176]) ).

fof(f7778,plain,
    spl77_345,
    inference(avatar_split_clause,[],[f3929,f7776]) ).

fof(f7776,plain,
    ( spl77_345
  <=> ! [X0] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(X0))
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_345])]) ).

fof(f3929,plain,
    ! [X0] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(X0))
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X0) ),
    inference(cnf_transformation,[],[f2158]) ).

fof(f2158,plain,
    ! [X0] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(X0))
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X0) ),
    inference(ennf_transformation,[],[f1248]) ).

fof(f1248,plain,
    ! [X0] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X0)
     => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(X0)) ),
    inference(rectify,[],[f798]) ).

fof(f798,axiom,
    ! [X25] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X25)
     => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(X25)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__gt__zero) ).

fof(f7774,plain,
    spl77_344,
    inference(avatar_split_clause,[],[f3927,f7772]) ).

fof(f7772,plain,
    ( spl77_344
  <=> ! [X0] :
        ( c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X0,X0)
        | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_344])]) ).

fof(f3927,plain,
    ! [X0] :
      ( c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X0,X0)
      | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 ),
    inference(cnf_transformation,[],[f2156]) ).

fof(f2156,plain,
    ! [X0] :
      ( c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X0,X0)
      | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 ),
    inference(ennf_transformation,[],[f1246]) ).

fof(f1246,plain,
    ! [X0] :
      ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0
     => c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X0,X0) ),
    inference(rectify,[],[f951]) ).

fof(f951,axiom,
    ! [X32] :
      ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X32
     => c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X32,X32) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__self) ).

fof(f7770,plain,
    spl77_343,
    inference(avatar_split_clause,[],[f3919,f7768]) ).

fof(f7768,plain,
    ( spl77_343
  <=> ! [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,[spl77_343])]) ).

fof(f3919,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,[],[f2148]) ).

fof(f2148,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,[],[f1238]) ).

fof(f1238,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,[],[f784]) ).

fof(f784,axiom,
    ! [X7] :
      ( class_Power_Opower(X7)
     => c_Power_Opower__class_Opower(X7) = c_Power_Opower_Opower(X7,c_Groups_Oone__class_Oone(X7),c_Groups_Otimes__class_Otimes(X7)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__power__power) ).

fof(f7766,plain,
    spl77_342,
    inference(avatar_split_clause,[],[f3902,f7764]) ).

fof(f7764,plain,
    ( spl77_342
  <=> ! [X0] : hBOOL(hAPP(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,[spl77_342])]) ).

fof(f3902,plain,
    ! [X0] : hBOOL(hAPP(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,[],[f1222]) ).

fof(f1222,plain,
    ! [X0] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X0))),
    inference(rectify,[],[f459]) ).

fof(f459,axiom,
    ! [X26] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26),X26))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__square) ).

fof(f7762,plain,
    spl77_341,
    inference(avatar_split_clause,[],[f3901,f7760]) ).

fof(f7760,plain,
    ( spl77_341
  <=> ! [X0] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) = c_Int_Oring__1__class_Oof__int(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_341])]) ).

fof(f3901,plain,
    ! [X0] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) = c_Int_Oring__1__class_Oof__int(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)),
    inference(cnf_transformation,[],[f1221]) ).

fof(f1221,plain,
    ! [X0] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) = c_Int_Oring__1__class_Oof__int(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)),
    inference(rectify,[],[f717]) ).

fof(f717,axiom,
    ! [X21] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X21) = c_Int_Oring__1__class_Oof__int(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X21)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__int__eq) ).

fof(f7758,plain,
    spl77_340,
    inference(avatar_split_clause,[],[f3900,f7756]) ).

fof(f7756,plain,
    ( spl77_340
  <=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_340])]) ).

fof(f3900,plain,
    ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))),
    inference(cnf_transformation,[],[f1220]) ).

fof(f1220,plain,
    ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))),
    inference(rectify,[],[f643]) ).

fof(f643,axiom,
    ! [X21] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X21))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__zminus__int) ).

fof(f7754,plain,
    spl77_339,
    inference(avatar_split_clause,[],[f3899,f7752]) ).

fof(f7752,plain,
    ( spl77_339
  <=> ! [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,[spl77_339])]) ).

fof(f3899,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,[],[f1219]) ).

fof(f1219,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,[],[f144]) ).

fof(f144,axiom,
    ! [X30] : 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),X30),X30),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_odd__nonzero) ).

fof(f7688,plain,
    ( ~ spl77_136
    | ~ spl77_338
    | ~ spl77_1
    | ~ spl77_323 ),
    inference(avatar_split_clause,[],[f7664,f7527,f5856,f7685,f6531]) ).

fof(f6531,plain,
    ( spl77_136
  <=> class_Orderings_Olinorder(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_136])]) ).

fof(f7685,plain,
    ( spl77_338
  <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK24,sK23) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_338])]) ).

fof(f7527,plain,
    ( spl77_323
  <=> ! [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,[spl77_323])]) ).

fof(f7664,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK24,sK23)
    | ~ class_Orderings_Olinorder(tc_Nat_Onat)
    | ~ spl77_1
    | ~ spl77_323 ),
    inference(resolution,[],[f7528,f5858]) ).

fof(f7528,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
        | ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
        | ~ class_Orderings_Olinorder(X2) )
    | ~ spl77_323 ),
    inference(avatar_component_clause,[],[f7527]) ).

fof(f7633,plain,
    ( spl77_337
    | ~ spl77_215
    | ~ spl77_286 ),
    inference(avatar_split_clause,[],[f7383,f7222,f6897,f7631]) ).

fof(f7631,plain,
    ( spl77_337
  <=> ! [X0] : sP2(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_337])]) ).

fof(f6897,plain,
    ( spl77_215
  <=> ! [X0] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_215])]) ).

fof(f7222,plain,
    ( spl77_286
  <=> ! [X0,X1] :
        ( sP2(X1,X0)
        | ~ hBOOL(hAPP(X1,hAPP(c_Int_Onat,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_286])]) ).

fof(f7383,plain,
    ( ! [X0] : sP2(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
    | ~ spl77_215
    | ~ spl77_286 ),
    inference(resolution,[],[f7223,f6898]) ).

fof(f6898,plain,
    ( ! [X0] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0))
    | ~ spl77_215 ),
    inference(avatar_component_clause,[],[f6897]) ).

fof(f7223,plain,
    ( ! [X0,X1] :
        ( ~ hBOOL(hAPP(X1,hAPP(c_Int_Onat,X0)))
        | sP2(X1,X0) )
    | ~ spl77_286 ),
    inference(avatar_component_clause,[],[f7222]) ).

fof(f7581,plain,
    spl77_336,
    inference(avatar_split_clause,[],[f5787,f7579]) ).

fof(f7579,plain,
    ( spl77_336
  <=> ! [X0,X1] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
        | sP5(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_336])]) ).

fof(f5787,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
      | sP5(X0,X1) ),
    inference(forward_demodulation,[],[f5786,f3871]) ).

fof(f5786,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))
      | sP5(X0,X1) ),
    inference(forward_demodulation,[],[f5426,f4025]) ).

fof(f5426,plain,
    ! [X0,X1] :
      ( sP5(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,[],[f4498,f3879]) ).

fof(f4498,plain,
    ! [X0,X1] :
      ( sP5(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,[],[f3392]) ).

fof(f3392,plain,
    ! [X0,X1] :
      ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
        | ~ sP5(X0,X1) )
      & ( sP5(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,[],[f3136]) ).

fof(f3136,plain,
    ! [X0,X1] :
      ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
    <=> sP5(X0,X1) ),
    inference(definition_folding,[],[f1619,f3135]) ).

fof(f1619,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,[],[f306]) ).

fof(f306,axiom,
    ! [X22,X23] :
      ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X23,X22)
    <=> ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X22
          & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X23 )
        | ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X22
          & c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X23 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__is__add) ).

fof(f7577,plain,
    spl77_335,
    inference(avatar_split_clause,[],[f5785,f7575]) ).

fof(f7575,plain,
    ( spl77_335
  <=> ! [X0,X1] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
        | ~ sP5(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_335])]) ).

fof(f5785,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
      | ~ sP5(X0,X1) ),
    inference(forward_demodulation,[],[f5784,f3871]) ).

fof(f5784,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))
      | ~ sP5(X0,X1) ),
    inference(forward_demodulation,[],[f5425,f4025]) ).

fof(f5425,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))
      | ~ sP5(X0,X1) ),
    inference(definition_unfolding,[],[f4499,f3879]) ).

fof(f4499,plain,
    ! [X0,X1] :
      ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
      | ~ sP5(X0,X1) ),
    inference(cnf_transformation,[],[f3392]) ).

fof(f7573,plain,
    spl77_334,
    inference(avatar_split_clause,[],[f5771,f7571]) ).

fof(f7571,plain,
    ( spl77_334
  <=> ! [X0,X1] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
        | sP4(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_334])]) ).

fof(f5771,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
      | sP4(X0,X1) ),
    inference(forward_demodulation,[],[f5770,f3871]) ).

fof(f5770,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))
      | sP4(X0,X1) ),
    inference(forward_demodulation,[],[f5419,f4025]) ).

fof(f5419,plain,
    ! [X0,X1] :
      ( sP4(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,[],[f4490,f3879]) ).

fof(f4490,plain,
    ! [X0,X1] :
      ( sP4(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,[],[f3389]) ).

fof(f3389,plain,
    ! [X0,X1] :
      ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
        | ~ sP4(X0,X1) )
      & ( sP4(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,[],[f3134]) ).

fof(f3134,plain,
    ! [X0,X1] :
      ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
    <=> sP4(X0,X1) ),
    inference(definition_folding,[],[f1618,f3133]) ).

fof(f1618,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,[],[f307]) ).

fof(f307,axiom,
    ! [X22,X23] :
      ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X23,X22)
    <=> ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X22
          & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X23 )
        | ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X22
          & c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X23 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__is__1) ).

fof(f7569,plain,
    spl77_333,
    inference(avatar_split_clause,[],[f5769,f7567]) ).

fof(f7567,plain,
    ( spl77_333
  <=> ! [X0,X1] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
        | ~ sP4(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_333])]) ).

fof(f5769,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
      | ~ sP4(X0,X1) ),
    inference(forward_demodulation,[],[f5768,f3871]) ).

fof(f5768,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))
      | ~ sP4(X0,X1) ),
    inference(forward_demodulation,[],[f5418,f4025]) ).

fof(f5418,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))
      | ~ sP4(X0,X1) ),
    inference(definition_unfolding,[],[f4491,f3879]) ).

fof(f4491,plain,
    ! [X0,X1] :
      ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
      | ~ sP4(X0,X1) ),
    inference(cnf_transformation,[],[f3389]) ).

fof(f7565,plain,
    spl77_332,
    inference(avatar_split_clause,[],[f5693,f7563]) ).

fof(f7563,plain,
    ( spl77_332
  <=> ! [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,[spl77_332])]) ).

fof(f5693,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,[],[f5692,f3871]) ).

fof(f5692,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,[],[f5318,f5313]) ).

fof(f5318,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,[],[f3904,f3879,f3879]) ).

fof(f3904,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,[],[f1224]) ).

fof(f1224,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,[],[f733]) ).

fof(f733,axiom,
    ! [X21] : 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))),X21),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc__0) ).

fof(f7561,plain,
    ( spl77_331
    | spl77_257
    | ~ spl77_288 ),
    inference(avatar_split_clause,[],[f7404,f7230,f7105,f7559]) ).

fof(f7559,plain,
    ( spl77_331
  <=> ! [X0,X1] : sP12(X0,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_331])]) ).

fof(f7105,plain,
    ( spl77_257
  <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_257])]) ).

fof(f7230,plain,
    ( spl77_288
  <=> ! [X2,X0,X1] :
        ( sP12(X0,X1,X2)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_288])]) ).

fof(f7404,plain,
    ( ! [X0,X1] : sP12(X0,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))
    | spl77_257
    | ~ spl77_288 ),
    inference(resolution,[],[f7231,f7107]) ).

fof(f7107,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | spl77_257 ),
    inference(avatar_component_clause,[],[f7105]) ).

fof(f7231,plain,
    ( ! [X2,X0,X1] :
        ( sP12(X0,X1,X2)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
    | ~ spl77_288 ),
    inference(avatar_component_clause,[],[f7230]) ).

fof(f7557,plain,
    spl77_330,
    inference(avatar_split_clause,[],[f5634,f7555]) ).

fof(f7555,plain,
    ( spl77_330
  <=> ! [X2,X1] :
        ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP13(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_330])]) ).

fof(f5634,plain,
    ! [X2,X1] :
      ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ sP13(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1,X2) ),
    inference(equality_resolution,[],[f4950]) ).

fof(f4950,plain,
    ! [X2,X0,X1] :
      ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0
      | ~ sP13(X0,X1,X2) ),
    inference(cnf_transformation,[],[f3533]) ).

fof(f3533,plain,
    ! [X0,X1,X2] :
      ( ( sP13(X0,X1,X2)
        | ~ sP12(X2,X1,X0)
        | ~ sP11(X2,X1,X0)
        | ( ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 ) )
      & ( ( sP12(X2,X1,X0)
          & sP11(X2,X1,X0)
          & ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ) )
        | ~ sP13(X0,X1,X2) ) ),
    inference(flattening,[],[f3532]) ).

fof(f3532,plain,
    ! [X0,X1,X2] :
      ( ( sP13(X0,X1,X2)
        | ~ sP12(X2,X1,X0)
        | ~ sP11(X2,X1,X0)
        | ( ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 ) )
      & ( ( sP12(X2,X1,X0)
          & sP11(X2,X1,X0)
          & ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ) )
        | ~ sP13(X0,X1,X2) ) ),
    inference(nnf_transformation,[],[f3147]) ).

fof(f7553,plain,
    spl77_329,
    inference(avatar_split_clause,[],[f5538,f7551]) ).

fof(f7551,plain,
    ( spl77_329
  <=> ! [X0,X3] :
        ( hBOOL(hAPP(X0,X3))
        | ~ sP2(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_329])]) ).

fof(f5538,plain,
    ! [X3,X0] :
      ( hBOOL(hAPP(X0,X3))
      | ~ sP2(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3)) ),
    inference(equality_resolution,[],[f4435]) ).

fof(f4435,plain,
    ! [X3,X0,X1] :
      ( hBOOL(hAPP(X0,X3))
      | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3) != X1
      | ~ sP2(X0,X1) ),
    inference(cnf_transformation,[],[f3354]) ).

fof(f3354,plain,
    ! [X0,X1] :
      ( ( sP2(X0,X1)
        | ( ~ hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
        | ( ~ hBOOL(hAPP(X0,sK58(X0,X1)))
          & hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK58(X0,X1)) = X1 ) )
      & ( ( ( hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
          & ! [X3] :
              ( hBOOL(hAPP(X0,X3))
              | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3) != X1 ) )
        | ~ sP2(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK58])],[f3352,f3353]) ).

fof(f3353,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ hBOOL(hAPP(X0,X2))
          & hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2) = X1 )
     => ( ~ hBOOL(hAPP(X0,sK58(X0,X1)))
        & hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK58(X0,X1)) = X1 ) ),
    introduced(choice_axiom,[]) ).

fof(f3352,plain,
    ! [X0,X1] :
      ( ( sP2(X0,X1)
        | ( ~ hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
        | ? [X2] :
            ( ~ hBOOL(hAPP(X0,X2))
            & hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2) = X1 ) )
      & ( ( ( hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
          & ! [X3] :
              ( hBOOL(hAPP(X0,X3))
              | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3) != X1 ) )
        | ~ sP2(X0,X1) ) ),
    inference(rectify,[],[f3351]) ).

fof(f3351,plain,
    ! [X1,X0] :
      ( ( sP2(X1,X0)
        | ( ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
        | ? [X2] :
            ( ~ hBOOL(hAPP(X1,X2))
            & hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2) = X0 ) )
      & ( ( ( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
          & ! [X2] :
              ( hBOOL(hAPP(X1,X2))
              | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2) != X0 ) )
        | ~ sP2(X1,X0) ) ),
    inference(flattening,[],[f3350]) ).

fof(f3350,plain,
    ! [X1,X0] :
      ( ( sP2(X1,X0)
        | ( ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
        | ? [X2] :
            ( ~ hBOOL(hAPP(X1,X2))
            & hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2) = X0 ) )
      & ( ( ( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
          & ! [X2] :
              ( hBOOL(hAPP(X1,X2))
              | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2) != X0 ) )
        | ~ sP2(X1,X0) ) ),
    inference(nnf_transformation,[],[f3129]) ).

fof(f3129,plain,
    ! [X1,X0] :
      ( sP2(X1,X0)
    <=> ( ( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
        & ! [X2] :
            ( hBOOL(hAPP(X1,X2))
            | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2) != X0 ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).

fof(f7549,plain,
    spl77_328,
    inference(avatar_split_clause,[],[f5484,f7547]) ).

fof(f7547,plain,
    ( spl77_328
  <=> ! [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,[spl77_328])]) ).

fof(f5484,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,[],[f4073]) ).

fof(f4073,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,[],[f2196]) ).

fof(f2196,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,[],[f1355]) ).

fof(f1355,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,[],[f909]) ).

fof(f909,axiom,
    ! [X82,X26] :
      ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X26
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X82),X26) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X82),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X82),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X26,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
      & ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X26
       => c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X82),X26) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__eq__if) ).

fof(f7545,plain,
    spl77_327,
    inference(avatar_split_clause,[],[f5312,f7543]) ).

fof(f7543,plain,
    ( spl77_327
  <=> ! [X0] : ~ hBOOL(hAPP(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,[spl77_327])]) ).

fof(f5312,plain,
    ! [X0] : ~ hBOOL(hAPP(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,[],[f3863,f3879]) ).

fof(f3863,plain,
    ! [X0] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X0)),X0)),
    inference(cnf_transformation,[],[f1183]) ).

fof(f1183,plain,
    ! [X0] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X0)),X0)),
    inference(rectify,[],[f438]) ).

fof(f438,axiom,
    ! [X21] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X21)),X21)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__le__n) ).

fof(f7541,plain,
    spl77_326,
    inference(avatar_split_clause,[],[f4945,f7539]) ).

fof(f7539,plain,
    ( spl77_326
  <=> ! [X2,X0,X1] :
        ( ~ hBOOL(hAPP(hAPP(X2,X1),X0))
        | ~ sP10(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_326])]) ).

fof(f4945,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP(hAPP(X2,X1),X0))
      | ~ sP10(X0,X1,X2) ),
    inference(cnf_transformation,[],[f3531]) ).

fof(f3531,plain,
    ! [X0,X1,X2] :
      ( ( ~ hBOOL(hAPP(hAPP(X2,X1),X0))
        & c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) )
      | ~ sP10(X0,X1,X2) ),
    inference(rectify,[],[f3530]) ).

fof(f3530,plain,
    ! [X2,X1,X0] :
      ( ( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
        & c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) )
      | ~ sP10(X2,X1,X0) ),
    inference(nnf_transformation,[],[f3143]) ).

fof(f3143,plain,
    ! [X2,X1,X0] :
      ( ( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
        & c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) )
      | ~ sP10(X2,X1,X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP10])]) ).

fof(f7537,plain,
    spl77_325,
    inference(avatar_split_clause,[],[f4835,f7535]) ).

fof(f7535,plain,
    ( spl77_325
  <=> ! [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,[spl77_325])]) ).

fof(f4835,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,[],[f2715]) ).

fof(f2715,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,[],[f2714]) ).

fof(f2714,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,[],[f1838]) ).

fof(f1838,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,[],[f28]) ).

fof(f28,axiom,
    ! [X32,X33,X7] :
      ( class_Orderings_Oorder(X7)
     => ( c_Orderings_Oord__class_Oless(X7,X33,X32)
       => ~ c_Orderings_Oord__class_Oless(X7,X32,X33) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I9_J) ).

fof(f7533,plain,
    spl77_324,
    inference(avatar_split_clause,[],[f4822,f7531]) ).

fof(f7531,plain,
    ( spl77_324
  <=> ! [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,[spl77_324])]) ).

fof(f4822,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,[],[f2694]) ).

fof(f2694,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,[],[f2693]) ).

fof(f2693,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,[],[f1827]) ).

fof(f1827,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,[],[f39]) ).

fof(f39,axiom,
    ! [X24,X25,X7] :
      ( class_Orderings_Opreorder(X7)
     => ( c_Orderings_Oord__class_Oless(X7,X25,X24)
       => ~ c_Orderings_Oord__class_Oless(X7,X24,X25) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__less) ).

fof(f7529,plain,
    spl77_323,
    inference(avatar_split_clause,[],[f4793,f7527]) ).

fof(f4793,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,[],[f3495]) ).

fof(f3495,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,[],[f3494]) ).

fof(f3494,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,[],[f2654]) ).

fof(f2654,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,[],[f1802]) ).

fof(f1802,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,[],[f33]) ).

fof(f33,axiom,
    ! [X34,X10,X7] :
      ( class_Orderings_Olinorder(X7)
     => ( ~ c_Orderings_Oord__class_Oless(X7,X10,X34)
      <=> ( X10 = X34
          | c_Orderings_Oord__class_Oless(X7,X34,X10) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__iff__gr__or__eq) ).

fof(f7525,plain,
    spl77_322,
    inference(avatar_split_clause,[],[f4748,f7523]) ).

fof(f7523,plain,
    ( spl77_322
  <=> ! [X2,X0,X1] :
        ( c_Nat_Osemiring__1__class_Oof__nat__aux(X2,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) = X0
        | ~ class_Rings_Osemiring__1(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_322])]) ).

fof(f4748,plain,
    ! [X2,X0,X1] :
      ( c_Nat_Osemiring__1__class_Oof__nat__aux(X2,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) = X0
      | ~ class_Rings_Osemiring__1(X2) ),
    inference(cnf_transformation,[],[f2590]) ).

fof(f2590,plain,
    ! [X0,X1,X2] :
      ( c_Nat_Osemiring__1__class_Oof__nat__aux(X2,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) = X0
      | ~ class_Rings_Osemiring__1(X2) ),
    inference(ennf_transformation,[],[f1766]) ).

fof(f1766,plain,
    ! [X0,X1,X2] :
      ( class_Rings_Osemiring__1(X2)
     => c_Nat_Osemiring__1__class_Oof__nat__aux(X2,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) = X0 ),
    inference(rectify,[],[f93]) ).

fof(f93,axiom,
    ! [X45,X46,X7] :
      ( class_Rings_Osemiring__1(X7)
     => c_Nat_Osemiring__1__class_Oof__nat__aux(X7,X46,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X45) = X45 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__aux_Osimps_I1_J) ).

fof(f7521,plain,
    spl77_321,
    inference(avatar_split_clause,[],[f4473,f7519]) ).

fof(f7519,plain,
    ( spl77_321
  <=> ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0)
        | ~ sP3(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_321])]) ).

fof(f4473,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0)
      | ~ sP3(X1,X0) ),
    inference(cnf_transformation,[],[f3380]) ).

fof(f3380,plain,
    ! [X0,X1] :
      ( ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0)
        | ~ sP3(X1,X0) )
      & ( sP3(X1,X0)
        | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0) ) ),
    inference(nnf_transformation,[],[f3132]) ).

fof(f3132,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0)
    <=> sP3(X1,X0) ),
    inference(definition_folding,[],[f1613,f3131]) ).

fof(f3131,plain,
    ! [X1,X0] :
      ( sP3(X1,X0)
    <=> ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1)
          & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
          & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) )
        | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).

fof(f1613,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0)
    <=> ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1)
          & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
          & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) )
        | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 ) ),
    inference(rectify,[],[f960]) ).

fof(f960,axiom,
    ! [X60,X45] :
      ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X45,X60)
    <=> ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X60,X45)
          & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X45),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X45,X60)
          & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X45)) )
        | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X60 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__eq__0__iff) ).

fof(f7517,plain,
    spl77_320,
    inference(avatar_split_clause,[],[f4472,f7515]) ).

fof(f4472,plain,
    ! [X0,X1] :
      ( sP3(X1,X0)
      | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0) ),
    inference(cnf_transformation,[],[f3380]) ).

fof(f7513,plain,
    spl77_319,
    inference(avatar_split_clause,[],[f4389,f7511]) ).

fof(f7511,plain,
    ( spl77_319
  <=> ! [X0,X1] :
        ( hBOOL(hAPP(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,[spl77_319])]) ).

fof(f4389,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X0))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
    inference(cnf_transformation,[],[f3318]) ).

fof(f3318,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
        | X0 = X1
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X0)) )
      & ( ( X0 != X1
          & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X0)) )
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ) ),
    inference(flattening,[],[f3317]) ).

fof(f3317,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
        | X0 = X1
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X0)) )
      & ( ( X0 != X1
          & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X0)) )
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ) ),
    inference(nnf_transformation,[],[f1588]) ).

fof(f1588,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
    <=> ( X0 != X1
        & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X0)) ) ),
    inference(rectify,[],[f458]) ).

fof(f458,axiom,
    ! [X51,X50] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X50,X51)
    <=> ( X50 != X51
        & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X50),X51)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__le) ).

fof(f7509,plain,
    spl77_318,
    inference(avatar_split_clause,[],[f4384,f7507]) ).

fof(f7507,plain,
    ( spl77_318
  <=> ! [X0,X1] :
        ( hBOOL(hAPP(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,[spl77_318])]) ).

fof(f4384,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X0))
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) ),
    inference(cnf_transformation,[],[f3315]) ).

fof(f3315,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
        | X0 = X1
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X0)) )
      & ( ( X0 != X1
          & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X0)) )
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) ) ),
    inference(flattening,[],[f3314]) ).

fof(f3314,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
        | X0 = X1
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X0)) )
      & ( ( X0 != X1
          & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X0)) )
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) ) ),
    inference(nnf_transformation,[],[f1586]) ).

fof(f1586,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
    <=> ( X0 != X1
        & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X0)) ) ),
    inference(rectify,[],[f570]) ).

fof(f570,axiom,
    ! [X34,X10] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X10,X34)
    <=> ( X10 != X34
        & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X10),X34)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__less__def) ).

fof(f7505,plain,
    spl77_317,
    inference(avatar_split_clause,[],[f4288,f7503]) ).

fof(f7503,plain,
    ( spl77_317
  <=> ! [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,[spl77_317])]) ).

fof(f4288,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,[],[f2369]) ).

fof(f2369,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,[],[f1510]) ).

fof(f1510,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,[],[f284]) ).

fof(f284,axiom,
    ! [X21,X26] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X26,X21) = X26
     => c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X21 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__eq__self__zero) ).

fof(f7501,plain,
    spl77_316,
    inference(avatar_split_clause,[],[f4226,f7499]) ).

fof(f7499,plain,
    ( spl77_316
  <=> ! [X0,X1] :
        ( hBOOL(hAPP(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,[spl77_316])]) ).

fof(f4226,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X0))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
    inference(cnf_transformation,[],[f2310]) ).

fof(f2310,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X0))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
    inference(ennf_transformation,[],[f1469]) ).

fof(f1469,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X0)) ),
    inference(rectify,[],[f442]) ).

fof(f442,axiom,
    ! [X21,X26] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X26,X21)
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26),X21)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__le__nat) ).

fof(f7497,plain,
    spl77_315,
    inference(avatar_split_clause,[],[f4197,f7495]) ).

fof(f7495,plain,
    ( spl77_315
  <=> ! [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,[spl77_315])]) ).

fof(f4197,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,[],[f2285]) ).

fof(f2285,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,[],[f1446]) ).

fof(f1446,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,[],[f149]) ).

fof(f149,axiom,
    ! [X32,X7] :
      ( class_Rings_Olinordered__semidom(X7)
     => c_Orderings_Oord__class_Oless(X7,X32,c_Groups_Oplus__class_Oplus(X7,X32,c_Groups_Oone__class_Oone(X7))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__one) ).

fof(f7493,plain,
    spl77_314,
    inference(avatar_split_clause,[],[f4196,f7491]) ).

fof(f7491,plain,
    ( spl77_314
  <=> ! [X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X0),c_Groups_Ozero__class_Ozero(X1))
        | ~ class_Rings_Olinordered__semidom(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_314])]) ).

fof(f4196,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X0),c_Groups_Ozero__class_Ozero(X1))
      | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(cnf_transformation,[],[f2284]) ).

fof(f2284,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X0),c_Groups_Ozero__class_Ozero(X1))
      | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(ennf_transformation,[],[f1445]) ).

fof(f1445,plain,
    ! [X0,X1] :
      ( class_Rings_Olinordered__semidom(X1)
     => ~ c_Orderings_Oord__class_Oless(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X0),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(rectify,[],[f109]) ).

fof(f109,axiom,
    ! [X26,X7] :
      ( class_Rings_Olinordered__semidom(X7)
     => ~ c_Orderings_Oord__class_Oless(X7,hAPP(c_Nat_Osemiring__1__class_Oof__nat(X7),X26),c_Groups_Ozero__class_Ozero(X7)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__less__0__iff) ).

fof(f7489,plain,
    spl77_313,
    inference(avatar_split_clause,[],[f4143,f7487]) ).

fof(f7487,plain,
    ( spl77_313
  <=> ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Odiv(X1,c_Groups_Ozero__class_Ozero(X1),X0)
        | ~ class_Divides_Osemiring__div(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_313])]) ).

fof(f4143,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Odiv(X1,c_Groups_Ozero__class_Ozero(X1),X0)
      | ~ class_Divides_Osemiring__div(X1) ),
    inference(cnf_transformation,[],[f2238]) ).

fof(f2238,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Odiv(X1,c_Groups_Ozero__class_Ozero(X1),X0)
      | ~ class_Divides_Osemiring__div(X1) ),
    inference(ennf_transformation,[],[f1401]) ).

fof(f1401,plain,
    ! [X0,X1] :
      ( class_Divides_Osemiring__div(X1)
     => c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Odiv(X1,c_Groups_Ozero__class_Ozero(X1),X0) ),
    inference(rectify,[],[f955]) ).

fof(f955,axiom,
    ! [X32,X7] :
      ( class_Divides_Osemiring__div(X7)
     => c_Groups_Ozero__class_Ozero(X7) = c_Divides_Odiv__class_Odiv(X7,c_Groups_Ozero__class_Ozero(X7),X32) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__0) ).

fof(f7485,plain,
    spl77_312,
    inference(avatar_split_clause,[],[f4142,f7483]) ).

fof(f7483,plain,
    ( spl77_312
  <=> ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Odiv(X1,X0,c_Groups_Ozero__class_Ozero(X1))
        | ~ class_Divides_Osemiring__div(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_312])]) ).

fof(f4142,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Odiv(X1,X0,c_Groups_Ozero__class_Ozero(X1))
      | ~ class_Divides_Osemiring__div(X1) ),
    inference(cnf_transformation,[],[f2237]) ).

fof(f2237,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Odiv(X1,X0,c_Groups_Ozero__class_Ozero(X1))
      | ~ class_Divides_Osemiring__div(X1) ),
    inference(ennf_transformation,[],[f1400]) ).

fof(f1400,plain,
    ! [X0,X1] :
      ( class_Divides_Osemiring__div(X1)
     => c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Odiv(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(rectify,[],[f956]) ).

fof(f956,axiom,
    ! [X32,X7] :
      ( class_Divides_Osemiring__div(X7)
     => c_Groups_Ozero__class_Ozero(X7) = c_Divides_Odiv__class_Odiv(X7,X32,c_Groups_Ozero__class_Ozero(X7)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__by__0) ).

fof(f7481,plain,
    spl77_311,
    inference(avatar_split_clause,[],[f4101,f7479]) ).

fof(f7479,plain,
    ( spl77_311
  <=> ! [X0,X1] :
        ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),hAPP(X1,X0)))
        | ~ c_SEQ_Osubseq(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_311])]) ).

fof(f4101,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),hAPP(X1,X0)))
      | ~ c_SEQ_Osubseq(X1) ),
    inference(cnf_transformation,[],[f2213]) ).

fof(f2213,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),hAPP(X1,X0)))
      | ~ c_SEQ_Osubseq(X1) ),
    inference(ennf_transformation,[],[f1376]) ).

fof(f1376,plain,
    ! [X0,X1] :
      ( c_SEQ_Osubseq(X1)
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),hAPP(X1,X0))) ),
    inference(rectify,[],[f465]) ).

fof(f465,axiom,
    ! [X22,X1] :
      ( c_SEQ_Osubseq(X1)
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22),hAPP(X1,X22))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_seq__suble) ).

fof(f7477,plain,
    ( spl77_310
    | ~ spl77_164
    | ~ spl77_289 ),
    inference(avatar_split_clause,[],[f7410,f7234,f6669,f7475]) ).

fof(f7475,plain,
    ( spl77_310
  <=> ! [X0,X1] : sP11(X0,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_310])]) ).

fof(f6669,plain,
    ( spl77_164
  <=> ! [X1] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_164])]) ).

fof(f7234,plain,
    ( spl77_289
  <=> ! [X2,X0,X1] :
        ( sP11(X0,X1,X2)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_289])]) ).

fof(f7410,plain,
    ( ! [X0,X1] : sP11(X0,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl77_164
    | ~ spl77_289 ),
    inference(resolution,[],[f7235,f6670]) ).

fof(f6670,plain,
    ( ! [X1] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X1)
    | ~ spl77_164 ),
    inference(avatar_component_clause,[],[f6669]) ).

fof(f7235,plain,
    ( ! [X2,X0,X1] :
        ( sP11(X0,X1,X2)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) )
    | ~ spl77_289 ),
    inference(avatar_component_clause,[],[f7234]) ).

fof(f7473,plain,
    spl77_309,
    inference(avatar_split_clause,[],[f4032,f7471]) ).

fof(f7471,plain,
    ( spl77_309
  <=> ! [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,[spl77_309])]) ).

fof(f4032,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,[],[f1315]) ).

fof(f1315,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,[],[f814]) ).

fof(f814,axiom,
    ! [X26,X21] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X26)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__0) ).

fof(f7469,plain,
    spl77_308,
    inference(avatar_split_clause,[],[f3930,f7467]) ).

fof(f7467,plain,
    ( spl77_308
  <=> ! [X0] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X0),X0)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_308])]) ).

fof(f3930,plain,
    ! [X0] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X0),X0)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ),
    inference(cnf_transformation,[],[f2159]) ).

fof(f2159,plain,
    ! [X0] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X0),X0)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ),
    inference(ennf_transformation,[],[f1249]) ).

fof(f1249,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,c_Transcendental_Oln(X0),X0) ),
    inference(rectify,[],[f792]) ).

fof(f792,axiom,
    ! [X25] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X25)
     => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X25),X25) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__less__self) ).

fof(f7465,plain,
    spl77_307,
    inference(avatar_split_clause,[],[f3925,f7463]) ).

fof(f7463,plain,
    ( spl77_307
  <=> ! [X0] :
        ( hBOOL(hAPP(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,[spl77_307])]) ).

fof(f3925,plain,
    ! [X0] :
      ( hBOOL(hAPP(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,[],[f2154]) ).

fof(f2154,plain,
    ! [X0] :
      ( hBOOL(hAPP(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,[],[f1244]) ).

fof(f1244,plain,
    ! [X0] :
      ( class_Rings_Olinordered__semidom(X0)
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0)),c_Groups_Oone__class_Oone(X0))) ),
    inference(rectify,[],[f494]) ).

fof(f494,axiom,
    ! [X7] :
      ( class_Rings_Olinordered__semidom(X7)
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7)),c_Groups_Oone__class_Oone(X7))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__one) ).

fof(f7461,plain,
    spl77_306,
    inference(avatar_split_clause,[],[f3924,f7459]) ).

fof(f7459,plain,
    ( spl77_306
  <=> ! [X0] :
        ( ~ hBOOL(hAPP(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,[spl77_306])]) ).

fof(f3924,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP(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,[],[f2153]) ).

fof(f2153,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP(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,[],[f1243]) ).

fof(f1243,plain,
    ! [X0] :
      ( class_Rings_Olinordered__semidom(X0)
     => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Oone__class_Oone(X0)),c_Groups_Ozero__class_Ozero(X0))) ),
    inference(rectify,[],[f493]) ).

fof(f493,axiom,
    ! [X7] :
      ( class_Rings_Olinordered__semidom(X7)
     => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Oone__class_Oone(X7)),c_Groups_Ozero__class_Ozero(X7))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__one__le__zero) ).

fof(f7457,plain,
    spl77_305,
    inference(avatar_split_clause,[],[f3921,f7455]) ).

fof(f7455,plain,
    ( spl77_305
  <=> ! [X0] :
        ( c_Groups_Ozero__class_Ozero(X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ class_Rings_Osemiring__1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_305])]) ).

fof(f3921,plain,
    ! [X0] :
      ( c_Groups_Ozero__class_Ozero(X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      | ~ class_Rings_Osemiring__1(X0) ),
    inference(cnf_transformation,[],[f2150]) ).

fof(f2150,plain,
    ! [X0] :
      ( c_Groups_Ozero__class_Ozero(X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      | ~ class_Rings_Osemiring__1(X0) ),
    inference(ennf_transformation,[],[f1240]) ).

fof(f1240,plain,
    ! [X0] :
      ( class_Rings_Osemiring__1(X0)
     => c_Groups_Ozero__class_Ozero(X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(rectify,[],[f95]) ).

fof(f95,axiom,
    ! [X7] :
      ( class_Rings_Osemiring__1(X7)
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X7),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(X7) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__0) ).

fof(f7453,plain,
    spl77_304,
    inference(avatar_split_clause,[],[f3920,f7451]) ).

fof(f7451,plain,
    ( spl77_304
  <=> ! [X0] :
        ( c_Groups_Oone__class_Oone(X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ class_Rings_Osemiring__1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_304])]) ).

fof(f3920,plain,
    ! [X0] :
      ( c_Groups_Oone__class_Oone(X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),c_Groups_Oone__class_Oone(tc_Nat_Onat))
      | ~ class_Rings_Osemiring__1(X0) ),
    inference(cnf_transformation,[],[f2149]) ).

fof(f2149,plain,
    ! [X0] :
      ( c_Groups_Oone__class_Oone(X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),c_Groups_Oone__class_Oone(tc_Nat_Onat))
      | ~ class_Rings_Osemiring__1(X0) ),
    inference(ennf_transformation,[],[f1239]) ).

fof(f1239,plain,
    ! [X0] :
      ( class_Rings_Osemiring__1(X0)
     => c_Groups_Oone__class_Oone(X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(rectify,[],[f153]) ).

fof(f153,axiom,
    ! [X7] :
      ( class_Rings_Osemiring__1(X7)
     => c_Groups_Oone__class_Oone(X7) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X7),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__1) ).

fof(f7449,plain,
    spl77_303,
    inference(avatar_split_clause,[],[f3898,f7447]) ).

fof(f7447,plain,
    ( spl77_303
  <=> ! [X0] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatceiling(X0)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_303])]) ).

fof(f3898,plain,
    ! [X0] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatceiling(X0)))),
    inference(cnf_transformation,[],[f1218]) ).

fof(f1218,plain,
    ! [X0] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatceiling(X0)))),
    inference(rectify,[],[f678]) ).

fof(f678,axiom,
    ! [X25] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X25),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatceiling(X25)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__natceiling__ge) ).

fof(f7445,plain,
    spl77_302,
    inference(avatar_split_clause,[],[f3896,f7443]) ).

fof(f7443,plain,
    ( spl77_302
  <=> ! [X0] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_302])]) ).

fof(f3896,plain,
    ! [X0] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))),
    inference(cnf_transformation,[],[f1216]) ).

fof(f1216,plain,
    ! [X0] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))),
    inference(rectify,[],[f516]) ).

fof(f516,axiom,
    ! [X21] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X21))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__zle__int) ).

fof(f7441,plain,
    spl77_301,
    inference(avatar_split_clause,[],[f3895,f7439]) ).

fof(f7439,plain,
    ( spl77_301
  <=> ! [X0] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_301])]) ).

fof(f3895,plain,
    ! [X0] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0))),
    inference(cnf_transformation,[],[f1215]) ).

fof(f1215,plain,
    ! [X0] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0))),
    inference(rectify,[],[f664]) ).

fof(f664,axiom,
    ! [X21] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X21))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__ge__zero) ).

fof(f7437,plain,
    spl77_300,
    inference(avatar_split_clause,[],[f3894,f7435]) ).

fof(f7435,plain,
    ( spl77_300
  <=> ! [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,[spl77_300])]) ).

fof(f3894,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,[],[f1214]) ).

fof(f1214,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,[],[f285]) ).

fof(f285,axiom,
    ! [X21] : 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)),X21),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__0) ).

fof(f7433,plain,
    spl77_299,
    inference(avatar_split_clause,[],[f3893,f7431]) ).

fof(f7431,plain,
    ( spl77_299
  <=> ! [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,[spl77_299])]) ).

fof(f3893,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,[],[f1213]) ).

fof(f1213,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,[],[f286]) ).

fof(f286,axiom,
    ! [X26] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__0__right) ).

fof(f7409,plain,
    ( spl77_298
    | ~ spl77_164
    | ~ spl77_288 ),
    inference(avatar_split_clause,[],[f7399,f7230,f6669,f7407]) ).

fof(f7407,plain,
    ( spl77_298
  <=> ! [X0,X1] : sP12(X0,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_298])]) ).

fof(f7399,plain,
    ( ! [X0,X1] : sP12(X0,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl77_164
    | ~ spl77_288 ),
    inference(resolution,[],[f7231,f6670]) ).

fof(f7269,plain,
    spl77_297,
    inference(avatar_split_clause,[],[f5827,f7266]) ).

fof(f7266,plain,
    ( spl77_297
  <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_297])]) ).

fof(f5827,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(forward_demodulation,[],[f5826,f3894]) ).

fof(f5826,plain,
    ! [X1] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(forward_demodulation,[],[f5580,f3894]) ).

fof(f5580,plain,
    ! [X0,X1] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)),
    inference(equality_resolution,[],[f4609]) ).

fof(f4609,plain,
    ! [X2,X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Odiv(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_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2 ),
    inference(cnf_transformation,[],[f2481]) ).

fof(f2481,plain,
    ! [X0,X1,X2] :
      ( ( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0) = c_Divides_Odiv__class_Odiv(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_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2 )
      & ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Odiv(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_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2 ) ),
    inference(ennf_transformation,[],[f1680]) ).

fof(f1680,plain,
    ! [X0,X1,X2] :
      ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2
       => c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0) = c_Divides_Odiv__class_Odiv(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_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2
       => c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Odiv(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(rectify,[],[f979]) ).

fof(f979,axiom,
    ! [X21,X26,X40] :
      ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X40
       => c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X26,X21) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X40),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X40),X21)) )
      & ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X40
       => c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X40),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X40),X21)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__div__cancel__disj) ).

fof(f7264,plain,
    spl77_296,
    inference(avatar_split_clause,[],[f5708,f7262]) ).

fof(f7262,plain,
    ( spl77_296
  <=> ! [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,[spl77_296])]) ).

fof(f5708,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,[],[f5707,f3871]) ).

fof(f5707,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,[],[f5335,f5313]) ).

fof(f5335,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,[],[f3977,f3879]) ).

fof(f3977,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,[],[f3197]) ).

fof(f3197,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,[],[f1283]) ).

fof(f1283,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,[],[f111]) ).

fof(f111,axiom,
    ! [X22] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X22 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc0) ).

fof(f7260,plain,
    spl77_295,
    inference(avatar_split_clause,[],[f5605,f7258]) ).

fof(f7258,plain,
    ( spl77_295
  <=> ! [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,[spl77_295])]) ).

fof(f5605,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,[],[f4738]) ).

fof(f4738,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,[],[f3485]) ).

fof(f7256,plain,
    spl77_294,
    inference(avatar_split_clause,[],[f5589,f7254]) ).

fof(f7254,plain,
    ( spl77_294
  <=> ! [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,[spl77_294])]) ).

fof(f5589,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,[],[f4649]) ).

fof(f4649,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,[],[f3451]) ).

fof(f7252,plain,
    spl77_293,
    inference(avatar_split_clause,[],[f5544,f7250]) ).

fof(f7250,plain,
    ( spl77_293
  <=> ! [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,[spl77_293])]) ).

fof(f5544,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,[],[f4464]) ).

fof(f4464,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,[],[f3376]) ).

fof(f7248,plain,
    spl77_292,
    inference(avatar_split_clause,[],[f5490,f7246]) ).

fof(f7246,plain,
    ( spl77_292
  <=> ! [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,[spl77_292])]) ).

fof(f5490,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,[],[f4108]) ).

fof(f4108,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,[],[f3237]) ).

fof(f7244,plain,
    spl77_291,
    inference(avatar_split_clause,[],[f5488,f7242]) ).

fof(f7242,plain,
    ( spl77_291
  <=> ! [X1] :
        ( c_Groups_Ozero__class_Ozero(X1) = c_Int_Oring__1__class_Oof__int(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ class_Int_Oring__char__0(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_291])]) ).

fof(f5488,plain,
    ! [X1] :
      ( c_Groups_Ozero__class_Ozero(X1) = c_Int_Oring__1__class_Oof__int(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | ~ class_Int_Oring__char__0(X1) ),
    inference(equality_resolution,[],[f4098]) ).

fof(f4098,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X1) = c_Int_Oring__1__class_Oof__int(X1,X0)
      | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0
      | ~ class_Int_Oring__char__0(X1) ),
    inference(cnf_transformation,[],[f3235]) ).

fof(f7240,plain,
    spl77_290,
    inference(avatar_split_clause,[],[f5311,f7238]) ).

fof(f7238,plain,
    ( spl77_290
  <=> ! [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,[spl77_290])]) ).

fof(f5311,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,[],[f3862,f3879]) ).

fof(f3862,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,[],[f1182]) ).

fof(f1182,plain,
    ! [X0] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(X0)),
    inference(rectify,[],[f86]) ).

fof(f86,axiom,
    ! [X21] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(X21)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__Suc) ).

fof(f7236,plain,
    spl77_289,
    inference(avatar_split_clause,[],[f4962,f7234]) ).

fof(f4962,plain,
    ! [X2,X0,X1] :
      ( sP11(X0,X1,X2)
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
    inference(cnf_transformation,[],[f3545]) ).

fof(f7232,plain,
    spl77_288,
    inference(avatar_split_clause,[],[f4956,f7230]) ).

fof(f4956,plain,
    ! [X2,X0,X1] :
      ( sP12(X0,X1,X2)
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(cnf_transformation,[],[f3539]) ).

fof(f7228,plain,
    spl77_287,
    inference(avatar_split_clause,[],[f4442,f7226]) ).

fof(f7226,plain,
    ( spl77_287
  <=> ! [X0,X1] :
        ( hBOOL(hAPP(X1,hAPP(c_Int_Onat,X0)))
        | ~ sP2(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_287])]) ).

fof(f4442,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP(X1,hAPP(c_Int_Onat,X0)))
      | ~ sP2(X1,X0) ),
    inference(cnf_transformation,[],[f3355]) ).

fof(f3355,plain,
    ! [X0,X1] :
      ( ( hBOOL(hAPP(X1,hAPP(c_Int_Onat,X0)))
        | ~ sP2(X1,X0) )
      & ( sP2(X1,X0)
        | ~ hBOOL(hAPP(X1,hAPP(c_Int_Onat,X0))) ) ),
    inference(nnf_transformation,[],[f3130]) ).

fof(f3130,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP(X1,hAPP(c_Int_Onat,X0)))
    <=> sP2(X1,X0) ),
    inference(definition_folding,[],[f2480,f3129]) ).

fof(f2480,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP(X1,hAPP(c_Int_Onat,X0)))
    <=> ( ( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
        & ! [X2] :
            ( hBOOL(hAPP(X1,X2))
            | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2) != X0 ) ) ),
    inference(ennf_transformation,[],[f1602]) ).

fof(f1602,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP(X1,hAPP(c_Int_Onat,X0)))
    <=> ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
         => hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
        & ! [X2] :
            ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2) = X0
           => hBOOL(hAPP(X1,X2)) ) ) ),
    inference(rectify,[],[f652]) ).

fof(f652,axiom,
    ! [X45,X29] :
      ( hBOOL(hAPP(X29,hAPP(c_Int_Onat,X45)))
    <=> ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X45,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
         => hBOOL(hAPP(X29,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
        & ! [X4] :
            ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4) = X45
           => hBOOL(hAPP(X29,X4)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__nat) ).

fof(f7224,plain,
    spl77_286,
    inference(avatar_split_clause,[],[f4441,f7222]) ).

fof(f4441,plain,
    ! [X0,X1] :
      ( sP2(X1,X0)
      | ~ hBOOL(hAPP(X1,hAPP(c_Int_Onat,X0))) ),
    inference(cnf_transformation,[],[f3355]) ).

fof(f7220,plain,
    spl77_285,
    inference(avatar_split_clause,[],[f4188,f7218]) ).

fof(f7218,plain,
    ( spl77_285
  <=> ! [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,[spl77_285])]) ).

fof(f4188,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,[],[f2276]) ).

fof(f2276,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,[],[f1437]) ).

fof(f1437,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,[],[f354]) ).

fof(f354,axiom,
    ! [X32,X7] :
      ( class_Rings_Ocomm__semiring__1(X7)
     => c_Groups_Oplus__class_Oplus(X7,c_Groups_Ozero__class_Ozero(X7),X32) = X32 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).

fof(f7216,plain,
    spl77_284,
    inference(avatar_split_clause,[],[f4187,f7214]) ).

fof(f7214,plain,
    ( spl77_284
  <=> ! [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,[spl77_284])]) ).

fof(f4187,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,[],[f2275]) ).

fof(f2275,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,[],[f1436]) ).

fof(f1436,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,[],[f353]) ).

fof(f353,axiom,
    ! [X32,X7] :
      ( class_Rings_Ocomm__semiring__1(X7)
     => c_Groups_Oplus__class_Oplus(X7,X32,c_Groups_Ozero__class_Ozero(X7)) = X32 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).

fof(f7212,plain,
    spl77_283,
    inference(avatar_split_clause,[],[f4176,f7210]) ).

fof(f7210,plain,
    ( spl77_283
  <=> ! [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,[spl77_283])]) ).

fof(f4176,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,[],[f2264]) ).

fof(f2264,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,[],[f1425]) ).

fof(f1425,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,[],[f192]) ).

fof(f192,axiom,
    ! [X32,X7] :
      ( class_Groups_Ocomm__monoid__add(X7)
     => c_Groups_Oplus__class_Oplus(X7,c_Groups_Ozero__class_Ozero(X7),X32) = X32 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0) ).

fof(f7208,plain,
    spl77_282,
    inference(avatar_split_clause,[],[f4175,f7206]) ).

fof(f7206,plain,
    ( spl77_282
  <=> ! [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,[spl77_282])]) ).

fof(f4175,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,[],[f2263]) ).

fof(f2263,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,[],[f1424]) ).

fof(f1424,plain,
    ! [X0,X1] :
      ( class_Groups_Omonoid__add(X1)
     => c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X0) = X0 ),
    inference(rectify,[],[f191]) ).

fof(f191,axiom,
    ! [X32,X7] :
      ( class_Groups_Omonoid__add(X7)
     => c_Groups_Oplus__class_Oplus(X7,c_Groups_Ozero__class_Ozero(X7),X32) = X32 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__left) ).

fof(f7204,plain,
    spl77_281,
    inference(avatar_split_clause,[],[f4174,f7202]) ).

fof(f7202,plain,
    ( spl77_281
  <=> ! [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,[spl77_281])]) ).

fof(f4174,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,[],[f2262]) ).

fof(f2262,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,[],[f1423]) ).

fof(f1423,plain,
    ! [X0,X1] :
      ( class_Groups_Omonoid__add(X1)
     => c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0 ),
    inference(rectify,[],[f194]) ).

fof(f194,axiom,
    ! [X32,X7] :
      ( class_Groups_Omonoid__add(X7)
     => c_Groups_Oplus__class_Oplus(X7,X32,c_Groups_Ozero__class_Ozero(X7)) = X32 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__right) ).

fof(f7200,plain,
    spl77_280,
    inference(avatar_split_clause,[],[f4173,f7198]) ).

fof(f7198,plain,
    ( spl77_280
  <=> ! [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,[spl77_280])]) ).

fof(f4173,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,[],[f2261]) ).

fof(f2261,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,[],[f1422]) ).

fof(f1422,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,[],[f195]) ).

fof(f195,axiom,
    ! [X32,X7] :
      ( class_Groups_Ocomm__monoid__add(X7)
     => c_Groups_Oplus__class_Oplus(X7,X32,c_Groups_Ozero__class_Ozero(X7)) = X32 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add_Ocomm__neutral) ).

fof(f7196,plain,
    ( spl77_279
    | ~ spl77_172
    | ~ spl77_234 ),
    inference(avatar_split_clause,[],[f7077,f6990,f6708,f7194]) ).

fof(f7194,plain,
    ( spl77_279
  <=> ! [X0] : sP0(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_279])]) ).

fof(f6708,plain,
    ( spl77_172
  <=> ! [X1] : sP0(hAPP(c_Int_Onat,X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_172])]) ).

fof(f6990,plain,
    ( spl77_234
  <=> ! [X0] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_234])]) ).

fof(f7077,plain,
    ( ! [X0] : sP0(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))
    | ~ spl77_172
    | ~ spl77_234 ),
    inference(superposition,[],[f6709,f6991]) ).

fof(f6991,plain,
    ( ! [X0] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)) = X0
    | ~ spl77_234 ),
    inference(avatar_component_clause,[],[f6990]) ).

fof(f6709,plain,
    ( ! [X1] : sP0(hAPP(c_Int_Onat,X1),X1)
    | ~ spl77_172 ),
    inference(avatar_component_clause,[],[f6708]) ).

fof(f7192,plain,
    spl77_278,
    inference(avatar_split_clause,[],[f4161,f7190]) ).

fof(f7190,plain,
    ( spl77_278
  <=> ! [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,[spl77_278])]) ).

fof(f4161,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,[],[f2253]) ).

fof(f2253,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,[],[f1414]) ).

fof(f1414,plain,
    ! [X0,X1] :
      ( class_Groups_Ogroup__add(X1)
     => c_Groups_Ominus__class_Ominus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0 ),
    inference(rectify,[],[f863]) ).

fof(f863,axiom,
    ! [X32,X7] :
      ( class_Groups_Ogroup__add(X7)
     => c_Groups_Ominus__class_Ominus(X7,X32,c_Groups_Ozero__class_Ozero(X7)) = X32 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__0__right) ).

fof(f7188,plain,
    spl77_277,
    inference(avatar_split_clause,[],[f4160,f7186]) ).

fof(f7186,plain,
    ( spl77_277
  <=> ! [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,[spl77_277])]) ).

fof(f4160,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,[],[f2252]) ).

fof(f2252,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,[],[f1413]) ).

fof(f1413,plain,
    ! [X0,X1] :
      ( class_Groups_Ogroup__add(X1)
     => c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0)) = X0 ),
    inference(rectify,[],[f154]) ).

fof(f154,axiom,
    ! [X32,X7] :
      ( class_Groups_Ogroup__add(X7)
     => c_Groups_Ouminus__class_Ouminus(X7,c_Groups_Ouminus__class_Ouminus(X7,X32)) = X32 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__minus) ).

fof(f7184,plain,
    spl77_276,
    inference(avatar_split_clause,[],[f4159,f7182]) ).

fof(f7182,plain,
    ( spl77_276
  <=> ! [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,[spl77_276])]) ).

fof(f4159,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,[],[f2251]) ).

fof(f2251,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,[],[f1412]) ).

fof(f1412,plain,
    ! [X0,X1] :
      ( class_Groups_Ogroup__add(X1)
     => c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ominus__class_Ominus(X1,X0,X0) ),
    inference(rectify,[],[f862]) ).

fof(f862,axiom,
    ! [X32,X7] :
      ( class_Groups_Ogroup__add(X7)
     => c_Groups_Ozero__class_Ozero(X7) = c_Groups_Ominus__class_Ominus(X7,X32,X32) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__self) ).

fof(f7180,plain,
    spl77_275,
    inference(avatar_split_clause,[],[f4141,f7178]) ).

fof(f7178,plain,
    ( spl77_275
  <=> ! [X0,X1] :
        ( c_Divides_Odiv__class_Odiv(X1,X0,c_Groups_Oone__class_Oone(X1)) = X0
        | ~ class_Divides_Osemiring__div(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_275])]) ).

fof(f4141,plain,
    ! [X0,X1] :
      ( c_Divides_Odiv__class_Odiv(X1,X0,c_Groups_Oone__class_Oone(X1)) = X0
      | ~ class_Divides_Osemiring__div(X1) ),
    inference(cnf_transformation,[],[f2236]) ).

fof(f2236,plain,
    ! [X0,X1] :
      ( c_Divides_Odiv__class_Odiv(X1,X0,c_Groups_Oone__class_Oone(X1)) = X0
      | ~ class_Divides_Osemiring__div(X1) ),
    inference(ennf_transformation,[],[f1399]) ).

fof(f1399,plain,
    ! [X0,X1] :
      ( class_Divides_Osemiring__div(X1)
     => c_Divides_Odiv__class_Odiv(X1,X0,c_Groups_Oone__class_Oone(X1)) = X0 ),
    inference(rectify,[],[f957]) ).

fof(f957,axiom,
    ! [X32,X7] :
      ( class_Divides_Osemiring__div(X7)
     => c_Divides_Odiv__class_Odiv(X7,X32,c_Groups_Oone__class_Oone(X7)) = X32 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__by__1) ).

fof(f7176,plain,
    spl77_274,
    inference(avatar_split_clause,[],[f4105,f7174]) ).

fof(f4105,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,[],[f2217]) ).

fof(f2217,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,[],[f1380]) ).

fof(f1380,plain,
    ! [X0,X1] :
      ( class_Lattices_Oboolean__algebra(X1)
     => c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0)) = X0 ),
    inference(rectify,[],[f605]) ).

fof(f605,axiom,
    ! [X25,X7] :
      ( class_Lattices_Oboolean__algebra(X7)
     => c_Groups_Ouminus__class_Ouminus(X7,c_Groups_Ouminus__class_Ouminus(X7,X25)) = X25 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__compl) ).

fof(f7172,plain,
    spl77_273,
    inference(avatar_split_clause,[],[f4031,f7170]) ).

fof(f7170,plain,
    ( spl77_273
  <=> ! [X0,X1] : hBOOL(hAPP(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,[spl77_273])]) ).

fof(f4031,plain,
    ! [X0,X1] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)),X1)),
    inference(cnf_transformation,[],[f1314]) ).

fof(f1314,plain,
    ! [X0,X1] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)),X1)),
    inference(rectify,[],[f865]) ).

fof(f865,axiom,
    ! [X21,X26] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X26,X21)),X26)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__le__self) ).

fof(f7168,plain,
    spl77_272,
    inference(avatar_split_clause,[],[f4030,f7166]) ).

fof(f7166,plain,
    ( spl77_272
  <=> ! [X0,X1] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0)),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_272])]) ).

fof(f4030,plain,
    ! [X0,X1] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0)),X1)),
    inference(cnf_transformation,[],[f1313]) ).

fof(f1313,plain,
    ! [X0,X1] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0)),X1)),
    inference(rectify,[],[f980]) ).

fof(f980,axiom,
    ! [X21,X26] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X26,X21)),X26)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__le__dividend) ).

fof(f7164,plain,
    spl77_271,
    inference(avatar_split_clause,[],[f4029,f7162]) ).

fof(f7162,plain,
    ( spl77_271
  <=> ! [X0,X1] : hBOOL(hAPP(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,[spl77_271])]) ).

fof(f4029,plain,
    ! [X0,X1] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))),
    inference(cnf_transformation,[],[f1312]) ).

fof(f1312,plain,
    ! [X0,X1] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))),
    inference(rectify,[],[f445]) ).

fof(f445,axiom,
    ! [X26,X21] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X26,X21))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add2) ).

fof(f7160,plain,
    spl77_270,
    inference(avatar_split_clause,[],[f4028,f7158]) ).

fof(f7158,plain,
    ( spl77_270
  <=> ! [X0,X1] : hBOOL(hAPP(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,[spl77_270])]) ).

fof(f4028,plain,
    ! [X0,X1] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))),
    inference(cnf_transformation,[],[f1311]) ).

fof(f1311,plain,
    ! [X0,X1] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))),
    inference(rectify,[],[f446]) ).

fof(f446,axiom,
    ! [X26,X21] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X26))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add1) ).

fof(f7156,plain,
    spl77_269,
    inference(avatar_split_clause,[],[f4027,f7154]) ).

fof(f7154,plain,
    ( spl77_269
  <=> ! [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,[spl77_269])]) ).

fof(f4027,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,[],[f1310]) ).

fof(f1310,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,[],[f840]) ).

fof(f840,axiom,
    ! [X26,X21] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X26),X21) = X26,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__inverse) ).

fof(f7152,plain,
    ( spl77_268
    | ~ spl77_173
    | ~ spl77_234 ),
    inference(avatar_split_clause,[],[f7076,f6990,f6712,f7150]) ).

fof(f7150,plain,
    ( spl77_268
  <=> ! [X0] : sP1(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_268])]) ).

fof(f6712,plain,
    ( spl77_173
  <=> ! [X0] : sP1(hAPP(c_Int_Onat,X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_173])]) ).

fof(f7076,plain,
    ( ! [X0] : sP1(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))
    | ~ spl77_173
    | ~ spl77_234 ),
    inference(superposition,[],[f6713,f6991]) ).

fof(f6713,plain,
    ( ! [X0] : sP1(hAPP(c_Int_Onat,X0),X0)
    | ~ spl77_173 ),
    inference(avatar_component_clause,[],[f6712]) ).

fof(f7148,plain,
    spl77_267,
    inference(avatar_split_clause,[],[f4026,f7146]) ).

fof(f7146,plain,
    ( spl77_267
  <=> ! [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,[spl77_267])]) ).

fof(f4026,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,[],[f1309]) ).

fof(f1309,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,[],[f841]) ).

fof(f841,axiom,
    ! [X21,X26] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X26,X21),X21) = X26,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__inverse2) ).

fof(f7144,plain,
    spl77_266,
    inference(avatar_split_clause,[],[f4025,f7142]) ).

fof(f7140,plain,
    spl77_265,
    inference(avatar_split_clause,[],[f4024,f7138]) ).

fof(f7138,plain,
    ( spl77_265
  <=> ! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_265])]) ).

fof(f4024,plain,
    ! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1),
    inference(cnf_transformation,[],[f1307]) ).

fof(f1307,plain,
    ! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1),
    inference(rectify,[],[f136]) ).

fof(f136,axiom,
    ! [X52,X30] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X30,X52) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X52,X30),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__commute) ).

fof(f7136,plain,
    spl77_264,
    inference(avatar_split_clause,[],[f3928,f7134]) ).

fof(f7134,plain,
    ( spl77_264
  <=> ! [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,[spl77_264])]) ).

fof(f3928,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,[],[f2157]) ).

fof(f2157,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,[],[f1247]) ).

fof(f1247,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,[],[f107]) ).

fof(f107,axiom,
    ! [X21] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X21
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X21) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr0I) ).

fof(f7132,plain,
    spl77_263,
    inference(avatar_split_clause,[],[f3916,f7130]) ).

fof(f3916,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,[],[f2145]) ).

fof(f2145,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,[],[f1235]) ).

fof(f1235,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,[],[f182]) ).

fof(f182,axiom,
    ! [X7] :
      ( class_Groups_Ogroup__add(X7)
     => c_Groups_Ozero__class_Ozero(X7) = c_Groups_Ouminus__class_Ouminus(X7,c_Groups_Ozero__class_Ozero(X7)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__zero) ).

fof(f7128,plain,
    spl77_262,
    inference(avatar_split_clause,[],[f3915,f7126]) ).

fof(f3915,plain,
    ! [X0] :
      ( c_Groups_Ozero__class_Ozero(X0) = c_Int_Oring__1__class_Oof__int(X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | ~ class_Rings_Oring__1(X0) ),
    inference(cnf_transformation,[],[f2144]) ).

fof(f2144,plain,
    ! [X0] :
      ( c_Groups_Ozero__class_Ozero(X0) = c_Int_Oring__1__class_Oof__int(X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | ~ class_Rings_Oring__1(X0) ),
    inference(ennf_transformation,[],[f1234]) ).

fof(f1234,plain,
    ! [X0] :
      ( class_Rings_Oring__1(X0)
     => c_Groups_Ozero__class_Ozero(X0) = c_Int_Oring__1__class_Oof__int(X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(rectify,[],[f702]) ).

fof(f702,axiom,
    ! [X7] :
      ( class_Rings_Oring__1(X7)
     => c_Groups_Ozero__class_Ozero(X7) = c_Int_Oring__1__class_Oof__int(X7,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__0) ).

fof(f7124,plain,
    spl77_261,
    inference(avatar_split_clause,[],[f3914,f7122]) ).

fof(f3914,plain,
    ! [X0] :
      ( c_Groups_Oone__class_Oone(X0) = c_Int_Oring__1__class_Oof__int(X0,c_Groups_Oone__class_Oone(tc_Int_Oint))
      | ~ class_Rings_Oring__1(X0) ),
    inference(cnf_transformation,[],[f2143]) ).

fof(f2143,plain,
    ! [X0] :
      ( c_Groups_Oone__class_Oone(X0) = c_Int_Oring__1__class_Oof__int(X0,c_Groups_Oone__class_Oone(tc_Int_Oint))
      | ~ class_Rings_Oring__1(X0) ),
    inference(ennf_transformation,[],[f1233]) ).

fof(f1233,plain,
    ! [X0] :
      ( class_Rings_Oring__1(X0)
     => c_Groups_Oone__class_Oone(X0) = c_Int_Oring__1__class_Oof__int(X0,c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    inference(rectify,[],[f707]) ).

fof(f707,axiom,
    ! [X7] :
      ( class_Rings_Oring__1(X7)
     => c_Groups_Oone__class_Oone(X7) = c_Int_Oring__1__class_Oof__int(X7,c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__1) ).

fof(f7120,plain,
    spl77_260,
    inference(avatar_split_clause,[],[f3891,f7118]) ).

fof(f7118,plain,
    ( spl77_260
  <=> ! [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,[spl77_260])]) ).

fof(f3891,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,[],[f1211]) ).

fof(f1211,plain,
    ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) = X0,
    inference(rectify,[],[f280]) ).

fof(f280,axiom,
    ! [X21] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X21) = X21,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__1) ).

fof(f7116,plain,
    spl77_259,
    inference(avatar_split_clause,[],[f3890,f7114]) ).

fof(f7114,plain,
    ( spl77_259
  <=> ! [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,[spl77_259])]) ).

fof(f3890,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,[],[f1210]) ).

fof(f1210,plain,
    ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X0) = X0,
    inference(rectify,[],[f139]) ).

fof(f139,axiom,
    ! [X30] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X30) = X30,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__1) ).

fof(f7112,plain,
    spl77_258,
    inference(avatar_split_clause,[],[f3889,f7110]) ).

fof(f7110,plain,
    ( spl77_258
  <=> ! [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,[spl77_258])]) ).

fof(f3889,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,[],[f1209]) ).

fof(f1209,plain,
    ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X0) = X0,
    inference(rectify,[],[f598]) ).

fof(f598,axiom,
    ! [X30] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X30) = X30,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__1) ).

fof(f7108,plain,
    ( ~ spl77_257
    | ~ spl77_226
    | ~ spl77_231 ),
    inference(avatar_split_clause,[],[f7072,f6978,f6954,f7105]) ).

fof(f6954,plain,
    ( spl77_226
  <=> c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_226])]) ).

fof(f6978,plain,
    ( spl77_231
  <=> ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_231])]) ).

fof(f7072,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl77_226
    | ~ spl77_231 ),
    inference(superposition,[],[f6979,f6956]) ).

fof(f6956,plain,
    ( c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ spl77_226 ),
    inference(avatar_component_clause,[],[f6954]) ).

fof(f6979,plain,
    ( ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl77_231 ),
    inference(avatar_component_clause,[],[f6978]) ).

fof(f7103,plain,
    spl77_256,
    inference(avatar_split_clause,[],[f3888,f7101]) ).

fof(f7101,plain,
    ( spl77_256
  <=> ! [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,[spl77_256])]) ).

fof(f3888,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,[],[f1208]) ).

fof(f1208,plain,
    ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0,
    inference(rectify,[],[f278]) ).

fof(f278,axiom,
    ! [X21] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X21,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__1__right) ).

fof(f7099,plain,
    spl77_255,
    inference(avatar_split_clause,[],[f3887,f7097]) ).

fof(f7097,plain,
    ( spl77_255
  <=> ! [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,[spl77_255])]) ).

fof(f3887,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,[],[f1207]) ).

fof(f1207,plain,
    ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X0,
    inference(rectify,[],[f137]) ).

fof(f137,axiom,
    ! [X30] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X30),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X30,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__1__right) ).

fof(f7095,plain,
    spl77_254,
    inference(avatar_split_clause,[],[f3886,f7093]) ).

fof(f7093,plain,
    ( spl77_254
  <=> ! [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,[spl77_254])]) ).

fof(f3886,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,[],[f1206]) ).

fof(f1206,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,[],[f128]) ).

fof(f128,axiom,
    ! [X30] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X30),X30),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zminus__inverse2) ).

fof(f7088,plain,
    ( ~ spl77_253
    | ~ spl77_225
    | ~ spl77_230 ),
    inference(avatar_split_clause,[],[f7070,f6974,f6949,f7085]) ).

fof(f7085,plain,
    ( spl77_253
  <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_253])]) ).

fof(f6949,plain,
    ( spl77_225
  <=> c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_225])]) ).

fof(f6974,plain,
    ( spl77_230
  <=> ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_230])]) ).

fof(f7070,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    | ~ spl77_225
    | ~ spl77_230 ),
    inference(superposition,[],[f6975,f6951]) ).

fof(f6951,plain,
    ( c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ spl77_225 ),
    inference(avatar_component_clause,[],[f6949]) ).

fof(f6975,plain,
    ( ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    | ~ spl77_230 ),
    inference(avatar_component_clause,[],[f6974]) ).

fof(f7065,plain,
    ( ~ spl77_252
    | ~ spl77_214
    | ~ spl77_221 ),
    inference(avatar_split_clause,[],[f6947,f6921,f6893,f7062]) ).

fof(f7062,plain,
    ( spl77_252
  <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_252])]) ).

fof(f6893,plain,
    ( spl77_214
  <=> ! [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,[spl77_214])]) ).

fof(f6947,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ spl77_214
    | ~ spl77_221 ),
    inference(superposition,[],[f6922,f6894]) ).

fof(f6894,plain,
    ( ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) = X0
    | ~ spl77_214 ),
    inference(avatar_component_clause,[],[f6893]) ).

fof(f7060,plain,
    spl77_251,
    inference(avatar_split_clause,[],[f5620,f7058]) ).

fof(f7058,plain,
    ( spl77_251
  <=> ! [X2,X1] :
        ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,X1),X1))
        | ~ class_Orderings_Oorder(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_251])]) ).

fof(f5620,plain,
    ! [X2,X1] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,X1),X1))
      | ~ class_Orderings_Oorder(X2) ),
    inference(equality_resolution,[],[f4844]) ).

fof(f4844,plain,
    ! [X2,X0,X1] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,X0),X1))
      | X0 != X1
      | ~ class_Orderings_Oorder(X2) ),
    inference(cnf_transformation,[],[f3503]) ).

fof(f3503,plain,
    ! [X0,X1,X2] :
      ( ( ( X0 = X1
          | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,X0),X1))
          | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,X1),X0)) )
        & ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,X0),X1))
            & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,X1),X0)) )
          | X0 != X1 ) )
      | ~ class_Orderings_Oorder(X2) ),
    inference(flattening,[],[f3502]) ).

fof(f3502,plain,
    ! [X0,X1,X2] :
      ( ( ( X0 = X1
          | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,X0),X1))
          | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,X1),X0)) )
        & ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,X0),X1))
            & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,X1),X0)) )
          | X0 != X1 ) )
      | ~ class_Orderings_Oorder(X2) ),
    inference(nnf_transformation,[],[f2728]) ).

fof(f2728,plain,
    ! [X0,X1,X2] :
      ( ( X0 = X1
      <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,X0),X1))
          & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,X1),X0)) ) )
      | ~ class_Orderings_Oorder(X2) ),
    inference(ennf_transformation,[],[f1845]) ).

fof(f1845,plain,
    ! [X0,X1,X2] :
      ( class_Orderings_Oorder(X2)
     => ( X0 = X1
      <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,X0),X1))
          & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,X1),X0)) ) ) ),
    inference(rectify,[],[f392]) ).

fof(f392,axiom,
    ! [X34,X10,X7] :
      ( class_Orderings_Oorder(X7)
     => ( X10 = X34
      <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X7,X34),X10))
          & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X7,X10),X34)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__eq__iff) ).

fof(f7056,plain,
    spl77_250,
    inference(avatar_split_clause,[],[f5557,f7054]) ).

fof(f7054,plain,
    ( spl77_250
  <=> ! [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,[spl77_250])]) ).

fof(f5557,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,[],[f4510]) ).

fof(f4510,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,[],[f3398]) ).

fof(f7052,plain,
    spl77_249,
    inference(avatar_split_clause,[],[f5310,f7050]) ).

fof(f7050,plain,
    ( spl77_249
  <=> ! [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,[spl77_249])]) ).

fof(f5310,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,[],[f3857,f3879]) ).

fof(f3857,plain,
    ! [X0] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X0)),
    inference(cnf_transformation,[],[f1177]) ).

fof(f1177,plain,
    ! [X0] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X0)),
    inference(rectify,[],[f53]) ).

fof(f53,axiom,
    ! [X21] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,c_Nat_OSuc(X21)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lessI) ).

fof(f7048,plain,
    spl77_248,
    inference(avatar_split_clause,[],[f5304,f7046]) ).

fof(f7046,plain,
    ( spl77_248
  <=> ! [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,[spl77_248])]) ).

fof(f5304,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,[],[f3848,f3879]) ).

fof(f3848,plain,
    ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X0),
    inference(cnf_transformation,[],[f1168]) ).

fof(f1168,plain,
    ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X0),
    inference(rectify,[],[f100]) ).

fof(f100,axiom,
    ! [X49] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X49),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osimps_I3_J) ).

fof(f7044,plain,
    spl77_247,
    inference(avatar_split_clause,[],[f5049,f7042]) ).

fof(f7042,plain,
    ( spl77_247
  <=> ! [X2,X0,X1,X3] : c_Fun_Oswap(X3,X2,X1,X1,X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_247])]) ).

fof(f5049,plain,
    ! [X2,X3,X0,X1] : c_Fun_Oswap(X3,X2,X1,X1,X0) = X0,
    inference(cnf_transformation,[],[f1943]) ).

fof(f1943,plain,
    ! [X0,X1,X2,X3] : c_Fun_Oswap(X3,X2,X1,X1,X0) = X0,
    inference(rectify,[],[f62]) ).

fof(f62,axiom,
    ! [X1,X18,X8,X7] : c_Fun_Oswap(X7,X8,X18,X18,X1) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_swap__self) ).

fof(f7040,plain,
    spl77_246,
    inference(avatar_split_clause,[],[f4952,f7038]) ).

fof(f7038,plain,
    ( spl77_246
  <=> ! [X2,X0,X1] :
        ( sP12(X2,X1,X0)
        | ~ sP13(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_246])]) ).

fof(f4952,plain,
    ! [X2,X0,X1] :
      ( sP12(X2,X1,X0)
      | ~ sP13(X0,X1,X2) ),
    inference(cnf_transformation,[],[f3533]) ).

fof(f7036,plain,
    spl77_245,
    inference(avatar_split_clause,[],[f4951,f7034]) ).

fof(f7034,plain,
    ( spl77_245
  <=> ! [X2,X0,X1] :
        ( sP11(X2,X1,X0)
        | ~ sP13(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_245])]) ).

fof(f4951,plain,
    ! [X2,X0,X1] :
      ( sP11(X2,X1,X0)
      | ~ sP13(X0,X1,X2) ),
    inference(cnf_transformation,[],[f3533]) ).

fof(f7032,plain,
    spl77_244,
    inference(avatar_split_clause,[],[f4944,f7030]) ).

fof(f7030,plain,
    ( spl77_244
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
        | ~ sP10(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_244])]) ).

fof(f4944,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
      | ~ sP10(X0,X1,X2) ),
    inference(cnf_transformation,[],[f3531]) ).

fof(f7028,plain,
    spl77_243,
    inference(avatar_split_clause,[],[f4420,f7026]) ).

fof(f7026,plain,
    ( spl77_243
  <=> ! [X0,X1] :
        ( hAPP(c_Int_Onat,X0) = X1
        | ~ sP1(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_243])]) ).

fof(f4420,plain,
    ! [X0,X1] :
      ( hAPP(c_Int_Onat,X0) = X1
      | ~ sP1(X1,X0) ),
    inference(cnf_transformation,[],[f3338]) ).

fof(f3338,plain,
    ! [X0,X1] :
      ( ( hAPP(c_Int_Onat,X0) = X1
        | ~ sP1(X1,X0) )
      & ( sP1(X1,X0)
        | hAPP(c_Int_Onat,X0) != X1 ) ),
    inference(nnf_transformation,[],[f3128]) ).

fof(f3128,plain,
    ! [X0,X1] :
      ( hAPP(c_Int_Onat,X0) = X1
    <=> sP1(X1,X0) ),
    inference(definition_folding,[],[f2479,f3127]) ).

fof(f2479,plain,
    ! [X0,X1] :
      ( hAPP(c_Int_Onat,X0) = X1
    <=> ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
          | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) )
        & ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) = X0
          | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) ) ) ),
    inference(ennf_transformation,[],[f1596]) ).

fof(f1596,plain,
    ! [X0,X1] :
      ( hAPP(c_Int_Onat,X0) = X1
    <=> ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0))
         => c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
        & ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0))
         => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) = X0 ) ) ),
    inference(rectify,[],[f651]) ).

fof(f651,axiom,
    ! [X51,X23] :
      ( hAPP(c_Int_Onat,X51) = X23
    <=> ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X51))
         => c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X23 )
        & ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X51))
         => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23) = X51 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__eq__iff2) ).

fof(f7024,plain,
    spl77_242,
    inference(avatar_split_clause,[],[f4412,f7022]) ).

fof(f7022,plain,
    ( spl77_242
  <=> ! [X0,X1] :
        ( hAPP(c_Int_Onat,X1) = X0
        | ~ sP0(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_242])]) ).

fof(f4412,plain,
    ! [X0,X1] :
      ( hAPP(c_Int_Onat,X1) = X0
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f3334]) ).

fof(f3334,plain,
    ! [X0,X1] :
      ( ( hAPP(c_Int_Onat,X1) = X0
        | ~ sP0(X0,X1) )
      & ( sP0(X0,X1)
        | hAPP(c_Int_Onat,X1) != X0 ) ),
    inference(nnf_transformation,[],[f3126]) ).

fof(f3126,plain,
    ! [X0,X1] :
      ( hAPP(c_Int_Onat,X1) = X0
    <=> sP0(X0,X1) ),
    inference(definition_folding,[],[f2478,f3125]) ).

fof(f2478,plain,
    ! [X0,X1] :
      ( hAPP(c_Int_Onat,X1) = X0
    <=> ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
          | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) )
        & ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) = X1
          | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ) ) ),
    inference(ennf_transformation,[],[f1595]) ).

fof(f1595,plain,
    ! [X0,X1] :
      ( hAPP(c_Int_Onat,X1) = X0
    <=> ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
         => c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
        & ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
         => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) = X1 ) ) ),
    inference(rectify,[],[f650]) ).

fof(f650,axiom,
    ! [X23,X51] :
      ( hAPP(c_Int_Onat,X51) = X23
    <=> ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X51))
         => c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X23 )
        & ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X51))
         => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23) = X51 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__eq__iff) ).

fof(f7020,plain,
    spl77_241,
    inference(avatar_split_clause,[],[f4207,f7018]) ).

fof(f7018,plain,
    ( spl77_241
  <=> ! [X0,X1] :
        ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X0),X0))
        | ~ class_Orderings_Opreorder(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_241])]) ).

fof(f4207,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X0),X0))
      | ~ class_Orderings_Opreorder(X1) ),
    inference(cnf_transformation,[],[f2294]) ).

fof(f2294,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X0),X0))
      | ~ class_Orderings_Opreorder(X1) ),
    inference(ennf_transformation,[],[f1455]) ).

fof(f1455,plain,
    ! [X0,X1] :
      ( class_Orderings_Opreorder(X1)
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X0),X0)) ),
    inference(rectify,[],[f375]) ).

fof(f375,axiom,
    ! [X25,X7] :
      ( class_Orderings_Opreorder(X7)
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X7,X25),X25)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__refl) ).

fof(f7016,plain,
    spl77_240,
    inference(avatar_split_clause,[],[f4088,f7014]) ).

fof(f7014,plain,
    ( spl77_240
  <=> ! [X0,X1] :
        ( c_SEQ_OCauchy(X1,X0)
        | ~ c_SEQ_Oconvergent(X1,X0)
        | ~ class_SEQ_Ocomplete__space(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_240])]) ).

fof(f4088,plain,
    ! [X0,X1] :
      ( c_SEQ_OCauchy(X1,X0)
      | ~ c_SEQ_Oconvergent(X1,X0)
      | ~ class_SEQ_Ocomplete__space(X1) ),
    inference(cnf_transformation,[],[f3232]) ).

fof(f3232,plain,
    ! [X0,X1] :
      ( ( ( c_SEQ_OCauchy(X1,X0)
          | ~ c_SEQ_Oconvergent(X1,X0) )
        & ( c_SEQ_Oconvergent(X1,X0)
          | ~ c_SEQ_OCauchy(X1,X0) ) )
      | ~ class_SEQ_Ocomplete__space(X1) ),
    inference(nnf_transformation,[],[f2204]) ).

fof(f2204,plain,
    ! [X0,X1] :
      ( ( c_SEQ_OCauchy(X1,X0)
      <=> c_SEQ_Oconvergent(X1,X0) )
      | ~ class_SEQ_Ocomplete__space(X1) ),
    inference(ennf_transformation,[],[f1367]) ).

fof(f1367,plain,
    ! [X0,X1] :
      ( class_SEQ_Ocomplete__space(X1)
     => ( c_SEQ_OCauchy(X1,X0)
      <=> c_SEQ_Oconvergent(X1,X0) ) ),
    inference(rectify,[],[f56]) ).

fof(f56,axiom,
    ! [X35,X7] :
      ( class_SEQ_Ocomplete__space(X7)
     => ( c_SEQ_OCauchy(X7,X35)
      <=> c_SEQ_Oconvergent(X7,X35) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Cauchy__convergent__iff) ).

fof(f7012,plain,
    spl77_239,
    inference(avatar_split_clause,[],[f4086,f7010]) ).

fof(f7010,plain,
    ( spl77_239
  <=> ! [X0,X1] :
        ( c_SEQ_Oconvergent(X1,X0)
        | ~ c_SEQ_OCauchy(X1,X0)
        | ~ class_SEQ_Ocomplete__space(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_239])]) ).

fof(f4086,plain,
    ! [X0,X1] :
      ( c_SEQ_Oconvergent(X1,X0)
      | ~ c_SEQ_OCauchy(X1,X0)
      | ~ class_SEQ_Ocomplete__space(X1) ),
    inference(cnf_transformation,[],[f2203]) ).

fof(f2203,plain,
    ! [X0,X1] :
      ( c_SEQ_Oconvergent(X1,X0)
      | ~ c_SEQ_OCauchy(X1,X0)
      | ~ class_SEQ_Ocomplete__space(X1) ),
    inference(flattening,[],[f2202]) ).

fof(f2202,plain,
    ! [X0,X1] :
      ( c_SEQ_Oconvergent(X1,X0)
      | ~ c_SEQ_OCauchy(X1,X0)
      | ~ class_SEQ_Ocomplete__space(X1) ),
    inference(ennf_transformation,[],[f1366]) ).

fof(f1366,plain,
    ! [X0,X1] :
      ( class_SEQ_Ocomplete__space(X1)
     => ( c_SEQ_OCauchy(X1,X0)
       => c_SEQ_Oconvergent(X1,X0) ) ),
    inference(rectify,[],[f55]) ).

fof(f55,axiom,
    ! [X35,X7] :
      ( class_SEQ_Ocomplete__space(X7)
     => ( c_SEQ_OCauchy(X7,X35)
       => c_SEQ_Oconvergent(X7,X35) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Cauchy__convergent) ).

fof(f7008,plain,
    spl77_238,
    inference(avatar_split_clause,[],[f4085,f7006]) ).

fof(f7006,plain,
    ( spl77_238
  <=> ! [X0,X1] :
        ( c_SEQ_OCauchy(X1,X0)
        | ~ c_SEQ_Oconvergent(X1,X0)
        | ~ class_RealVector_Ometric__space(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_238])]) ).

fof(f4085,plain,
    ! [X0,X1] :
      ( c_SEQ_OCauchy(X1,X0)
      | ~ c_SEQ_Oconvergent(X1,X0)
      | ~ class_RealVector_Ometric__space(X1) ),
    inference(cnf_transformation,[],[f2201]) ).

fof(f2201,plain,
    ! [X0,X1] :
      ( c_SEQ_OCauchy(X1,X0)
      | ~ c_SEQ_Oconvergent(X1,X0)
      | ~ class_RealVector_Ometric__space(X1) ),
    inference(flattening,[],[f2200]) ).

fof(f2200,plain,
    ! [X0,X1] :
      ( c_SEQ_OCauchy(X1,X0)
      | ~ c_SEQ_Oconvergent(X1,X0)
      | ~ class_RealVector_Ometric__space(X1) ),
    inference(ennf_transformation,[],[f1365]) ).

fof(f1365,plain,
    ! [X0,X1] :
      ( class_RealVector_Ometric__space(X1)
     => ( c_SEQ_Oconvergent(X1,X0)
       => c_SEQ_OCauchy(X1,X0) ) ),
    inference(rectify,[],[f54]) ).

fof(f54,axiom,
    ! [X35,X7] :
      ( class_RealVector_Ometric__space(X7)
     => ( c_SEQ_Oconvergent(X7,X35)
       => c_SEQ_OCauchy(X7,X35) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_convergent__Cauchy) ).

fof(f7004,plain,
    spl77_237,
    inference(avatar_split_clause,[],[f3969,f7002]) ).

fof(f7002,plain,
    ( spl77_237
  <=> ! [X0] :
        ( c_SEQ_Osubseq(X0)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK32(X0),sK33(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_237])]) ).

fof(f3969,plain,
    ! [X0] :
      ( c_SEQ_Osubseq(X0)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK32(X0),sK33(X0)) ),
    inference(cnf_transformation,[],[f3190]) ).

fof(f7000,plain,
    spl77_236,
    inference(avatar_split_clause,[],[f3923,f6998]) ).

fof(f6998,plain,
    ( spl77_236
  <=> ! [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,[spl77_236])]) ).

fof(f3923,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,[],[f2152]) ).

fof(f2152,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,[],[f1242]) ).

fof(f1242,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,[],[f246]) ).

fof(f246,axiom,
    ! [X7] :
      ( class_Rings_Olinordered__semidom(X7)
     => c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),c_Groups_Oone__class_Oone(X7)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__one) ).

fof(f6996,plain,
    spl77_235,
    inference(avatar_split_clause,[],[f3922,f6994]) ).

fof(f6994,plain,
    ( spl77_235
  <=> ! [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,[spl77_235])]) ).

fof(f3922,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,[],[f2151]) ).

fof(f2151,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,[],[f1241]) ).

fof(f1241,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,[],[f247]) ).

fof(f247,axiom,
    ! [X7] :
      ( class_Rings_Olinordered__semidom(X7)
     => ~ c_Orderings_Oord__class_Oless(X7,c_Groups_Oone__class_Oone(X7),c_Groups_Ozero__class_Ozero(X7)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__one__less__zero) ).

fof(f6992,plain,
    spl77_234,
    inference(avatar_split_clause,[],[f3881,f6990]) ).

fof(f3881,plain,
    ! [X0] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)) = X0,
    inference(cnf_transformation,[],[f1201]) ).

fof(f1201,plain,
    ! [X0] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)) = X0,
    inference(rectify,[],[f618]) ).

fof(f618,axiom,
    ! [X21] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X21)) = X21,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__int) ).

fof(f6988,plain,
    spl77_233,
    inference(avatar_split_clause,[],[f3878,f6986]) ).

fof(f6986,plain,
    ( spl77_233
  <=> ! [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,[spl77_233])]) ).

fof(f3878,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,[],[f1198]) ).

fof(f1198,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,[],[f856]) ).

fof(f856,axiom,
    ! [X21] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X21),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__0__eq__0) ).

fof(f6984,plain,
    spl77_232,
    inference(avatar_split_clause,[],[f3877,f6982]) ).

fof(f3877,plain,
    ! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0),
    inference(cnf_transformation,[],[f1197]) ).

fof(f1197,plain,
    ! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0),
    inference(rectify,[],[f954]) ).

fof(f954,axiom,
    ! [X33] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X33),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zero) ).

fof(f6980,plain,
    spl77_231,
    inference(avatar_split_clause,[],[f3876,f6978]) ).

fof(f3876,plain,
    ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(cnf_transformation,[],[f1196]) ).

fof(f1196,plain,
    ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(rectify,[],[f253]) ).

fof(f253,axiom,
    ! [X40] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X40),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__less__0__conv) ).

fof(f6976,plain,
    spl77_230,
    inference(avatar_split_clause,[],[f3875,f6974]) ).

fof(f3875,plain,
    ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
    inference(cnf_transformation,[],[f1195]) ).

fof(f1195,plain,
    ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
    inference(rectify,[],[f672]) ).

fof(f672,axiom,
    ! [X21] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X21),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__real__of__nat__less__zero) ).

fof(f6972,plain,
    spl77_229,
    inference(avatar_split_clause,[],[f3840,f6969]) ).

fof(f6969,plain,
    ( spl77_229
  <=> hBOOL(hAPP(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,[spl77_229])]) ).

fof(f3840,plain,
    hBOOL(hAPP(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,[],[f510]) ).

fof(f510,axiom,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).

fof(f6967,plain,
    spl77_228,
    inference(avatar_split_clause,[],[f3837,f6964]) ).

fof(f3837,plain,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(cnf_transformation,[],[f251]) ).

fof(f251,axiom,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__0) ).

fof(f6962,plain,
    spl77_227,
    inference(avatar_split_clause,[],[f3836,f6959]) ).

fof(f3836,plain,
    c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(cnf_transformation,[],[f670]) ).

fof(f670,axiom,
    c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__zero) ).

fof(f6957,plain,
    spl77_226,
    inference(avatar_split_clause,[],[f3834,f6954]) ).

fof(f3834,plain,
    c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(cnf_transformation,[],[f326]) ).

fof(f326,axiom,
    c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__numerals_I2_J) ).

fof(f6952,plain,
    spl77_225,
    inference(avatar_split_clause,[],[f3833,f6949]) ).

fof(f3833,plain,
    c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(cnf_transformation,[],[f677]) ).

fof(f677,axiom,
    c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__1) ).

fof(f6946,plain,
    ( spl77_224
    | ~ spl77_172
    | ~ spl77_202 ),
    inference(avatar_split_clause,[],[f6929,f6841,f6708,f6943]) ).

fof(f6943,plain,
    ( spl77_224
  <=> sP0(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_224])]) ).

fof(f6841,plain,
    ( spl77_202
  <=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_202])]) ).

fof(f6929,plain,
    ( sP0(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ spl77_172
    | ~ spl77_202 ),
    inference(superposition,[],[f6709,f6843]) ).

fof(f6843,plain,
    ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ spl77_202 ),
    inference(avatar_component_clause,[],[f6841]) ).

fof(f6937,plain,
    ( spl77_223
    | ~ spl77_173
    | ~ spl77_202 ),
    inference(avatar_split_clause,[],[f6928,f6841,f6712,f6934]) ).

fof(f6934,plain,
    ( spl77_223
  <=> sP1(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_223])]) ).

fof(f6928,plain,
    ( sP1(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ spl77_173
    | ~ spl77_202 ),
    inference(superposition,[],[f6713,f6843]) ).

fof(f6927,plain,
    spl77_222,
    inference(avatar_split_clause,[],[f5691,f6925]) ).

fof(f6925,plain,
    ( spl77_222
  <=> ! [X0] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_222])]) ).

fof(f5691,plain,
    ! [X0] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0,
    inference(forward_demodulation,[],[f5690,f3871]) ).

fof(f5690,plain,
    ! [X0] : c_Divides_Odiv__class_Odiv(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))) = X0,
    inference(forward_demodulation,[],[f5314,f5313]) ).

fof(f5314,plain,
    ! [X0] : c_Divides_Odiv__class_Odiv(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))) = X0,
    inference(definition_unfolding,[],[f3882,f3879]) ).

fof(f3882,plain,
    ! [X0] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X0,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = X0,
    inference(cnf_transformation,[],[f1202]) ).

fof(f1202,plain,
    ! [X0] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X0,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = X0,
    inference(rectify,[],[f977]) ).

fof(f977,axiom,
    ! [X26] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X26,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = X26,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__1) ).

fof(f6923,plain,
    spl77_221,
    inference(avatar_split_clause,[],[f5302,f6921]) ).

fof(f5302,plain,
    ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X0,
    inference(definition_unfolding,[],[f3844,f3879]) ).

fof(f3844,plain,
    ! [X0] : c_Nat_OSuc(X0) != X0,
    inference(cnf_transformation,[],[f1164]) ).

fof(f1164,plain,
    ! [X0] : c_Nat_OSuc(X0) != X0,
    inference(rectify,[],[f65]) ).

fof(f65,axiom,
    ! [X21] : c_Nat_OSuc(X21) != X21,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).

fof(f6919,plain,
    spl77_220,
    inference(avatar_split_clause,[],[f5099,f6917]) ).

fof(f6917,plain,
    ( spl77_220
  <=> ! [X0,X3,X2,X1] :
        ( sP22(X2,X3,X0,X1)
        | ~ class_Rings_Olinordered__ring__strict(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_220])]) ).

fof(f5099,plain,
    ! [X2,X3,X0,X1] :
      ( sP22(X2,X3,X0,X1)
      | ~ class_Rings_Olinordered__ring__strict(X3) ),
    inference(cnf_transformation,[],[f3164]) ).

fof(f3164,plain,
    ! [X0,X1,X2,X3] :
      ( sP22(X2,X3,X0,X1)
      | ~ class_Rings_Olinordered__ring__strict(X3) ),
    inference(definition_folding,[],[f2875,f3163,f3162]) ).

fof(f3162,plain,
    ! [X1,X0,X3,X2] :
      ( sP21(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,[sP21])]) ).

fof(f3163,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))
      <=> sP21(X1,X0,X3,X2) )
      | ~ sP22(X2,X3,X0,X1) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP22])]) ).

fof(f2875,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,[],[f1972]) ).

fof(f1972,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,[],[f243]) ).

fof(f243,axiom,
    ! [X17,X18,X16,X7] :
      ( class_Rings_Olinordered__ring__strict(X7)
     => ( c_Orderings_Oord__class_Oless(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X16),X18),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X16),X17))
      <=> ( ( c_Orderings_Oord__class_Oless(X7,X17,X18)
            & c_Orderings_Oord__class_Oless(X7,X16,c_Groups_Ozero__class_Ozero(X7)) )
          | ( c_Orderings_Oord__class_Oless(X7,X18,X17)
            & c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X16) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__disj) ).

fof(f6915,plain,
    spl77_219,
    inference(avatar_split_clause,[],[f5090,f6913]) ).

fof(f6913,plain,
    ( spl77_219
  <=> ! [X0,X3,X2,X1] :
        ( sP20(X1,X3,X0,X2)
        | ~ class_Rings_Olinordered__ring__strict(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_219])]) ).

fof(f5090,plain,
    ! [X2,X3,X0,X1] :
      ( sP20(X1,X3,X0,X2)
      | ~ class_Rings_Olinordered__ring__strict(X3) ),
    inference(cnf_transformation,[],[f3161]) ).

fof(f3161,plain,
    ! [X0,X1,X2,X3] :
      ( sP20(X1,X3,X0,X2)
      | ~ class_Rings_Olinordered__ring__strict(X3) ),
    inference(definition_folding,[],[f2874,f3160,f3159]) ).

fof(f3159,plain,
    ! [X2,X0,X3,X1] :
      ( sP19(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,[sP19])]) ).

fof(f3160,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))
      <=> sP19(X2,X0,X3,X1) )
      | ~ sP20(X1,X3,X0,X2) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP20])]) ).

fof(f2874,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,[],[f1971]) ).

fof(f1971,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,[],[f244]) ).

fof(f244,axiom,
    ! [X17,X16,X18,X7] :
      ( class_Rings_Olinordered__ring__strict(X7)
     => ( c_Orderings_Oord__class_Oless(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X18),X16),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X17),X16))
      <=> ( ( c_Orderings_Oord__class_Oless(X7,X17,X18)
            & c_Orderings_Oord__class_Oless(X7,X16,c_Groups_Ozero__class_Ozero(X7)) )
          | ( c_Orderings_Oord__class_Oless(X7,X18,X17)
            & c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X16) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__right__disj) ).

fof(f6911,plain,
    spl77_218,
    inference(avatar_split_clause,[],[f4020,f6909]) ).

fof(f6909,plain,
    ( spl77_218
  <=> ! [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,[spl77_218])]) ).

fof(f4020,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,[],[f1303]) ).

fof(f1303,plain,
    ! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X0),
    inference(rectify,[],[f294]) ).

fof(f294,axiom,
    ! [X42,X41] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X41,X42),X42),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__add__less2) ).

fof(f6907,plain,
    spl77_217,
    inference(avatar_split_clause,[],[f4019,f6905]) ).

fof(f6905,plain,
    ( spl77_217
  <=> ! [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,[spl77_217])]) ).

fof(f4019,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,[],[f1302]) ).

fof(f1302,plain,
    ! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X1),
    inference(rectify,[],[f293]) ).

fof(f293,axiom,
    ! [X41,X42] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X42,X41),X42),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__add__less1) ).

fof(f6903,plain,
    spl77_216,
    inference(avatar_split_clause,[],[f3917,f6901]) ).

fof(f6901,plain,
    ( spl77_216
  <=> ! [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,[spl77_216])]) ).

fof(f3917,plain,
    ! [X0] :
      ( c_Groups_Oone__class_Oone(X0) != c_Groups_Ozero__class_Ozero(X0)
      | ~ class_Rings_Ozero__neq__one(X0) ),
    inference(cnf_transformation,[],[f2146]) ).

fof(f2146,plain,
    ! [X0] :
      ( c_Groups_Oone__class_Oone(X0) != c_Groups_Ozero__class_Ozero(X0)
      | ~ class_Rings_Ozero__neq__one(X0) ),
    inference(ennf_transformation,[],[f1236]) ).

fof(f1236,plain,
    ! [X0] :
      ( class_Rings_Ozero__neq__one(X0)
     => c_Groups_Oone__class_Oone(X0) != c_Groups_Ozero__class_Ozero(X0) ),
    inference(rectify,[],[f215]) ).

fof(f215,axiom,
    ! [X7] :
      ( class_Rings_Ozero__neq__one(X7)
     => c_Groups_Ozero__class_Ozero(X7) != c_Groups_Oone__class_Oone(X7) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__neq__one) ).

fof(f6899,plain,
    spl77_215,
    inference(avatar_split_clause,[],[f3873,f6897]) ).

fof(f3873,plain,
    ! [X0] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)),
    inference(cnf_transformation,[],[f1193]) ).

fof(f1193,plain,
    ! [X0] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)),
    inference(rectify,[],[f376]) ).

fof(f376,axiom,
    ! [X21] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X21)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le0) ).

fof(f6895,plain,
    spl77_214,
    inference(avatar_split_clause,[],[f3872,f6893]) ).

fof(f3872,plain,
    ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) = X0,
    inference(cnf_transformation,[],[f1192]) ).

fof(f1192,plain,
    ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) = X0,
    inference(rectify,[],[f281]) ).

fof(f281,axiom,
    ! [X21] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X21) = X21,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).

fof(f6891,plain,
    spl77_213,
    inference(avatar_split_clause,[],[f3871,f6889]) ).

fof(f6889,plain,
    ( spl77_213
  <=> ! [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,[spl77_213])]) ).

fof(f6887,plain,
    spl77_212,
    inference(avatar_split_clause,[],[f3870,f6885]) ).

fof(f6885,plain,
    ( spl77_212
  <=> ! [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,[spl77_212])]) ).

fof(f3870,plain,
    ! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) = X0,
    inference(cnf_transformation,[],[f1190]) ).

fof(f1190,plain,
    ! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) = X0,
    inference(rectify,[],[f140]) ).

fof(f140,axiom,
    ! [X30] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X30) = X30,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__0) ).

fof(f6883,plain,
    spl77_211,
    inference(avatar_split_clause,[],[f3869,f6881]) ).

fof(f6881,plain,
    ( spl77_211
  <=> ! [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,[spl77_211])]) ).

fof(f3869,plain,
    ! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X0,
    inference(cnf_transformation,[],[f1189]) ).

fof(f1189,plain,
    ! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X0,
    inference(rectify,[],[f138]) ).

fof(f138,axiom,
    ! [X30] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X30,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X30,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__0__right) ).

fof(f6879,plain,
    spl77_210,
    inference(avatar_split_clause,[],[f3868,f6877]) ).

fof(f6877,plain,
    ( spl77_210
  <=> ! [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,[spl77_210])]) ).

fof(f3868,plain,
    ! [X0] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
    inference(cnf_transformation,[],[f1188]) ).

fof(f1188,plain,
    ! [X0] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
    inference(rectify,[],[f857]) ).

fof(f857,axiom,
    ! [X26] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X26,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X26,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__nat_Odiff__0) ).

fof(f6875,plain,
    spl77_209,
    inference(avatar_split_clause,[],[f3867,f6873]) ).

fof(f6873,plain,
    ( spl77_209
  <=> ! [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,[spl77_209])]) ).

fof(f3867,plain,
    ! [X0] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) = X0,
    inference(cnf_transformation,[],[f1187]) ).

fof(f1187,plain,
    ! [X0] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) = X0,
    inference(rectify,[],[f142]) ).

fof(f142,axiom,
    ! [X30] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X30)) = X30,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__zminus) ).

fof(f6871,plain,
    spl77_208,
    inference(avatar_split_clause,[],[f3866,f6869]) ).

fof(f6869,plain,
    ( spl77_208
  <=> ! [X0] : c_RComplete_Onatfloor(hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_208])]) ).

fof(f3866,plain,
    ! [X0] : c_RComplete_Onatfloor(hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0)) = X0,
    inference(cnf_transformation,[],[f1186]) ).

fof(f1186,plain,
    ! [X0] : c_RComplete_Onatfloor(hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0)) = X0,
    inference(rectify,[],[f665]) ).

fof(f665,axiom,
    ! [X21] : c_RComplete_Onatfloor(hAPP(c_RealDef_Oreal(tc_Nat_Onat),X21)) = X21,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__real__of__nat) ).

fof(f6867,plain,
    spl77_207,
    inference(avatar_split_clause,[],[f3865,f6865]) ).

fof(f6865,plain,
    ( spl77_207
  <=> ! [X0] : c_RComplete_Onatceiling(hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_207])]) ).

fof(f3865,plain,
    ! [X0] : c_RComplete_Onatceiling(hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0)) = X0,
    inference(cnf_transformation,[],[f1185]) ).

fof(f1185,plain,
    ! [X0] : c_RComplete_Onatceiling(hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0)) = X0,
    inference(rectify,[],[f666]) ).

fof(f666,axiom,
    ! [X21] : c_RComplete_Onatceiling(hAPP(c_RealDef_Oreal(tc_Nat_Onat),X21)) = X21,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__real__of__nat) ).

fof(f6863,plain,
    spl77_206,
    inference(avatar_split_clause,[],[f3864,f6861]) ).

fof(f6861,plain,
    ( spl77_206
  <=> ! [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,[spl77_206])]) ).

fof(f3864,plain,
    ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X0),
    inference(cnf_transformation,[],[f1184]) ).

fof(f1184,plain,
    ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X0),
    inference(rectify,[],[f858]) ).

fof(f858,axiom,
    ! [X26] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X26,X26),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__self__eq__0) ).

fof(f6859,plain,
    spl77_205,
    inference(avatar_split_clause,[],[f3832,f6856]) ).

fof(f6856,plain,
    ( spl77_205
  <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_205])]) ).

fof(f3832,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)),
    inference(cnf_transformation,[],[f374]) ).

fof(f374,axiom,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rp) ).

fof(f6854,plain,
    spl77_204,
    inference(avatar_split_clause,[],[f3830,f6851]) ).

fof(f6851,plain,
    ( spl77_204
  <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_204])]) ).

fof(f3830,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(cnf_transformation,[],[f624]) ).

fof(f624,axiom,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__0) ).

fof(f6849,plain,
    spl77_203,
    inference(avatar_split_clause,[],[f3829,f6846]) ).

fof(f6846,plain,
    ( spl77_203
  <=> 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,[spl77_203])]) ).

fof(f3829,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,[],[f143]) ).

fof(f143,axiom,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__0) ).

fof(f6844,plain,
    spl77_202,
    inference(avatar_split_clause,[],[f3828,f6841]) ).

fof(f3828,plain,
    c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(cnf_transformation,[],[f630]) ).

fof(f630,axiom,
    c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__numerals_I2_J) ).

fof(f6839,plain,
    spl77_201,
    inference(avatar_split_clause,[],[f5805,f6836]) ).

fof(f6836,plain,
    ( spl77_201
  <=> 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,[spl77_201])]) ).

fof(f5805,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,[],[f5572,f5484]) ).

fof(f5572,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,[],[f4557]) ).

fof(f4557,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,[],[f3426]) ).

fof(f3426,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,[],[f3425]) ).

fof(f3425,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,[],[f1644]) ).

fof(f1644,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,[],[f744]) ).

fof(f744,axiom,
    ! [X22,X10] :
      ( 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),X10),X22))
    <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X10)
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X22 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__power__nat__eq) ).

fof(f6834,plain,
    spl77_200,
    inference(avatar_split_clause,[],[f5616,f6832]) ).

fof(f6832,plain,
    ( spl77_200
  <=> ! [X2,X1] :
        ( ~ c_Orderings_Oord__class_Oless(X2,X1,X1)
        | ~ class_Orderings_Oorder(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_200])]) ).

fof(f5616,plain,
    ! [X2,X1] :
      ( ~ c_Orderings_Oord__class_Oless(X2,X1,X1)
      | ~ class_Orderings_Oorder(X2) ),
    inference(equality_resolution,[],[f4832]) ).

fof(f4832,plain,
    ! [X2,X0,X1] :
      ( X0 != X1
      | ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
      | ~ class_Orderings_Oorder(X2) ),
    inference(cnf_transformation,[],[f2709]) ).

fof(f2709,plain,
    ! [X0,X1,X2] :
      ( X0 != X1
      | ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
      | ~ class_Orderings_Oorder(X2) ),
    inference(flattening,[],[f2708]) ).

fof(f2708,plain,
    ! [X0,X1,X2] :
      ( X0 != X1
      | ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
      | ~ class_Orderings_Oorder(X2) ),
    inference(ennf_transformation,[],[f1835]) ).

fof(f1835,plain,
    ! [X0,X1,X2] :
      ( class_Orderings_Oorder(X2)
     => ( c_Orderings_Oord__class_Oless(X2,X1,X0)
       => X0 != X1 ) ),
    inference(rectify,[],[f37]) ).

fof(f37,axiom,
    ! [X24,X25,X7] :
      ( class_Orderings_Oorder(X7)
     => ( c_Orderings_Oord__class_Oless(X7,X25,X24)
       => X24 != X25 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__neq) ).

fof(f6830,plain,
    spl77_199,
    inference(avatar_split_clause,[],[f5612,f6828]) ).

fof(f6828,plain,
    ( spl77_199
  <=> ! [X2,X1] :
        ( ~ c_Orderings_Oord__class_Oless(X2,X1,X1)
        | ~ class_Orderings_Olinorder(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_199])]) ).

fof(f5612,plain,
    ! [X2,X1] :
      ( ~ c_Orderings_Oord__class_Oless(X2,X1,X1)
      | ~ class_Orderings_Olinorder(X2) ),
    inference(equality_resolution,[],[f4789]) ).

fof(f4789,plain,
    ! [X2,X0,X1] :
      ( X0 != X1
      | ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
      | ~ class_Orderings_Olinorder(X2) ),
    inference(cnf_transformation,[],[f3492]) ).

fof(f3492,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,[],[f3491]) ).

fof(f3491,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,[],[f2652]) ).

fof(f2652,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,[],[f1800]) ).

fof(f1800,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,[],[f32]) ).

fof(f32,axiom,
    ! [X34,X10,X7] :
      ( class_Orderings_Olinorder(X7)
     => ( X10 != X34
      <=> ( c_Orderings_Oord__class_Oless(X7,X34,X10)
          | c_Orderings_Oord__class_Oless(X7,X10,X34) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neq__iff) ).

fof(f6826,plain,
    spl77_198,
    inference(avatar_split_clause,[],[f4686,f6824]) ).

fof(f6824,plain,
    ( spl77_198
  <=> ! [X2,X0,X1] :
        ( sP9(X1,X2,X0)
        | ~ class_Rings_Olinordered__ring__strict(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_198])]) ).

fof(f4686,plain,
    ! [X2,X0,X1] :
      ( sP9(X1,X2,X0)
      | ~ class_Rings_Olinordered__ring__strict(X2) ),
    inference(cnf_transformation,[],[f3142]) ).

fof(f3142,plain,
    ! [X0,X1,X2] :
      ( sP9(X1,X2,X0)
      | ~ class_Rings_Olinordered__ring__strict(X2) ),
    inference(definition_folding,[],[f2543,f3141,f3140]) ).

fof(f3140,plain,
    ! [X0,X2,X1] :
      ( sP8(X0,X2,X1)
    <=> ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2)),X0))
          & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,X1),c_Groups_Ozero__class_Ozero(X2))) )
        | ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,X0),c_Groups_Ozero__class_Ozero(X2)))
          & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2)),X1)) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).

fof(f3141,plain,
    ! [X1,X2,X0] :
      ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)),c_Groups_Ozero__class_Ozero(X2)))
      <=> sP8(X0,X2,X1) )
      | ~ sP9(X1,X2,X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP9])]) ).

fof(f2543,plain,
    ! [X0,X1,X2] :
      ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)),c_Groups_Ozero__class_Ozero(X2)))
      <=> ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2)),X0))
            & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,X1),c_Groups_Ozero__class_Ozero(X2))) )
          | ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,X0),c_Groups_Ozero__class_Ozero(X2)))
            & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2)),X1)) ) ) )
      | ~ class_Rings_Olinordered__ring__strict(X2) ),
    inference(ennf_transformation,[],[f1728]) ).

fof(f1728,plain,
    ! [X0,X1,X2] :
      ( class_Rings_Olinordered__ring__strict(X2)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)),c_Groups_Ozero__class_Ozero(X2)))
      <=> ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2)),X0))
            & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,X1),c_Groups_Ozero__class_Ozero(X2))) )
          | ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,X0),c_Groups_Ozero__class_Ozero(X2)))
            & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2)),X1)) ) ) ) ),
    inference(rectify,[],[f469]) ).

fof(f469,axiom,
    ! [X17,X18,X7] :
      ( class_Rings_Olinordered__ring__strict(X7)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X18),X17)),c_Groups_Ozero__class_Ozero(X7)))
      <=> ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7)),X17))
            & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X7,X18),c_Groups_Ozero__class_Ozero(X7))) )
          | ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X7,X17),c_Groups_Ozero__class_Ozero(X7)))
            & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7)),X18)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__0__iff) ).

fof(f6822,plain,
    spl77_197,
    inference(avatar_split_clause,[],[f4677,f6820]) ).

fof(f6820,plain,
    ( spl77_197
  <=> ! [X2,X0,X1] :
        ( sP7(X1,X0,X2)
        | ~ class_Rings_Olinordered__ring__strict(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_197])]) ).

fof(f4677,plain,
    ! [X2,X0,X1] :
      ( sP7(X1,X0,X2)
      | ~ class_Rings_Olinordered__ring__strict(X2) ),
    inference(cnf_transformation,[],[f3139]) ).

fof(f3139,plain,
    ! [X0,X1,X2] :
      ( sP7(X1,X0,X2)
      | ~ class_Rings_Olinordered__ring__strict(X2) ),
    inference(definition_folding,[],[f2542,f3138,f3137]) ).

fof(f3137,plain,
    ! [X2,X0,X1] :
      ( sP6(X2,X0,X1)
    <=> ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,X0),c_Groups_Ozero__class_Ozero(X2)))
          & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,X1),c_Groups_Ozero__class_Ozero(X2))) )
        | ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2)),X0))
          & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2)),X1)) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).

fof(f3138,plain,
    ! [X1,X0,X2] :
      ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)))
      <=> sP6(X2,X0,X1) )
      | ~ sP7(X1,X0,X2) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).

fof(f2542,plain,
    ! [X0,X1,X2] :
      ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)))
      <=> ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,X0),c_Groups_Ozero__class_Ozero(X2)))
            & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,X1),c_Groups_Ozero__class_Ozero(X2))) )
          | ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2)),X0))
            & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2)),X1)) ) ) )
      | ~ class_Rings_Olinordered__ring__strict(X2) ),
    inference(ennf_transformation,[],[f1727]) ).

fof(f1727,plain,
    ! [X0,X1,X2] :
      ( class_Rings_Olinordered__ring__strict(X2)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)))
      <=> ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,X0),c_Groups_Ozero__class_Ozero(X2)))
            & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,X1),c_Groups_Ozero__class_Ozero(X2))) )
          | ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2)),X0))
            & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2)),X1)) ) ) ) ),
    inference(rectify,[],[f468]) ).

fof(f468,axiom,
    ! [X17,X18,X7] :
      ( class_Rings_Olinordered__ring__strict(X7)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X18),X17)))
      <=> ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X7,X17),c_Groups_Ozero__class_Ozero(X7)))
            & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X7,X18),c_Groups_Ozero__class_Ozero(X7))) )
          | ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7)),X17))
            & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7)),X18)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__mult__iff) ).

fof(f6818,plain,
    spl77_196,
    inference(avatar_split_clause,[],[f4208,f6816]) ).

fof(f6816,plain,
    ( spl77_196
  <=> ! [X0,X1] :
        ( class_Orderings_Oorder(tc_fun(X0,X1))
        | ~ class_Orderings_Oorder(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_196])]) ).

fof(f4208,plain,
    ! [X0,X1] :
      ( class_Orderings_Oorder(tc_fun(X0,X1))
      | ~ class_Orderings_Oorder(X1) ),
    inference(cnf_transformation,[],[f2295]) ).

fof(f2295,plain,
    ! [X0,X1] :
      ( class_Orderings_Oorder(tc_fun(X0,X1))
      | ~ class_Orderings_Oorder(X1) ),
    inference(ennf_transformation,[],[f1456]) ).

fof(f1456,plain,
    ! [X0,X1] :
      ( class_Orderings_Oorder(X1)
     => class_Orderings_Oorder(tc_fun(X0,X1)) ),
    inference(rectify,[],[f999]) ).

fof(f999,axiom,
    ! [X97,X98] :
      ( class_Orderings_Oorder(X98)
     => class_Orderings_Oorder(tc_fun(X97,X98)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oorder) ).

fof(f6814,plain,
    spl77_195,
    inference(avatar_split_clause,[],[f4206,f6812]) ).

fof(f6812,plain,
    ( spl77_195
  <=> ! [X0,X1] :
        ( class_Orderings_Opreorder(tc_fun(X0,X1))
        | ~ class_Orderings_Opreorder(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_195])]) ).

fof(f4206,plain,
    ! [X0,X1] :
      ( class_Orderings_Opreorder(tc_fun(X0,X1))
      | ~ class_Orderings_Opreorder(X1) ),
    inference(cnf_transformation,[],[f2293]) ).

fof(f2293,plain,
    ! [X0,X1] :
      ( class_Orderings_Opreorder(tc_fun(X0,X1))
      | ~ class_Orderings_Opreorder(X1) ),
    inference(ennf_transformation,[],[f1454]) ).

fof(f1454,plain,
    ! [X0,X1] :
      ( class_Orderings_Opreorder(X1)
     => class_Orderings_Opreorder(tc_fun(X0,X1)) ),
    inference(rectify,[],[f998]) ).

fof(f998,axiom,
    ! [X97,X98] :
      ( class_Orderings_Opreorder(X98)
     => class_Orderings_Opreorder(tc_fun(X97,X98)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Opreorder) ).

fof(f6810,plain,
    spl77_194,
    inference(avatar_split_clause,[],[f4205,f6808]) ).

fof(f6808,plain,
    ( spl77_194
  <=> ! [X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless(X1,X0,X0)
        | ~ class_Orderings_Opreorder(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_194])]) ).

fof(f4205,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(X1,X0,X0)
      | ~ class_Orderings_Opreorder(X1) ),
    inference(cnf_transformation,[],[f2292]) ).

fof(f2292,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(X1,X0,X0)
      | ~ class_Orderings_Opreorder(X1) ),
    inference(ennf_transformation,[],[f1453]) ).

fof(f1453,plain,
    ! [X0,X1] :
      ( class_Orderings_Opreorder(X1)
     => ~ c_Orderings_Oord__class_Oless(X1,X0,X0) ),
    inference(rectify,[],[f31]) ).

fof(f31,axiom,
    ! [X25,X7] :
      ( class_Orderings_Opreorder(X7)
     => ~ c_Orderings_Oord__class_Oless(X7,X25,X25) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__irrefl) ).

fof(f6806,plain,
    spl77_193,
    inference(avatar_split_clause,[],[f4204,f6804]) ).

fof(f6804,plain,
    ( spl77_193
  <=> ! [X0,X1] :
        ( class_Orderings_Oord(tc_fun(X0,X1))
        | ~ class_Orderings_Oord(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_193])]) ).

fof(f4204,plain,
    ! [X0,X1] :
      ( class_Orderings_Oord(tc_fun(X0,X1))
      | ~ class_Orderings_Oord(X1) ),
    inference(cnf_transformation,[],[f2291]) ).

fof(f2291,plain,
    ! [X0,X1] :
      ( class_Orderings_Oord(tc_fun(X0,X1))
      | ~ class_Orderings_Oord(X1) ),
    inference(ennf_transformation,[],[f1452]) ).

fof(f1452,plain,
    ! [X0,X1] :
      ( class_Orderings_Oord(X1)
     => class_Orderings_Oord(tc_fun(X0,X1)) ),
    inference(rectify,[],[f1000]) ).

fof(f1000,axiom,
    ! [X97,X98] :
      ( class_Orderings_Oord(X98)
     => class_Orderings_Oord(tc_fun(X97,X98)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).

fof(f6802,plain,
    spl77_192,
    inference(avatar_split_clause,[],[f4203,f6800]) ).

fof(f6800,plain,
    ( spl77_192
  <=> ! [X0,X1] :
        ( class_Groups_Ominus(tc_fun(X0,X1))
        | ~ class_Groups_Ominus(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_192])]) ).

fof(f4203,plain,
    ! [X0,X1] :
      ( class_Groups_Ominus(tc_fun(X0,X1))
      | ~ class_Groups_Ominus(X1) ),
    inference(cnf_transformation,[],[f2290]) ).

fof(f2290,plain,
    ! [X0,X1] :
      ( class_Groups_Ominus(tc_fun(X0,X1))
      | ~ class_Groups_Ominus(X1) ),
    inference(ennf_transformation,[],[f1451]) ).

fof(f1451,plain,
    ! [X0,X1] :
      ( class_Groups_Ominus(X1)
     => class_Groups_Ominus(tc_fun(X0,X1)) ),
    inference(rectify,[],[f1002]) ).

fof(f1002,axiom,
    ! [X97,X98] :
      ( class_Groups_Ominus(X98)
     => class_Groups_Ominus(tc_fun(X97,X98)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Groups_Ominus) ).

fof(f6798,plain,
    spl77_191,
    inference(avatar_split_clause,[],[f4202,f6796]) ).

fof(f6796,plain,
    ( spl77_191
  <=> ! [X0,X1] :
        ( class_Groups_Ouminus(tc_fun(X0,X1))
        | ~ class_Groups_Ouminus(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_191])]) ).

fof(f4202,plain,
    ! [X0,X1] :
      ( class_Groups_Ouminus(tc_fun(X0,X1))
      | ~ class_Groups_Ouminus(X1) ),
    inference(cnf_transformation,[],[f2289]) ).

fof(f2289,plain,
    ! [X0,X1] :
      ( class_Groups_Ouminus(tc_fun(X0,X1))
      | ~ class_Groups_Ouminus(X1) ),
    inference(ennf_transformation,[],[f1450]) ).

fof(f1450,plain,
    ! [X0,X1] :
      ( class_Groups_Ouminus(X1)
     => class_Groups_Ouminus(tc_fun(X0,X1)) ),
    inference(rectify,[],[f1001]) ).

fof(f1001,axiom,
    ! [X97,X98] :
      ( class_Groups_Ouminus(X98)
     => class_Groups_Ouminus(tc_fun(X97,X98)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Groups_Ouminus) ).

fof(f6794,plain,
    spl77_190,
    inference(avatar_split_clause,[],[f4104,f6792]) ).

fof(f6792,plain,
    ( spl77_190
  <=> ! [X0,X1] :
        ( class_Lattices_Oboolean__algebra(tc_fun(X0,X1))
        | ~ class_Lattices_Oboolean__algebra(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_190])]) ).

fof(f4104,plain,
    ! [X0,X1] :
      ( class_Lattices_Oboolean__algebra(tc_fun(X0,X1))
      | ~ class_Lattices_Oboolean__algebra(X1) ),
    inference(cnf_transformation,[],[f2216]) ).

fof(f2216,plain,
    ! [X0,X1] :
      ( class_Lattices_Oboolean__algebra(tc_fun(X0,X1))
      | ~ class_Lattices_Oboolean__algebra(X1) ),
    inference(ennf_transformation,[],[f1379]) ).

fof(f1379,plain,
    ! [X0,X1] :
      ( class_Lattices_Oboolean__algebra(X1)
     => class_Lattices_Oboolean__algebra(tc_fun(X0,X1)) ),
    inference(rectify,[],[f997]) ).

fof(f997,axiom,
    ! [X97,X98] :
      ( class_Lattices_Oboolean__algebra(X98)
     => class_Lattices_Oboolean__algebra(tc_fun(X97,X98)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Oboolean__algebra) ).

fof(f6790,plain,
    spl77_189,
    inference(avatar_split_clause,[],[f3861,f6788]) ).

fof(f6788,plain,
    ( spl77_189
  <=> ! [X0] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_189])]) ).

fof(f3861,plain,
    ! [X0] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),X0)),
    inference(cnf_transformation,[],[f1181]) ).

fof(f1181,plain,
    ! [X0] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),X0)),
    inference(rectify,[],[f580]) ).

fof(f580,axiom,
    ! [X21] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21),X21)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__refl) ).

fof(f6786,plain,
    spl77_188,
    inference(avatar_split_clause,[],[f3860,f6784]) ).

fof(f3860,plain,
    ! [X0] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0),X0)),
    inference(cnf_transformation,[],[f1180]) ).

fof(f1180,plain,
    ! [X0] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0),X0)),
    inference(rectify,[],[f574]) ).

fof(f574,axiom,
    ! [X52] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X52),X52)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__refl) ).

fof(f6782,plain,
    spl77_187,
    inference(avatar_split_clause,[],[f3859,f6780]) ).

fof(f3859,plain,
    ! [X0] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X0)),
    inference(cnf_transformation,[],[f1179]) ).

fof(f1179,plain,
    ! [X0] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X0)),
    inference(rectify,[],[f568]) ).

fof(f568,axiom,
    ! [X52] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X52),X52)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__refl) ).

fof(f6778,plain,
    spl77_186,
    inference(avatar_split_clause,[],[f3827,f6775]) ).

fof(f6775,plain,
    ( spl77_186
  <=> 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,[spl77_186])]) ).

fof(f3827,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,[],[f196]) ).

fof(f196,axiom,
    c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__0__less__1) ).

fof(f6773,plain,
    spl77_185,
    inference(avatar_split_clause,[],[f3825,f6770]) ).

fof(f6770,plain,
    ( spl77_185
  <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_185])]) ).

fof(f3825,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
    inference(cnf_transformation,[],[f617]) ).

fof(f617,axiom,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__zero) ).

fof(f6768,plain,
    spl77_184,
    inference(avatar_split_clause,[],[f3824,f6765]) ).

fof(f6765,plain,
    ( spl77_184
  <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_184])]) ).

fof(f3824,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
    inference(cnf_transformation,[],[f621]) ).

fof(f621,axiom,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__zero) ).

fof(f6763,plain,
    spl77_183,
    inference(avatar_split_clause,[],[f3823,f6760]) ).

fof(f6760,plain,
    ( spl77_183
  <=> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Oln(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_183])]) ).

fof(f3823,plain,
    c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Oln(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
    inference(cnf_transformation,[],[f795]) ).

fof(f795,axiom,
    c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Oln(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__one) ).

fof(f6758,plain,
    spl77_182,
    inference(avatar_split_clause,[],[f3822,f6755]) ).

fof(f6755,plain,
    ( spl77_182
  <=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_182])]) ).

fof(f3822,plain,
    c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
    inference(cnf_transformation,[],[f623]) ).

fof(f623,axiom,
    c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__one) ).

fof(f6753,plain,
    spl77_181,
    inference(avatar_split_clause,[],[f3821,f6750]) ).

fof(f6750,plain,
    ( spl77_181
  <=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_181])]) ).

fof(f3821,plain,
    c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
    inference(cnf_transformation,[],[f622]) ).

fof(f622,axiom,
    c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__one) ).

fof(f6748,plain,
    spl77_180,
    inference(avatar_split_clause,[],[f5775,f6745]) ).

fof(f6745,plain,
    ( spl77_180
  <=> sP5(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_180])]) ).

fof(f5775,plain,
    sP5(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(forward_demodulation,[],[f5774,f3871]) ).

fof(f5774,plain,
    sP5(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,[],[f5556,f4025]) ).

fof(f5556,plain,
    sP5(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,[],[f5555]) ).

fof(f5555,plain,
    ! [X1] :
      ( sP5(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,[],[f5421]) ).

fof(f5421,plain,
    ! [X0,X1] :
      ( sP5(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,[],[f4496,f3879]) ).

fof(f4496,plain,
    ! [X0,X1] :
      ( sP5(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,[],[f3391]) ).

fof(f6743,plain,
    spl77_179,
    inference(avatar_split_clause,[],[f5773,f6740]) ).

fof(f6740,plain,
    ( spl77_179
  <=> sP5(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_179])]) ).

fof(f5773,plain,
    sP5(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(forward_demodulation,[],[f5772,f3871]) ).

fof(f5772,plain,
    sP5(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,[],[f5554,f4025]) ).

fof(f5554,plain,
    sP5(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,[],[f5553]) ).

fof(f5553,plain,
    ! [X1] :
      ( sP5(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,[],[f5420]) ).

fof(f5420,plain,
    ! [X0,X1] :
      ( sP5(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,[],[f4497,f3879]) ).

fof(f4497,plain,
    ! [X0,X1] :
      ( sP5(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,[],[f3391]) ).

fof(f6738,plain,
    spl77_178,
    inference(avatar_split_clause,[],[f5759,f6735]) ).

fof(f6735,plain,
    ( spl77_178
  <=> sP4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_178])]) ).

fof(f5759,plain,
    sP4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(forward_demodulation,[],[f5758,f3871]) ).

fof(f5758,plain,
    sP4(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,[],[f5552,f4025]) ).

fof(f5552,plain,
    sP4(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,[],[f5551]) ).

fof(f5551,plain,
    ! [X1] :
      ( sP4(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,[],[f5414]) ).

fof(f5414,plain,
    ! [X0,X1] :
      ( sP4(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,[],[f4488,f3879]) ).

fof(f4488,plain,
    ! [X0,X1] :
      ( sP4(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,[],[f3388]) ).

fof(f6733,plain,
    spl77_177,
    inference(avatar_split_clause,[],[f5757,f6730]) ).

fof(f6730,plain,
    ( spl77_177
  <=> sP4(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_177])]) ).

fof(f5757,plain,
    sP4(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(forward_demodulation,[],[f5756,f3871]) ).

fof(f5756,plain,
    sP4(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,[],[f5550,f4025]) ).

fof(f5550,plain,
    sP4(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,[],[f5549]) ).

fof(f5549,plain,
    ! [X1] :
      ( sP4(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,[],[f5413]) ).

fof(f5413,plain,
    ! [X0,X1] :
      ( sP4(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,[],[f4489,f3879]) ).

fof(f4489,plain,
    ! [X0,X1] :
      ( sP4(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,[],[f3388]) ).

fof(f6728,plain,
    spl77_176,
    inference(avatar_split_clause,[],[f5754,f6725]) ).

fof(f6725,plain,
    ( spl77_176
  <=> sP1(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_176])]) ).

fof(f5754,plain,
    sP1(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(forward_demodulation,[],[f5528,f3837]) ).

fof(f5528,plain,
    sP1(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(equality_resolution,[],[f5527]) ).

fof(f5527,plain,
    ! [X1] :
      ( sP1(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
      | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ),
    inference(equality_resolution,[],[f4418]) ).

fof(f4418,plain,
    ! [X0,X1] :
      ( sP1(X0,X1)
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
      | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) != X1 ),
    inference(cnf_transformation,[],[f3337]) ).

fof(f6723,plain,
    spl77_175,
    inference(avatar_split_clause,[],[f5753,f6720]) ).

fof(f6720,plain,
    ( spl77_175
  <=> sP0(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_175])]) ).

fof(f5753,plain,
    sP0(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(forward_demodulation,[],[f5523,f3837]) ).

fof(f5523,plain,
    sP0(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(equality_resolution,[],[f5522]) ).

fof(f5522,plain,
    ! [X1] :
      ( sP0(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
      | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ),
    inference(equality_resolution,[],[f4410]) ).

fof(f4410,plain,
    ! [X0,X1] :
      ( sP0(X0,X1)
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
      | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) != X1 ),
    inference(cnf_transformation,[],[f3333]) ).

fof(f6718,plain,
    spl77_174,
    inference(avatar_split_clause,[],[f5637,f6716]) ).

fof(f6716,plain,
    ( spl77_174
  <=> ! [X0,X1] : sP14(X0,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_174])]) ).

fof(f5637,plain,
    ! [X0,X1] : sP14(X0,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(equality_resolution,[],[f4970]) ).

fof(f4970,plain,
    ! [X2,X0,X1] :
      ( sP14(X0,X1,X2)
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2 ),
    inference(cnf_transformation,[],[f3551]) ).

fof(f6714,plain,
    spl77_173,
    inference(avatar_split_clause,[],[f5531,f6712]) ).

fof(f5531,plain,
    ! [X0] : sP1(hAPP(c_Int_Onat,X0),X0),
    inference(equality_resolution,[],[f4419]) ).

fof(f4419,plain,
    ! [X0,X1] :
      ( sP1(X1,X0)
      | hAPP(c_Int_Onat,X0) != X1 ),
    inference(cnf_transformation,[],[f3338]) ).

fof(f6710,plain,
    spl77_172,
    inference(avatar_split_clause,[],[f5526,f6708]) ).

fof(f5526,plain,
    ! [X1] : sP0(hAPP(c_Int_Onat,X1),X1),
    inference(equality_resolution,[],[f4411]) ).

fof(f4411,plain,
    ! [X0,X1] :
      ( sP0(X0,X1)
      | hAPP(c_Int_Onat,X1) != X0 ),
    inference(cnf_transformation,[],[f3334]) ).

fof(f6706,plain,
    spl77_171,
    inference(avatar_split_clause,[],[f3854,f6704]) ).

fof(f6704,plain,
    ( spl77_171
  <=> ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_171])]) ).

fof(f3854,plain,
    ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(cnf_transformation,[],[f1174]) ).

fof(f1174,plain,
    ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(rectify,[],[f89]) ).

fof(f89,axiom,
    ! [X21] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__zeroE) ).

fof(f6702,plain,
    spl77_170,
    inference(avatar_split_clause,[],[f3819,f6699]) ).

fof(f6699,plain,
    ( spl77_170
  <=> c_RealDef_Oreal(tc_Nat_Onat) = c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_170])]) ).

fof(f3819,plain,
    c_RealDef_Oreal(tc_Nat_Onat) = c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f667]) ).

fof(f667,axiom,
    c_RealDef_Oreal(tc_Nat_Onat) = c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__eq__of__nat) ).

fof(f6697,plain,
    ~ spl77_169,
    inference(avatar_split_clause,[],[f3818,f6694]) ).

fof(f6694,plain,
    ( spl77_169
  <=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_169])]) ).

fof(f3818,plain,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
    inference(cnf_transformation,[],[f145]) ).

fof(f145,axiom,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__0__neq__1) ).

fof(f6692,plain,
    ~ spl77_168,
    inference(avatar_split_clause,[],[f3817,f6689]) ).

fof(f6689,plain,
    ( spl77_168
  <=> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_168])]) ).

fof(f3817,plain,
    c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f586]) ).

fof(f586,axiom,
    c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__zero__not__eq__one) ).

fof(f6687,plain,
    ( ~ spl77_167
    | spl77_166 ),
    inference(avatar_split_clause,[],[f6682,f6677,f6684]) ).

fof(f6677,plain,
    ( spl77_166
  <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),sK23),hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),sK24)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_166])]) ).

fof(f6682,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_f____,hAPP(v_ga____,sK23)),hAPP(v_f____,hAPP(v_ga____,sK24)))
    | spl77_166 ),
    inference(forward_demodulation,[],[f6681,f5273]) ).

fof(f5273,plain,
    ! [X2,X3,X0,X1,X4,X5] : hAPP(hAPP(c_Fun_Ocomp(X5,X4,X3,X2),X1),X0) = hAPP(X2,hAPP(X1,X0)),
    inference(cnf_transformation,[],[f2114]) ).

fof(f2114,plain,
    ! [X0,X1,X2,X3,X4,X5] : hAPP(hAPP(c_Fun_Ocomp(X5,X4,X3,X2),X1),X0) = hAPP(X2,hAPP(X1,X0)),
    inference(rectify,[],[f7]) ).

fof(f7,axiom,
    ! [X10,X0,X1,X9,X7,X8] : hAPP(hAPP(c_Fun_Ocomp(X8,X7,X9,X1),X0),X10) = hAPP(X1,hAPP(X0,X10)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__apply) ).

fof(f6681,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),sK23),hAPP(v_f____,hAPP(v_ga____,sK24)))
    | spl77_166 ),
    inference(forward_demodulation,[],[f6679,f5273]) ).

fof(f6679,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),sK23),hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),sK24))
    | spl77_166 ),
    inference(avatar_component_clause,[],[f6677]) ).

fof(f6680,plain,
    ~ spl77_166,
    inference(avatar_split_clause,[],[f3656,f6677]) ).

fof(f3656,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),sK23),hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),sK24)),
    inference(cnf_transformation,[],[f3166]) ).

fof(f3166,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),sK23),hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),sK24))
    & c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK23,sK24) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK23,sK24])],[f2141,f3165]) ).

fof(f3165,plain,
    ( ? [X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),X0),hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),X1))
        & c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) )
   => ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),sK23),hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),sK24))
      & c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK23,sK24) ) ),
    introduced(choice_axiom,[]) ).

fof(f2141,plain,
    ? [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),X0),hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),X1))
      & c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
    inference(ennf_transformation,[],[f1163]) ).

fof(f1163,plain,
    ~ ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),X0),hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),X1)) ),
    inference(rectify,[],[f1162]) ).

fof(f1162,negated_conjecture,
    ~ ! [X3,X4] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),X3),hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),X4)) ),
    inference(negated_conjecture,[],[f1161]) ).

fof(f1161,conjecture,
    ! [X3,X4] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),X3),hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

fof(f6675,plain,
    spl77_165,
    inference(avatar_split_clause,[],[f5545,f6673]) ).

fof(f6673,plain,
    ( spl77_165
  <=> ! [X0] : sP3(X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_165])]) ).

fof(f5545,plain,
    ! [X0] : sP3(X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(equality_resolution,[],[f4469]) ).

fof(f4469,plain,
    ! [X0,X1] :
      ( sP3(X0,X1)
      | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X1 ),
    inference(cnf_transformation,[],[f3379]) ).

fof(f3379,plain,
    ! [X0,X1] :
      ( ( sP3(X0,X1)
        | ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
            | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1)
            | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) )
          & c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X1 ) )
      & ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
          & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1)
          & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) )
        | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X1
        | ~ sP3(X0,X1) ) ),
    inference(rectify,[],[f3378]) ).

fof(f3378,plain,
    ! [X1,X0] :
      ( ( sP3(X1,X0)
        | ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1)
            | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
            | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) )
          & c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ) )
      & ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1)
          & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
          & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) )
        | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0
        | ~ sP3(X1,X0) ) ),
    inference(flattening,[],[f3377]) ).

fof(f3377,plain,
    ! [X1,X0] :
      ( ( sP3(X1,X0)
        | ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1)
            | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
            | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) )
          & c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ) )
      & ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1)
          & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
          & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) )
        | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0
        | ~ sP3(X1,X0) ) ),
    inference(nnf_transformation,[],[f3131]) ).

fof(f6671,plain,
    spl77_164,
    inference(avatar_split_clause,[],[f5517,f6669]) ).

fof(f5517,plain,
    ! [X1] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X1),
    inference(equality_resolution,[],[f4390]) ).

fof(f4390,plain,
    ! [X0,X1] :
      ( X0 != X1
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
    inference(cnf_transformation,[],[f3318]) ).

fof(f6667,plain,
    spl77_163,
    inference(avatar_split_clause,[],[f5516,f6665]) ).

fof(f6665,plain,
    ( spl77_163
  <=> ! [X1] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_163])]) ).

fof(f5516,plain,
    ! [X1] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X1),
    inference(equality_resolution,[],[f4385]) ).

fof(f4385,plain,
    ! [X0,X1] :
      ( X0 != X1
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) ),
    inference(cnf_transformation,[],[f3315]) ).

fof(f6663,plain,
    spl77_162,
    inference(avatar_split_clause,[],[f3846,f6661]) ).

fof(f6661,plain,
    ( spl77_162
  <=> ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_162])]) ).

fof(f3846,plain,
    ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X0),
    inference(cnf_transformation,[],[f1166]) ).

fof(f1166,plain,
    ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X0),
    inference(rectify,[],[f15]) ).

fof(f15,axiom,
    ! [X21] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,X21),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__irrefl__nat) ).

fof(f6659,plain,
    spl77_161,
    inference(avatar_split_clause,[],[f3816,f6656]) ).

fof(f6656,plain,
    ( spl77_161
  <=> class_Orderings_Oorder(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_161])]) ).

fof(f3816,plain,
    class_Orderings_Oorder(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1090]) ).

fof(f1090,axiom,
    class_Orderings_Oorder(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).

fof(f6654,plain,
    spl77_160,
    inference(avatar_split_clause,[],[f3815,f6651]) ).

fof(f6651,plain,
    ( spl77_160
  <=> class_Orderings_Oorder(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_160])]) ).

fof(f3815,plain,
    class_Orderings_Oorder(tc_Int_Oint),
    inference(cnf_transformation,[],[f1047]) ).

fof(f1047,axiom,
    class_Orderings_Oorder(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oorder) ).

fof(f6649,plain,
    spl77_159,
    inference(avatar_split_clause,[],[f3814,f6646]) ).

fof(f6646,plain,
    ( spl77_159
  <=> class_Orderings_Oorder(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_159])]) ).

fof(f3814,plain,
    class_Orderings_Oorder(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1149]) ).

fof(f1149,axiom,
    class_Orderings_Oorder(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Oorder) ).

fof(f6644,plain,
    spl77_158,
    inference(avatar_split_clause,[],[f3813,f6641]) ).

fof(f6641,plain,
    ( spl77_158
  <=> class_Orderings_Oorder(tc_HOL_Obool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_158])]) ).

fof(f3813,plain,
    class_Orderings_Oorder(tc_HOL_Obool),
    inference(cnf_transformation,[],[f1099]) ).

fof(f1099,axiom,
    class_Orderings_Oorder(tc_HOL_Obool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oorder) ).

fof(f6639,plain,
    spl77_157,
    inference(avatar_split_clause,[],[f3812,f6636]) ).

fof(f6636,plain,
    ( spl77_157
  <=> class_Orderings_Opreorder(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_157])]) ).

fof(f3812,plain,
    class_Orderings_Opreorder(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1083]) ).

fof(f1083,axiom,
    class_Orderings_Opreorder(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).

fof(f6634,plain,
    spl77_156,
    inference(avatar_split_clause,[],[f3811,f6631]) ).

fof(f6631,plain,
    ( spl77_156
  <=> class_Orderings_Opreorder(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_156])]) ).

fof(f3811,plain,
    class_Orderings_Opreorder(tc_Int_Oint),
    inference(cnf_transformation,[],[f1038]) ).

fof(f1038,axiom,
    class_Orderings_Opreorder(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Opreorder) ).

fof(f6629,plain,
    spl77_155,
    inference(avatar_split_clause,[],[f3810,f6626]) ).

fof(f6626,plain,
    ( spl77_155
  <=> class_Orderings_Opreorder(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_155])]) ).

fof(f3810,plain,
    class_Orderings_Opreorder(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1140]) ).

fof(f1140,axiom,
    class_Orderings_Opreorder(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Opreorder) ).

fof(f6624,plain,
    spl77_154,
    inference(avatar_split_clause,[],[f3809,f6621]) ).

fof(f6621,plain,
    ( spl77_154
  <=> class_Orderings_Opreorder(tc_HOL_Obool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_154])]) ).

fof(f3809,plain,
    class_Orderings_Opreorder(tc_HOL_Obool),
    inference(cnf_transformation,[],[f1098]) ).

fof(f1098,axiom,
    class_Orderings_Opreorder(tc_HOL_Obool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Opreorder) ).

fof(f6619,plain,
    spl77_153,
    inference(avatar_split_clause,[],[f3808,f6616]) ).

fof(f6616,plain,
    ( spl77_153
  <=> class_Orderings_Oord(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_153])]) ).

fof(f3808,plain,
    class_Orderings_Oord(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1092]) ).

fof(f1092,axiom,
    class_Orderings_Oord(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).

fof(f6614,plain,
    spl77_152,
    inference(avatar_split_clause,[],[f3807,f6611]) ).

fof(f6611,plain,
    ( spl77_152
  <=> class_Orderings_Oord(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_152])]) ).

fof(f3807,plain,
    class_Orderings_Oord(tc_Int_Oint),
    inference(cnf_transformation,[],[f1050]) ).

fof(f1050,axiom,
    class_Orderings_Oord(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oord) ).

fof(f6609,plain,
    spl77_151,
    inference(avatar_split_clause,[],[f3806,f6606]) ).

fof(f6606,plain,
    ( spl77_151
  <=> class_Orderings_Oord(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_151])]) ).

fof(f3806,plain,
    class_Orderings_Oord(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1152]) ).

fof(f1152,axiom,
    class_Orderings_Oord(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Oord) ).

fof(f6604,plain,
    spl77_150,
    inference(avatar_split_clause,[],[f3805,f6601]) ).

fof(f6601,plain,
    ( spl77_150
  <=> class_Orderings_Oord(tc_HOL_Obool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_150])]) ).

fof(f3805,plain,
    class_Orderings_Oord(tc_HOL_Obool),
    inference(cnf_transformation,[],[f1100]) ).

fof(f1100,axiom,
    class_Orderings_Oord(tc_HOL_Obool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oord) ).

fof(f6599,plain,
    spl77_149,
    inference(avatar_split_clause,[],[f3804,f6596]) ).

fof(f6596,plain,
    ( spl77_149
  <=> class_Groups_Ominus(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_149])]) ).

fof(f3804,plain,
    class_Groups_Ominus(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1093]) ).

fof(f1093,axiom,
    class_Groups_Ominus(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ominus) ).

fof(f6594,plain,
    spl77_148,
    inference(avatar_split_clause,[],[f3803,f6591]) ).

fof(f6591,plain,
    ( spl77_148
  <=> class_Groups_Ominus(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_148])]) ).

fof(f3803,plain,
    class_Groups_Ominus(tc_Int_Oint),
    inference(cnf_transformation,[],[f1053]) ).

fof(f1053,axiom,
    class_Groups_Ominus(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ominus) ).

fof(f6589,plain,
    spl77_147,
    inference(avatar_split_clause,[],[f3802,f6586]) ).

fof(f6586,plain,
    ( spl77_147
  <=> class_Groups_Ominus(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_147])]) ).

fof(f3802,plain,
    class_Groups_Ominus(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1155]) ).

fof(f1155,axiom,
    class_Groups_Ominus(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ominus) ).

fof(f6584,plain,
    spl77_146,
    inference(avatar_split_clause,[],[f3801,f6581]) ).

fof(f6581,plain,
    ( spl77_146
  <=> class_Groups_Ominus(tc_HOL_Obool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_146])]) ).

fof(f3801,plain,
    class_Groups_Ominus(tc_HOL_Obool),
    inference(cnf_transformation,[],[f1102]) ).

fof(f1102,axiom,
    class_Groups_Ominus(tc_HOL_Obool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Groups_Ominus) ).

fof(f6579,plain,
    spl77_145,
    inference(avatar_split_clause,[],[f3800,f6576]) ).

fof(f6576,plain,
    ( spl77_145
  <=> class_Groups_Ouminus(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_145])]) ).

fof(f3800,plain,
    class_Groups_Ouminus(tc_Int_Oint),
    inference(cnf_transformation,[],[f1051]) ).

fof(f1051,axiom,
    class_Groups_Ouminus(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ouminus) ).

fof(f6574,plain,
    spl77_144,
    inference(avatar_split_clause,[],[f3799,f6571]) ).

fof(f6571,plain,
    ( spl77_144
  <=> class_Groups_Ouminus(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_144])]) ).

fof(f3799,plain,
    class_Groups_Ouminus(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1153]) ).

fof(f1153,axiom,
    class_Groups_Ouminus(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ouminus) ).

fof(f6569,plain,
    spl77_143,
    inference(avatar_split_clause,[],[f3798,f6566]) ).

fof(f6566,plain,
    ( spl77_143
  <=> class_Groups_Ouminus(tc_HOL_Obool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_143])]) ).

fof(f3798,plain,
    class_Groups_Ouminus(tc_HOL_Obool),
    inference(cnf_transformation,[],[f1101]) ).

fof(f1101,axiom,
    class_Groups_Ouminus(tc_HOL_Obool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Groups_Ouminus) ).

fof(f6564,plain,
    spl77_142,
    inference(avatar_split_clause,[],[f3797,f6561]) ).

fof(f6561,plain,
    ( spl77_142
  <=> class_Rings_Olinordered__semidom(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_142])]) ).

fof(f3797,plain,
    class_Rings_Olinordered__semidom(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1071]) ).

fof(f1071,axiom,
    class_Rings_Olinordered__semidom(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semidom) ).

fof(f6559,plain,
    spl77_141,
    inference(avatar_split_clause,[],[f3796,f6556]) ).

fof(f6556,plain,
    ( spl77_141
  <=> class_Rings_Olinordered__semidom(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_141])]) ).

fof(f3796,plain,
    class_Rings_Olinordered__semidom(tc_Int_Oint),
    inference(cnf_transformation,[],[f1022]) ).

fof(f1022,axiom,
    class_Rings_Olinordered__semidom(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semidom) ).

fof(f6554,plain,
    spl77_140,
    inference(avatar_split_clause,[],[f3795,f6551]) ).

fof(f6551,plain,
    ( spl77_140
  <=> class_Rings_Olinordered__semidom(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_140])]) ).

fof(f3795,plain,
    class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1123]) ).

fof(f1123,axiom,
    class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semidom) ).

fof(f6549,plain,
    spl77_139,
    inference(avatar_split_clause,[],[f3794,f6546]) ).

fof(f6546,plain,
    ( spl77_139
  <=> class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_139])]) ).

fof(f3794,plain,
    class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1078]) ).

fof(f1078,axiom,
    class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).

fof(f6544,plain,
    spl77_138,
    inference(avatar_split_clause,[],[f3793,f6541]) ).

fof(f6541,plain,
    ( spl77_138
  <=> class_Rings_Ocomm__semiring__1(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_138])]) ).

fof(f3793,plain,
    class_Rings_Ocomm__semiring__1(tc_Int_Oint),
    inference(cnf_transformation,[],[f1031]) ).

fof(f1031,axiom,
    class_Rings_Ocomm__semiring__1(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__1) ).

fof(f6539,plain,
    spl77_137,
    inference(avatar_split_clause,[],[f3792,f6536]) ).

fof(f3792,plain,
    class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1133]) ).

fof(f1133,axiom,
    class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__1) ).

fof(f6534,plain,
    spl77_136,
    inference(avatar_split_clause,[],[f3791,f6531]) ).

fof(f3791,plain,
    class_Orderings_Olinorder(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1084]) ).

fof(f1084,axiom,
    class_Orderings_Olinorder(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).

fof(f6529,plain,
    spl77_135,
    inference(avatar_split_clause,[],[f3790,f6526]) ).

fof(f6526,plain,
    ( spl77_135
  <=> class_Orderings_Olinorder(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_135])]) ).

fof(f3790,plain,
    class_Orderings_Olinorder(tc_Int_Oint),
    inference(cnf_transformation,[],[f1039]) ).

fof(f1039,axiom,
    class_Orderings_Olinorder(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Olinorder) ).

fof(f6524,plain,
    spl77_134,
    inference(avatar_split_clause,[],[f3789,f6521]) ).

fof(f6521,plain,
    ( spl77_134
  <=> class_Orderings_Olinorder(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_134])]) ).

fof(f3789,plain,
    class_Orderings_Olinorder(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1141]) ).

fof(f1141,axiom,
    class_Orderings_Olinorder(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Olinorder) ).

fof(f6519,plain,
    spl77_133,
    inference(avatar_split_clause,[],[f3788,f6516]) ).

fof(f6516,plain,
    ( spl77_133
  <=> class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_133])]) ).

fof(f3788,plain,
    class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1063]) ).

fof(f1063,axiom,
    class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring__strict) ).

fof(f6514,plain,
    spl77_132,
    inference(avatar_split_clause,[],[f3787,f6511]) ).

fof(f6511,plain,
    ( spl77_132
  <=> class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_132])]) ).

fof(f3787,plain,
    class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
    inference(cnf_transformation,[],[f1008]) ).

fof(f1008,axiom,
    class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__strict) ).

fof(f6509,plain,
    spl77_131,
    inference(avatar_split_clause,[],[f3786,f6506]) ).

fof(f6506,plain,
    ( spl77_131
  <=> class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_131])]) ).

fof(f3786,plain,
    class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1108]) ).

fof(f1108,axiom,
    class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__strict) ).

fof(f6504,plain,
    spl77_130,
    inference(avatar_split_clause,[],[f3785,f6501]) ).

fof(f6501,plain,
    ( spl77_130
  <=> class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_130])]) ).

fof(f3785,plain,
    class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1065]) ).

fof(f1065,axiom,
    class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__comm__monoid__add) ).

fof(f6499,plain,
    spl77_129,
    inference(avatar_split_clause,[],[f3784,f6496]) ).

fof(f6496,plain,
    ( spl77_129
  <=> class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_129])]) ).

fof(f3784,plain,
    class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
    inference(cnf_transformation,[],[f1010]) ).

fof(f1010,axiom,
    class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__comm__monoid__add) ).

fof(f6494,plain,
    spl77_128,
    inference(avatar_split_clause,[],[f3783,f6491]) ).

fof(f6491,plain,
    ( spl77_128
  <=> class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_128])]) ).

fof(f3783,plain,
    class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1111]) ).

fof(f1111,axiom,
    class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add) ).

fof(f6489,plain,
    spl77_127,
    inference(avatar_split_clause,[],[f3782,f6486]) ).

fof(f6486,plain,
    ( spl77_127
  <=> class_Groups_Omonoid__mult(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_127])]) ).

fof(f3782,plain,
    class_Groups_Omonoid__mult(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1085]) ).

fof(f1085,axiom,
    class_Groups_Omonoid__mult(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__mult) ).

fof(f6484,plain,
    spl77_126,
    inference(avatar_split_clause,[],[f3781,f6481]) ).

fof(f6481,plain,
    ( spl77_126
  <=> class_Groups_Omonoid__mult(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_126])]) ).

fof(f3781,plain,
    class_Groups_Omonoid__mult(tc_Int_Oint),
    inference(cnf_transformation,[],[f1040]) ).

fof(f1040,axiom,
    class_Groups_Omonoid__mult(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__mult) ).

fof(f6479,plain,
    spl77_125,
    inference(avatar_split_clause,[],[f3780,f6476]) ).

fof(f6476,plain,
    ( spl77_125
  <=> class_Groups_Omonoid__mult(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_125])]) ).

fof(f3780,plain,
    class_Groups_Omonoid__mult(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1142]) ).

fof(f1142,axiom,
    class_Groups_Omonoid__mult(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__mult) ).

fof(f6474,plain,
    spl77_124,
    inference(avatar_split_clause,[],[f3779,f6471]) ).

fof(f6471,plain,
    ( spl77_124
  <=> class_Rings_Osemiring__1(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_124])]) ).

fof(f3779,plain,
    class_Rings_Osemiring__1(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1087]) ).

fof(f1087,axiom,
    class_Rings_Osemiring__1(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__1) ).

fof(f6469,plain,
    spl77_123,
    inference(avatar_split_clause,[],[f3778,f6466]) ).

fof(f6466,plain,
    ( spl77_123
  <=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_123])]) ).

fof(f3778,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1061]) ).

fof(f1061,axiom,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le) ).

fof(f6464,plain,
    spl77_122,
    inference(avatar_split_clause,[],[f3777,f6461]) ).

fof(f6461,plain,
    ( spl77_122
  <=> class_Rings_Osemiring__1(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_122])]) ).

fof(f3777,plain,
    class_Rings_Osemiring__1(tc_Int_Oint),
    inference(cnf_transformation,[],[f1043]) ).

fof(f1043,axiom,
    class_Rings_Osemiring__1(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring__1) ).

fof(f6459,plain,
    spl77_121,
    inference(avatar_split_clause,[],[f3776,f6456]) ).

fof(f6456,plain,
    ( spl77_121
  <=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_121])]) ).

fof(f3776,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
    inference(cnf_transformation,[],[f1005]) ).

fof(f1005,axiom,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le) ).

fof(f6454,plain,
    spl77_120,
    inference(avatar_split_clause,[],[f3775,f6451]) ).

fof(f6451,plain,
    ( spl77_120
  <=> class_Rings_Osemiring__1(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_120])]) ).

fof(f3775,plain,
    class_Rings_Osemiring__1(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1145]) ).

fof(f1145,axiom,
    class_Rings_Osemiring__1(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring__1) ).

fof(f6449,plain,
    spl77_119,
    inference(avatar_split_clause,[],[f3774,f6446]) ).

fof(f6446,plain,
    ( spl77_119
  <=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_119])]) ).

fof(f3774,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1105]) ).

fof(f1105,axiom,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le) ).

fof(f6444,plain,
    spl77_118,
    inference(avatar_split_clause,[],[f3773,f6441]) ).

fof(f6441,plain,
    ( spl77_118
  <=> class_Power_Opower(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_118])]) ).

fof(f3773,plain,
    class_Power_Opower(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1094]) ).

fof(f1094,axiom,
    class_Power_Opower(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Power_Opower) ).

fof(f6439,plain,
    spl77_117,
    inference(avatar_split_clause,[],[f3772,f6436]) ).

fof(f6436,plain,
    ( spl77_117
  <=> class_Power_Opower(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_117])]) ).

fof(f3772,plain,
    class_Power_Opower(tc_Int_Oint),
    inference(cnf_transformation,[],[f1054]) ).

fof(f1054,axiom,
    class_Power_Opower(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Power_Opower) ).

fof(f6434,plain,
    spl77_116,
    inference(avatar_split_clause,[],[f3771,f6431]) ).

fof(f6431,plain,
    ( spl77_116
  <=> class_Power_Opower(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_116])]) ).

fof(f3771,plain,
    class_Power_Opower(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1156]) ).

fof(f1156,axiom,
    class_Power_Opower(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Power_Opower) ).

fof(f6429,plain,
    spl77_115,
    inference(avatar_split_clause,[],[f3770,f6426]) ).

fof(f6426,plain,
    ( spl77_115
  <=> class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_115])]) ).

fof(f3770,plain,
    class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1067]) ).

fof(f1067,axiom,
    class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__cancel__semiring) ).

fof(f6424,plain,
    spl77_114,
    inference(avatar_split_clause,[],[f3769,f6421]) ).

fof(f6421,plain,
    ( spl77_114
  <=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_114])]) ).

fof(f3769,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1060]) ).

fof(f1060,axiom,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) ).

fof(f6419,plain,
    spl77_113,
    inference(avatar_split_clause,[],[f3768,f6416]) ).

fof(f6416,plain,
    ( spl77_113
  <=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_113])]) ).

fof(f3768,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
    inference(cnf_transformation,[],[f1004]) ).

fof(f1004,axiom,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add) ).

fof(f6414,plain,
    spl77_112,
    inference(avatar_split_clause,[],[f3767,f6411]) ).

fof(f6411,plain,
    ( spl77_112
  <=> class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_112])]) ).

fof(f3767,plain,
    class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
    inference(cnf_transformation,[],[f1014]) ).

fof(f1014,axiom,
    class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__cancel__semiring) ).

fof(f6409,plain,
    spl77_111,
    inference(avatar_split_clause,[],[f3766,f6406]) ).

fof(f6406,plain,
    ( spl77_111
  <=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_111])]) ).

fof(f3766,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1104]) ).

fof(f1104,axiom,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add) ).

fof(f6404,plain,
    spl77_110,
    inference(avatar_split_clause,[],[f3765,f6401]) ).

fof(f6401,plain,
    ( spl77_110
  <=> class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_110])]) ).

fof(f3765,plain,
    class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1115]) ).

fof(f1115,axiom,
    class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__cancel__semiring) ).

fof(f6399,plain,
    spl77_109,
    inference(avatar_split_clause,[],[f3764,f6396]) ).

fof(f6396,plain,
    ( spl77_109
  <=> class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_109])]) ).

fof(f3764,plain,
    class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1069]) ).

fof(f1069,axiom,
    class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).

fof(f6394,plain,
    spl77_108,
    inference(avatar_split_clause,[],[f3763,f6391]) ).

fof(f6391,plain,
    ( spl77_108
  <=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_108])]) ).

fof(f3763,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1059]) ).

fof(f1059,axiom,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).

fof(f6389,plain,
    spl77_107,
    inference(avatar_split_clause,[],[f3762,f6386]) ).

fof(f6386,plain,
    ( spl77_107
  <=> class_Rings_Oordered__semiring(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_107])]) ).

fof(f3762,plain,
    class_Rings_Oordered__semiring(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1075]) ).

fof(f1075,axiom,
    class_Rings_Oordered__semiring(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__semiring) ).

fof(f6384,plain,
    spl77_106,
    inference(avatar_split_clause,[],[f3761,f6381]) ).

fof(f6381,plain,
    ( spl77_106
  <=> class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_106])]) ).

fof(f3761,plain,
    class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
    inference(cnf_transformation,[],[f1020]) ).

fof(f1020,axiom,
    class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__semigroup__add) ).

fof(f6379,plain,
    spl77_105,
    inference(avatar_split_clause,[],[f3760,f6376]) ).

fof(f6376,plain,
    ( spl77_105
  <=> class_Rings_Oordered__semiring(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_105])]) ).

fof(f3760,plain,
    class_Rings_Oordered__semiring(tc_Int_Oint),
    inference(cnf_transformation,[],[f1026]) ).

fof(f1026,axiom,
    class_Rings_Oordered__semiring(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__semiring) ).

fof(f6374,plain,
    spl77_104,
    inference(avatar_split_clause,[],[f3759,f6371]) ).

fof(f6371,plain,
    ( spl77_104
  <=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_104])]) ).

fof(f3759,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
    inference(cnf_transformation,[],[f1003]) ).

fof(f1003,axiom,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).

fof(f6369,plain,
    spl77_103,
    inference(avatar_split_clause,[],[f3758,f6366]) ).

fof(f6366,plain,
    ( spl77_103
  <=> class_Rings_Oordered__semiring(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_103])]) ).

fof(f3758,plain,
    class_Rings_Oordered__semiring(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1128]) ).

fof(f1128,axiom,
    class_Rings_Oordered__semiring(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__semiring) ).

fof(f6364,plain,
    spl77_102,
    inference(avatar_split_clause,[],[f3757,f6361]) ).

fof(f6361,plain,
    ( spl77_102
  <=> class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_102])]) ).

fof(f3757,plain,
    class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1121]) ).

fof(f1121,axiom,
    class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__semigroup__add) ).

fof(f6359,plain,
    spl77_101,
    inference(avatar_split_clause,[],[f3756,f6356]) ).

fof(f6356,plain,
    ( spl77_101
  <=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_101])]) ).

fof(f3756,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1103]) ).

fof(f1103,axiom,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).

fof(f6354,plain,
    spl77_100,
    inference(avatar_split_clause,[],[f3755,f6351]) ).

fof(f6351,plain,
    ( spl77_100
  <=> class_Rings_Ozero__neq__one(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_100])]) ).

fof(f3755,plain,
    class_Rings_Ozero__neq__one(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1082]) ).

fof(f1082,axiom,
    class_Rings_Ozero__neq__one(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ozero__neq__one) ).

fof(f6349,plain,
    spl77_99,
    inference(avatar_split_clause,[],[f3754,f6346]) ).

fof(f6346,plain,
    ( spl77_99
  <=> class_Rings_Omult__zero(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_99])]) ).

fof(f3754,plain,
    class_Rings_Omult__zero(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1089]) ).

fof(f1089,axiom,
    class_Rings_Omult__zero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Omult__zero) ).

fof(f6344,plain,
    spl77_98,
    inference(avatar_split_clause,[],[f3753,f6341]) ).

fof(f6341,plain,
    ( spl77_98
  <=> class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_98])]) ).

fof(f3753,plain,
    class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1064]) ).

fof(f1064,axiom,
    class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) ).

fof(f6339,plain,
    spl77_97,
    inference(avatar_split_clause,[],[f3752,f6336]) ).

fof(f6336,plain,
    ( spl77_97
  <=> class_Rings_Ono__zero__divisors(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_97])]) ).

fof(f3752,plain,
    class_Rings_Ono__zero__divisors(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1076]) ).

fof(f1076,axiom,
    class_Rings_Ono__zero__divisors(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ono__zero__divisors) ).

fof(f6334,plain,
    spl77_96,
    inference(avatar_split_clause,[],[f3751,f6331]) ).

fof(f6331,plain,
    ( spl77_96
  <=> class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_96])]) ).

fof(f3751,plain,
    class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1073]) ).

fof(f1073,axiom,
    class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__mult) ).

fof(f6329,plain,
    spl77_95,
    inference(avatar_split_clause,[],[f3750,f6326]) ).

fof(f6326,plain,
    ( spl77_95
  <=> class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_95])]) ).

fof(f3750,plain,
    class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
    inference(cnf_transformation,[],[f1024]) ).

fof(f1024,axiom,
    class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__mult) ).

fof(f6324,plain,
    spl77_94,
    inference(avatar_split_clause,[],[f3749,f6321]) ).

fof(f6321,plain,
    ( spl77_94
  <=> class_Rings_Omult__zero(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_94])]) ).

fof(f3749,plain,
    class_Rings_Omult__zero(tc_Int_Oint),
    inference(cnf_transformation,[],[f1046]) ).

fof(f1046,axiom,
    class_Rings_Omult__zero(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Omult__zero) ).

fof(f6319,plain,
    spl77_93,
    inference(avatar_split_clause,[],[f3748,f6316]) ).

fof(f6316,plain,
    ( spl77_93
  <=> class_Rings_Ozero__neq__one(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_93])]) ).

fof(f3748,plain,
    class_Rings_Ozero__neq__one(tc_Int_Oint),
    inference(cnf_transformation,[],[f1036]) ).

fof(f1036,axiom,
    class_Rings_Ozero__neq__one(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ozero__neq__one) ).

fof(f6314,plain,
    spl77_92,
    inference(avatar_split_clause,[],[f3747,f6311]) ).

fof(f6311,plain,
    ( spl77_92
  <=> class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_92])]) ).

fof(f3747,plain,
    class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
    inference(cnf_transformation,[],[f1009]) ).

fof(f1009,axiom,
    class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add) ).

fof(f6309,plain,
    spl77_91,
    inference(avatar_split_clause,[],[f3746,f6306]) ).

fof(f6306,plain,
    ( spl77_91
  <=> class_Rings_Ono__zero__divisors(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_91])]) ).

fof(f3746,plain,
    class_Rings_Ono__zero__divisors(tc_Int_Oint),
    inference(cnf_transformation,[],[f1027]) ).

fof(f1027,axiom,
    class_Rings_Ono__zero__divisors(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ono__zero__divisors) ).

fof(f6304,plain,
    spl77_90,
    inference(avatar_split_clause,[],[f3745,f6301]) ).

fof(f6301,plain,
    ( spl77_90
  <=> class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_90])]) ).

fof(f3745,plain,
    class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1126]) ).

fof(f1126,axiom,
    class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocomm__monoid__mult) ).

fof(f6299,plain,
    spl77_89,
    inference(avatar_split_clause,[],[f3744,f6296]) ).

fof(f6296,plain,
    ( spl77_89
  <=> class_Rings_Ono__zero__divisors(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_89])]) ).

fof(f3744,plain,
    class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1129]) ).

fof(f1129,axiom,
    class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ono__zero__divisors) ).

fof(f6294,plain,
    spl77_88,
    inference(avatar_split_clause,[],[f3743,f6291]) ).

fof(f6291,plain,
    ( spl77_88
  <=> class_Rings_Omult__zero(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_88])]) ).

fof(f3743,plain,
    class_Rings_Omult__zero(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1148]) ).

fof(f1148,axiom,
    class_Rings_Omult__zero(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Omult__zero) ).

fof(f6289,plain,
    spl77_87,
    inference(avatar_split_clause,[],[f3742,f6286]) ).

fof(f6286,plain,
    ( spl77_87
  <=> class_Rings_Ozero__neq__one(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_87])]) ).

fof(f3742,plain,
    class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1138]) ).

fof(f1138,axiom,
    class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ozero__neq__one) ).

fof(f6284,plain,
    spl77_86,
    inference(avatar_split_clause,[],[f3741,f6281]) ).

fof(f6281,plain,
    ( spl77_86
  <=> class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_86])]) ).

fof(f3741,plain,
    class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1109]) ).

fof(f1109,axiom,
    class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add) ).

fof(f6279,plain,
    spl77_85,
    inference(avatar_split_clause,[],[f3740,f6276]) ).

fof(f6276,plain,
    ( spl77_85
  <=> class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_85])]) ).

fof(f3740,plain,
    class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1077]) ).

fof(f1077,axiom,
    class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__add) ).

fof(f6274,plain,
    spl77_84,
    inference(avatar_split_clause,[],[f3739,f6271]) ).

fof(f6271,plain,
    ( spl77_84
  <=> class_Rings_Olinordered__semiring(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_84])]) ).

fof(f3739,plain,
    class_Rings_Olinordered__semiring(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1070]) ).

fof(f1070,axiom,
    class_Rings_Olinordered__semiring(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring) ).

fof(f6269,plain,
    spl77_83,
    inference(avatar_split_clause,[],[f3738,f6266]) ).

fof(f6266,plain,
    ( spl77_83
  <=> class_Groups_Omonoid__add(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_83])]) ).

fof(f3738,plain,
    class_Groups_Omonoid__add(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1086]) ).

fof(f1086,axiom,
    class_Groups_Omonoid__add(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__add) ).

fof(f6264,plain,
    spl77_82,
    inference(avatar_split_clause,[],[f3737,f6261]) ).

fof(f6261,plain,
    ( spl77_82
  <=> class_Rings_Osemiring__0(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_82])]) ).

fof(f3737,plain,
    class_Rings_Osemiring__0(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1088]) ).

fof(f1088,axiom,
    class_Rings_Osemiring__0(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__0) ).

fof(f6259,plain,
    spl77_81,
    inference(avatar_split_clause,[],[f3736,f6256]) ).

fof(f6256,plain,
    ( spl77_81
  <=> class_Rings_Olinordered__semiring(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_81])]) ).

fof(f3736,plain,
    class_Rings_Olinordered__semiring(tc_Int_Oint),
    inference(cnf_transformation,[],[f1021]) ).

fof(f1021,axiom,
    class_Rings_Olinordered__semiring(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring) ).

fof(f6254,plain,
    spl77_80,
    inference(avatar_split_clause,[],[f3735,f6251]) ).

fof(f6251,plain,
    ( spl77_80
  <=> class_Rings_Osemiring__0(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_80])]) ).

fof(f3735,plain,
    class_Rings_Osemiring__0(tc_Int_Oint),
    inference(cnf_transformation,[],[f1044]) ).

fof(f1044,axiom,
    class_Rings_Osemiring__0(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring__0) ).

fof(f6249,plain,
    spl77_79,
    inference(avatar_split_clause,[],[f3734,f6246]) ).

fof(f6246,plain,
    ( spl77_79
  <=> class_Groups_Omonoid__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_79])]) ).

fof(f3734,plain,
    class_Groups_Omonoid__add(tc_Int_Oint),
    inference(cnf_transformation,[],[f1042]) ).

fof(f1042,axiom,
    class_Groups_Omonoid__add(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__add) ).

fof(f6244,plain,
    spl77_78,
    inference(avatar_split_clause,[],[f3733,f6241]) ).

fof(f6241,plain,
    ( spl77_78
  <=> class_Groups_Ocomm__monoid__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_78])]) ).

fof(f3733,plain,
    class_Groups_Ocomm__monoid__add(tc_Int_Oint),
    inference(cnf_transformation,[],[f1028]) ).

fof(f1028,axiom,
    class_Groups_Ocomm__monoid__add(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__add) ).

fof(f6239,plain,
    spl77_77,
    inference(avatar_split_clause,[],[f3732,f6236]) ).

fof(f6236,plain,
    ( spl77_77
  <=> class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_77])]) ).

fof(f3732,plain,
    class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1130]) ).

fof(f1130,axiom,
    class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocomm__monoid__add) ).

fof(f6234,plain,
    spl77_76,
    inference(avatar_split_clause,[],[f3731,f6231]) ).

fof(f6231,plain,
    ( spl77_76
  <=> class_Groups_Omonoid__add(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_76])]) ).

fof(f3731,plain,
    class_Groups_Omonoid__add(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1144]) ).

fof(f1144,axiom,
    class_Groups_Omonoid__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__add) ).

fof(f6229,plain,
    spl77_75,
    inference(avatar_split_clause,[],[f3730,f6226]) ).

fof(f6226,plain,
    ( spl77_75
  <=> class_Rings_Olinordered__semiring(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_75])]) ).

fof(f3730,plain,
    class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1122]) ).

fof(f1122,axiom,
    class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring) ).

fof(f6224,plain,
    spl77_74,
    inference(avatar_split_clause,[],[f3729,f6221]) ).

fof(f6221,plain,
    ( spl77_74
  <=> class_Rings_Osemiring__0(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_74])]) ).

fof(f3729,plain,
    class_Rings_Osemiring__0(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1146]) ).

fof(f1146,axiom,
    class_Rings_Osemiring__0(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring__0) ).

fof(f6219,plain,
    spl77_73,
    inference(avatar_split_clause,[],[f3728,f6216]) ).

fof(f6216,plain,
    ( spl77_73
  <=> class_Rings_Ocomm__semiring(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_73])]) ).

fof(f3728,plain,
    class_Rings_Ocomm__semiring(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1080]) ).

fof(f1080,axiom,
    class_Rings_Ocomm__semiring(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring) ).

fof(f6214,plain,
    spl77_72,
    inference(avatar_split_clause,[],[f3727,f6211]) ).

fof(f6211,plain,
    ( spl77_72
  <=> class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_72])]) ).

fof(f3727,plain,
    class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1072]) ).

fof(f1072,axiom,
    class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__mult) ).

fof(f6209,plain,
    spl77_71,
    inference(avatar_split_clause,[],[f3726,f6206]) ).

fof(f6206,plain,
    ( spl77_71
  <=> class_Groups_Oab__semigroup__add(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_71])]) ).

fof(f3726,plain,
    class_Groups_Oab__semigroup__add(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1074]) ).

fof(f1074,axiom,
    class_Groups_Oab__semigroup__add(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__add) ).

fof(f6204,plain,
    spl77_70,
    inference(avatar_split_clause,[],[f3725,f6201]) ).

fof(f6201,plain,
    ( spl77_70
  <=> class_Groups_Ozero(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_70])]) ).

fof(f3725,plain,
    class_Groups_Ozero(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1095]) ).

fof(f1095,axiom,
    class_Groups_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ozero) ).

fof(f6199,plain,
    spl77_69,
    inference(avatar_split_clause,[],[f3724,f6196]) ).

fof(f6196,plain,
    ( spl77_69
  <=> class_Groups_Oone(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_69])]) ).

fof(f3724,plain,
    class_Groups_Oone(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1096]) ).

fof(f1096,axiom,
    class_Groups_Oone(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oone) ).

fof(f6194,plain,
    spl77_68,
    inference(avatar_split_clause,[],[f3723,f6191]) ).

fof(f6191,plain,
    ( spl77_68
  <=> class_Nat_Osemiring__char__0(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_68])]) ).

fof(f3723,plain,
    class_Nat_Osemiring__char__0(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1081]) ).

fof(f1081,axiom,
    class_Nat_Osemiring__char__0(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Nat_Osemiring__char__0) ).

fof(f6189,plain,
    spl77_67,
    inference(avatar_split_clause,[],[f3722,f6186]) ).

fof(f6186,plain,
    ( spl77_67
  <=> class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_67])]) ).

fof(f3722,plain,
    class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1068]) ).

fof(f1068,axiom,
    class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__comm__semiring) ).

fof(f6184,plain,
    spl77_66,
    inference(avatar_split_clause,[],[f3721,f6181]) ).

fof(f6181,plain,
    ( spl77_66
  <=> class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_66])]) ).

fof(f3721,plain,
    class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1062]) ).

fof(f1062,axiom,
    class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict) ).

fof(f6179,plain,
    spl77_65,
    inference(avatar_split_clause,[],[f3720,f6176]) ).

fof(f6176,plain,
    ( spl77_65
  <=> class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_65])]) ).

fof(f3720,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1066]) ).

fof(f1066,axiom,
    class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) ).

fof(f6174,plain,
    spl77_64,
    inference(avatar_split_clause,[],[f3719,f6171]) ).

fof(f6171,plain,
    ( spl77_64
  <=> class_Rings_Osemiring(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_64])]) ).

fof(f3719,plain,
    class_Rings_Osemiring(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1091]) ).

fof(f1091,axiom,
    class_Rings_Osemiring(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring) ).

fof(f6169,plain,
    spl77_63,
    inference(avatar_split_clause,[],[f3718,f6166]) ).

fof(f6166,plain,
    ( spl77_63
  <=> class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_63])]) ).

fof(f3718,plain,
    class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
    inference(cnf_transformation,[],[f1006]) ).

fof(f1006,axiom,
    class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__comm__semiring__strict) ).

fof(f6164,plain,
    spl77_62,
    inference(avatar_split_clause,[],[f3717,f6161]) ).

fof(f6161,plain,
    ( spl77_62
  <=> class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_62])]) ).

fof(f3717,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
    inference(cnf_transformation,[],[f1012]) ).

fof(f1012,axiom,
    class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__ab__semigroup__add) ).

fof(f6159,plain,
    spl77_61,
    inference(avatar_split_clause,[],[f3716,f6156]) ).

fof(f6156,plain,
    ( spl77_61
  <=> class_Rings_Oordered__comm__semiring(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_61])]) ).

fof(f3716,plain,
    class_Rings_Oordered__comm__semiring(tc_Int_Oint),
    inference(cnf_transformation,[],[f1017]) ).

fof(f1017,axiom,
    class_Rings_Oordered__comm__semiring(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__comm__semiring) ).

fof(f6154,plain,
    spl77_60,
    inference(avatar_split_clause,[],[f3715,f6151]) ).

fof(f6151,plain,
    ( spl77_60
  <=> class_Nat_Osemiring__char__0(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_60])]) ).

fof(f3715,plain,
    class_Nat_Osemiring__char__0(tc_Int_Oint),
    inference(cnf_transformation,[],[f1034]) ).

fof(f1034,axiom,
    class_Nat_Osemiring__char__0(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Nat_Osemiring__char__0) ).

fof(f6149,plain,
    spl77_59,
    inference(avatar_split_clause,[],[f3714,f6146]) ).

fof(f6146,plain,
    ( spl77_59
  <=> class_Groups_Ozero(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_59])]) ).

fof(f3714,plain,
    class_Groups_Ozero(tc_Int_Oint),
    inference(cnf_transformation,[],[f1055]) ).

fof(f1055,axiom,
    class_Groups_Ozero(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ozero) ).

fof(f6144,plain,
    spl77_58,
    inference(avatar_split_clause,[],[f3713,f6141]) ).

fof(f6141,plain,
    ( spl77_58
  <=> class_Groups_Oone(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_58])]) ).

fof(f3713,plain,
    class_Groups_Oone(tc_Int_Oint),
    inference(cnf_transformation,[],[f1058]) ).

fof(f1058,axiom,
    class_Groups_Oone(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oone) ).

fof(f6139,plain,
    spl77_57,
    inference(avatar_split_clause,[],[f3712,f6136]) ).

fof(f6136,plain,
    ( spl77_57
  <=> class_Groups_Oab__semigroup__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_57])]) ).

fof(f3712,plain,
    class_Groups_Oab__semigroup__add(tc_Int_Oint),
    inference(cnf_transformation,[],[f1025]) ).

fof(f1025,axiom,
    class_Groups_Oab__semigroup__add(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__add) ).

fof(f6134,plain,
    spl77_56,
    inference(avatar_split_clause,[],[f3711,f6131]) ).

fof(f6131,plain,
    ( spl77_56
  <=> class_Groups_Oab__semigroup__mult(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_56])]) ).

fof(f3711,plain,
    class_Groups_Oab__semigroup__mult(tc_Int_Oint),
    inference(cnf_transformation,[],[f1023]) ).

fof(f1023,axiom,
    class_Groups_Oab__semigroup__mult(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__mult) ).

fof(f6129,plain,
    spl77_55,
    inference(avatar_split_clause,[],[f3710,f6126]) ).

fof(f6126,plain,
    ( spl77_55
  <=> class_Rings_Osemiring(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_55])]) ).

fof(f3710,plain,
    class_Rings_Osemiring(tc_Int_Oint),
    inference(cnf_transformation,[],[f1049]) ).

fof(f1049,axiom,
    class_Rings_Osemiring(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring) ).

fof(f6124,plain,
    spl77_54,
    inference(avatar_split_clause,[],[f3709,f6121]) ).

fof(f6121,plain,
    ( spl77_54
  <=> class_Rings_Ocomm__semiring(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_54])]) ).

fof(f3709,plain,
    class_Rings_Ocomm__semiring(tc_Int_Oint),
    inference(cnf_transformation,[],[f1033]) ).

fof(f1033,axiom,
    class_Rings_Ocomm__semiring(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring) ).

fof(f6119,plain,
    spl77_53,
    inference(avatar_split_clause,[],[f3708,f6116]) ).

fof(f6116,plain,
    ( spl77_53
  <=> class_Groups_Oone(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_53])]) ).

fof(f3708,plain,
    class_Groups_Oone(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1160]) ).

fof(f1160,axiom,
    class_Groups_Oone(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oone) ).

fof(f6114,plain,
    spl77_52,
    inference(avatar_split_clause,[],[f3707,f6111]) ).

fof(f6111,plain,
    ( spl77_52
  <=> class_Groups_Oab__semigroup__add(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_52])]) ).

fof(f3707,plain,
    class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1127]) ).

fof(f1127,axiom,
    class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__semigroup__add) ).

fof(f6109,plain,
    spl77_51,
    inference(avatar_split_clause,[],[f3706,f6106]) ).

fof(f6106,plain,
    ( spl77_51
  <=> class_Nat_Osemiring__char__0(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_51])]) ).

fof(f3706,plain,
    class_Nat_Osemiring__char__0(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1135]) ).

fof(f1135,axiom,
    class_Nat_Osemiring__char__0(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Nat_Osemiring__char__0) ).

fof(f6104,plain,
    spl77_50,
    inference(avatar_split_clause,[],[f3705,f6101]) ).

fof(f6101,plain,
    ( spl77_50
  <=> class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_50])]) ).

fof(f3705,plain,
    class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1118]) ).

fof(f1118,axiom,
    class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__comm__semiring) ).

fof(f6099,plain,
    spl77_49,
    inference(avatar_split_clause,[],[f3704,f6096]) ).

fof(f6096,plain,
    ( spl77_49
  <=> class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_49])]) ).

fof(f3704,plain,
    class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1106]) ).

fof(f1106,axiom,
    class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict) ).

fof(f6094,plain,
    spl77_48,
    inference(avatar_split_clause,[],[f3703,f6091]) ).

fof(f6091,plain,
    ( spl77_48
  <=> class_Groups_Ozero(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_48])]) ).

fof(f3703,plain,
    class_Groups_Ozero(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1157]) ).

fof(f1157,axiom,
    class_Groups_Ozero(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ozero) ).

fof(f6089,plain,
    spl77_47,
    inference(avatar_split_clause,[],[f3702,f6086]) ).

fof(f6086,plain,
    ( spl77_47
  <=> class_Rings_Ocomm__semiring(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_47])]) ).

fof(f3702,plain,
    class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1134]) ).

fof(f1134,axiom,
    class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring) ).

fof(f6084,plain,
    spl77_46,
    inference(avatar_split_clause,[],[f3701,f6081]) ).

fof(f6081,plain,
    ( spl77_46
  <=> class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_46])]) ).

fof(f3701,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1113]) ).

fof(f1113,axiom,
    class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add) ).

fof(f6079,plain,
    spl77_45,
    inference(avatar_split_clause,[],[f3700,f6076]) ).

fof(f6076,plain,
    ( spl77_45
  <=> class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_45])]) ).

fof(f3700,plain,
    class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1124]) ).

fof(f1124,axiom,
    class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__semigroup__mult) ).

fof(f6074,plain,
    spl77_44,
    inference(avatar_split_clause,[],[f3699,f6071]) ).

fof(f6071,plain,
    ( spl77_44
  <=> class_Rings_Osemiring(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_44])]) ).

fof(f3699,plain,
    class_Rings_Osemiring(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1151]) ).

fof(f1151,axiom,
    class_Rings_Osemiring(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring) ).

fof(f6069,plain,
    spl77_43,
    inference(avatar_split_clause,[],[f3698,f6066]) ).

fof(f6066,plain,
    ( spl77_43
  <=> class_Groups_Ogroup__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_43])]) ).

fof(f3698,plain,
    class_Groups_Ogroup__add(tc_Int_Oint),
    inference(cnf_transformation,[],[f1045]) ).

fof(f1045,axiom,
    class_Groups_Ogroup__add(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ogroup__add) ).

fof(f6064,plain,
    spl77_42,
    inference(avatar_split_clause,[],[f3697,f6061]) ).

fof(f3697,plain,
    class_Groups_Ogroup__add(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1147]) ).

fof(f1147,axiom,
    class_Groups_Ogroup__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ogroup__add) ).

fof(f6059,plain,
    spl77_41,
    inference(avatar_split_clause,[],[f3696,f6056]) ).

fof(f6056,plain,
    ( spl77_41
  <=> class_Groups_Oordered__ab__group__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_41])]) ).

fof(f3696,plain,
    class_Groups_Oordered__ab__group__add(tc_Int_Oint),
    inference(cnf_transformation,[],[f1019]) ).

fof(f1019,axiom,
    class_Groups_Oordered__ab__group__add(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__group__add) ).

fof(f6054,plain,
    spl77_40,
    inference(avatar_split_clause,[],[f3695,f6051]) ).

fof(f6051,plain,
    ( spl77_40
  <=> class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_40])]) ).

fof(f3695,plain,
    class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1120]) ).

fof(f1120,axiom,
    class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__group__add) ).

fof(f6049,plain,
    spl77_39,
    inference(avatar_split_clause,[],[f3694,f6046]) ).

fof(f6046,plain,
    ( spl77_39
  <=> class_Rings_Olinordered__ring__strict(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_39])]) ).

fof(f3694,plain,
    class_Rings_Olinordered__ring__strict(tc_Int_Oint),
    inference(cnf_transformation,[],[f1015]) ).

fof(f1015,axiom,
    class_Rings_Olinordered__ring__strict(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring__strict) ).

fof(f6044,plain,
    spl77_38,
    inference(avatar_split_clause,[],[f3693,f6041]) ).

fof(f6041,plain,
    ( spl77_38
  <=> class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_38])]) ).

fof(f3693,plain,
    class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1116]) ).

fof(f1116,axiom,
    class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__ring__strict) ).

fof(f6039,plain,
    spl77_37,
    inference(avatar_split_clause,[],[f3692,f6036]) ).

fof(f6036,plain,
    ( spl77_37
  <=> class_Divides_Osemiring__div(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_37])]) ).

fof(f3692,plain,
    class_Divides_Osemiring__div(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1079]) ).

fof(f1079,axiom,
    class_Divides_Osemiring__div(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Divides_Osemiring__div) ).

fof(f6034,plain,
    spl77_36,
    inference(avatar_split_clause,[],[f3691,f6031]) ).

fof(f6031,plain,
    ( spl77_36
  <=> class_Divides_Osemiring__div(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_36])]) ).

fof(f3691,plain,
    class_Divides_Osemiring__div(tc_Int_Oint),
    inference(cnf_transformation,[],[f1032]) ).

fof(f1032,axiom,
    class_Divides_Osemiring__div(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Divides_Osemiring__div) ).

fof(f6029,plain,
    spl77_35,
    inference(avatar_split_clause,[],[f3690,f6026]) ).

fof(f3690,plain,
    class_Rings_Oring__1(tc_Int_Oint),
    inference(cnf_transformation,[],[f1052]) ).

fof(f1052,axiom,
    class_Rings_Oring__1(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1) ).

fof(f6024,plain,
    spl77_34,
    inference(avatar_split_clause,[],[f3689,f6021]) ).

fof(f3689,plain,
    class_Rings_Oring__1(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1154]) ).

fof(f1154,axiom,
    class_Rings_Oring__1(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__1) ).

fof(f6019,plain,
    spl77_33,
    inference(avatar_split_clause,[],[f3688,f6016]) ).

fof(f6016,plain,
    ( spl77_33
  <=> class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_33])]) ).

fof(f3688,plain,
    class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
    inference(cnf_transformation,[],[f1011]) ).

fof(f1011,axiom,
    class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Olinordered__ab__group__add) ).

fof(f6014,plain,
    spl77_32,
    inference(avatar_split_clause,[],[f3687,f6011]) ).

fof(f6011,plain,
    ( spl77_32
  <=> class_Rings_Olinordered__idom(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_32])]) ).

fof(f3687,plain,
    class_Rings_Olinordered__idom(tc_Int_Oint),
    inference(cnf_transformation,[],[f1030]) ).

fof(f1030,axiom,
    class_Rings_Olinordered__idom(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__idom) ).

fof(f6009,plain,
    spl77_31,
    inference(avatar_split_clause,[],[f3686,f6006]) ).

fof(f6006,plain,
    ( spl77_31
  <=> class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_31])]) ).

fof(f3686,plain,
    class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1112]) ).

fof(f1112,axiom,
    class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Olinordered__ab__group__add) ).

fof(f6004,plain,
    spl77_30,
    inference(avatar_split_clause,[],[f3685,f6001]) ).

fof(f6001,plain,
    ( spl77_30
  <=> class_Rings_Olinordered__idom(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_30])]) ).

fof(f3685,plain,
    class_Rings_Olinordered__idom(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1132]) ).

fof(f1132,axiom,
    class_Rings_Olinordered__idom(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__idom) ).

fof(f5999,plain,
    spl77_29,
    inference(avatar_split_clause,[],[f3684,f5996]) ).

fof(f5996,plain,
    ( spl77_29
  <=> class_Rings_Oordered__ring(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_29])]) ).

fof(f3684,plain,
    class_Rings_Oordered__ring(tc_Int_Oint),
    inference(cnf_transformation,[],[f1037]) ).

fof(f1037,axiom,
    class_Rings_Oordered__ring(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring) ).

fof(f5994,plain,
    spl77_28,
    inference(avatar_split_clause,[],[f3683,f5991]) ).

fof(f5991,plain,
    ( spl77_28
  <=> class_Groups_Oab__group__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_28])]) ).

fof(f3683,plain,
    class_Groups_Oab__group__add(tc_Int_Oint),
    inference(cnf_transformation,[],[f1035]) ).

fof(f1035,axiom,
    class_Groups_Oab__group__add(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__group__add) ).

fof(f5989,plain,
    spl77_27,
    inference(avatar_split_clause,[],[f3682,f5986]) ).

fof(f5986,plain,
    ( spl77_27
  <=> class_Groups_Oab__group__add(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_27])]) ).

fof(f3682,plain,
    class_Groups_Oab__group__add(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1136]) ).

fof(f1136,axiom,
    class_Groups_Oab__group__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__group__add) ).

fof(f5984,plain,
    spl77_26,
    inference(avatar_split_clause,[],[f3681,f5981]) ).

fof(f5981,plain,
    ( spl77_26
  <=> class_Rings_Oordered__ring(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_26])]) ).

fof(f3681,plain,
    class_Rings_Oordered__ring(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1139]) ).

fof(f1139,axiom,
    class_Rings_Oordered__ring(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__ring) ).

fof(f5979,plain,
    spl77_25,
    inference(avatar_split_clause,[],[f3680,f5976]) ).

fof(f5976,plain,
    ( spl77_25
  <=> class_Rings_Oring(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_25])]) ).

fof(f3680,plain,
    class_Rings_Oring(tc_Int_Oint),
    inference(cnf_transformation,[],[f1056]) ).

fof(f1056,axiom,
    class_Rings_Oring(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring) ).

fof(f5974,plain,
    spl77_24,
    inference(avatar_split_clause,[],[f3679,f5971]) ).

fof(f5971,plain,
    ( spl77_24
  <=> class_Rings_Oring(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_24])]) ).

fof(f3679,plain,
    class_Rings_Oring(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1158]) ).

fof(f1158,axiom,
    class_Rings_Oring(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring) ).

fof(f5969,plain,
    spl77_23,
    inference(avatar_split_clause,[],[f3678,f5966]) ).

fof(f3678,plain,
    class_Lattices_Oboolean__algebra(tc_HOL_Obool),
    inference(cnf_transformation,[],[f1097]) ).

fof(f1097,axiom,
    class_Lattices_Oboolean__algebra(tc_HOL_Obool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Oboolean__algebra) ).

fof(f5964,plain,
    spl77_22,
    inference(avatar_split_clause,[],[f3677,f5961]) ).

fof(f5961,plain,
    ( spl77_22
  <=> class_Rings_Olinordered__ring(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_22])]) ).

fof(f3677,plain,
    class_Rings_Olinordered__ring(tc_Int_Oint),
    inference(cnf_transformation,[],[f1029]) ).

fof(f1029,axiom,
    class_Rings_Olinordered__ring(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring) ).

fof(f5959,plain,
    spl77_21,
    inference(avatar_split_clause,[],[f3676,f5956]) ).

fof(f5956,plain,
    ( spl77_21
  <=> class_Rings_Olinordered__ring(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_21])]) ).

fof(f3676,plain,
    class_Rings_Olinordered__ring(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1131]) ).

fof(f1131,axiom,
    class_Rings_Olinordered__ring(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__ring) ).

fof(f5954,plain,
    spl77_20,
    inference(avatar_split_clause,[],[f3675,f5951]) ).

fof(f5951,plain,
    ( spl77_20
  <=> c_SEQ_Osubseq(v_f____) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_20])]) ).

fof(f3675,plain,
    c_SEQ_Osubseq(v_f____),
    inference(cnf_transformation,[],[f4]) ).

fof(f4,axiom,
    c_SEQ_Osubseq(v_f____),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_f_I1_J) ).

fof(f5949,plain,
    spl77_19,
    inference(avatar_split_clause,[],[f3674,f5946]) ).

fof(f5946,plain,
    ( spl77_19
  <=> c_SEQ_Osubseq(v_ga____) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_19])]) ).

fof(f3674,plain,
    c_SEQ_Osubseq(v_ga____),
    inference(cnf_transformation,[],[f5]) ).

fof(f5,axiom,
    c_SEQ_Osubseq(v_ga____),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_g_I1_J) ).

fof(f5944,plain,
    spl77_18,
    inference(avatar_split_clause,[],[f3673,f5941]) ).

fof(f5941,plain,
    ( spl77_18
  <=> class_Int_Oring__char__0(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_18])]) ).

fof(f3673,plain,
    class_Int_Oring__char__0(tc_Int_Oint),
    inference(cnf_transformation,[],[f1048]) ).

fof(f1048,axiom,
    class_Int_Oring__char__0(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Int_Oring__char__0) ).

fof(f5939,plain,
    spl77_17,
    inference(avatar_split_clause,[],[f3672,f5936]) ).

fof(f5936,plain,
    ( spl77_17
  <=> class_Rings_Ocomm__ring__1(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_17])]) ).

fof(f3672,plain,
    class_Rings_Ocomm__ring__1(tc_Int_Oint),
    inference(cnf_transformation,[],[f1041]) ).

fof(f1041,axiom,
    class_Rings_Ocomm__ring__1(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring__1) ).

fof(f5934,plain,
    spl77_16,
    inference(avatar_split_clause,[],[f3671,f5931]) ).

fof(f5931,plain,
    ( spl77_16
  <=> class_Rings_Ocomm__ring__1(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_16])]) ).

fof(f3671,plain,
    class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1143]) ).

fof(f1143,axiom,
    class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__ring__1) ).

fof(f5929,plain,
    spl77_15,
    inference(avatar_split_clause,[],[f3670,f5926]) ).

fof(f5926,plain,
    ( spl77_15
  <=> class_Int_Oring__char__0(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_15])]) ).

fof(f3670,plain,
    class_Int_Oring__char__0(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1150]) ).

fof(f1150,axiom,
    class_Int_Oring__char__0(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Int_Oring__char__0) ).

fof(f5924,plain,
    spl77_14,
    inference(avatar_split_clause,[],[f3669,f5921]) ).

fof(f5921,plain,
    ( spl77_14
  <=> class_Rings_Oidom(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_14])]) ).

fof(f3669,plain,
    class_Rings_Oidom(tc_Int_Oint),
    inference(cnf_transformation,[],[f1057]) ).

fof(f1057,axiom,
    class_Rings_Oidom(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oidom) ).

fof(f5919,plain,
    spl77_13,
    inference(avatar_split_clause,[],[f3668,f5916]) ).

fof(f5916,plain,
    ( spl77_13
  <=> class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_13])]) ).

fof(f3668,plain,
    class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
    inference(cnf_transformation,[],[f1013]) ).

fof(f1013,axiom,
    class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1__no__zero__divisors) ).

fof(f5914,plain,
    spl77_12,
    inference(avatar_split_clause,[],[f3667,f5911]) ).

fof(f5911,plain,
    ( spl77_12
  <=> class_Rings_Oidom(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_12])]) ).

fof(f3667,plain,
    class_Rings_Oidom(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1159]) ).

fof(f1159,axiom,
    class_Rings_Oidom(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oidom) ).

fof(f5909,plain,
    spl77_11,
    inference(avatar_split_clause,[],[f3666,f5906]) ).

fof(f5906,plain,
    ( spl77_11
  <=> class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_11])]) ).

fof(f3666,plain,
    class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1114]) ).

fof(f1114,axiom,
    class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors) ).

fof(f5904,plain,
    spl77_10,
    inference(avatar_split_clause,[],[f3665,f5901]) ).

fof(f5901,plain,
    ( spl77_10
  <=> class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_10])]) ).

fof(f3665,plain,
    class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
    inference(cnf_transformation,[],[f1007]) ).

fof(f1007,axiom,
    class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1__strict) ).

fof(f5899,plain,
    spl77_9,
    inference(avatar_split_clause,[],[f3664,f5896]) ).

fof(f5896,plain,
    ( spl77_9
  <=> class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_9])]) ).

fof(f3664,plain,
    class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
    inference(cnf_transformation,[],[f1016]) ).

fof(f1016,axiom,
    class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__no__zero__divisors) ).

fof(f5894,plain,
    spl77_8,
    inference(avatar_split_clause,[],[f3663,f5891]) ).

fof(f5891,plain,
    ( spl77_8
  <=> class_Rings_Olinordered__semiring__1(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_8])]) ).

fof(f3663,plain,
    class_Rings_Olinordered__semiring__1(tc_Int_Oint),
    inference(cnf_transformation,[],[f1018]) ).

fof(f1018,axiom,
    class_Rings_Olinordered__semiring__1(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1) ).

fof(f5889,plain,
    spl77_7,
    inference(avatar_split_clause,[],[f3662,f5886]) ).

fof(f5886,plain,
    ( spl77_7
  <=> class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_7])]) ).

fof(f3662,plain,
    class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1107]) ).

fof(f1107,axiom,
    class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict) ).

fof(f5884,plain,
    spl77_6,
    inference(avatar_split_clause,[],[f3661,f5881]) ).

fof(f5881,plain,
    ( spl77_6
  <=> class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_6])]) ).

fof(f3661,plain,
    class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1119]) ).

fof(f1119,axiom,
    class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__1) ).

fof(f5879,plain,
    spl77_5,
    inference(avatar_split_clause,[],[f3660,f5876]) ).

fof(f5876,plain,
    ( spl77_5
  <=> class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_5])]) ).

fof(f3660,plain,
    class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1117]) ).

fof(f1117,axiom,
    class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__no__zero__divisors) ).

fof(f5874,plain,
    spl77_4,
    inference(avatar_split_clause,[],[f3659,f5871]) ).

fof(f5871,plain,
    ( spl77_4
  <=> class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_4])]) ).

fof(f3659,plain,
    class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1110]) ).

fof(f1110,axiom,
    class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).

fof(f5869,plain,
    spl77_3,
    inference(avatar_split_clause,[],[f3658,f5866]) ).

fof(f5866,plain,
    ( spl77_3
  <=> class_SEQ_Ocomplete__space(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_3])]) ).

fof(f3658,plain,
    class_SEQ_Ocomplete__space(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1137]) ).

fof(f1137,axiom,
    class_SEQ_Ocomplete__space(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__SEQ_Ocomplete__space) ).

fof(f5864,plain,
    spl77_2,
    inference(avatar_split_clause,[],[f3657,f5861]) ).

fof(f5861,plain,
    ( spl77_2
  <=> class_RealVector_Ometric__space(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl77_2])]) ).

fof(f3657,plain,
    class_RealVector_Ometric__space(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1125]) ).

fof(f1125,axiom,
    class_RealVector_Ometric__space(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Ometric__space) ).

fof(f5859,plain,
    spl77_1,
    inference(avatar_split_clause,[],[f3655,f5856]) ).

fof(f3655,plain,
    c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK23,sK24),
    inference(cnf_transformation,[],[f3166]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : SWW209+1 : TPTP v8.1.2. Released v5.2.0.
% 0.11/0.13  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.35  % Computer : n010.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Tue Apr 30 02:46:20 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.13/0.35  % (32258)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.43  % (32282)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.20/0.43  % (32283)WARNING: value z3 for option sas not known
% 0.20/0.44  % (32281)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.20/0.44  % (32284)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.20/0.44  % (32283)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)
% 0.20/0.44  % (32285)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)
% 0.20/0.44  % (32286)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.20/0.44  % (32287)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)
% 0.20/0.58  % (32285)First to succeed.
% 1.38/0.60  % (32285)Refutation found. Thanks to Tanya!
% 1.38/0.60  % SZS status Theorem for theBenchmark
% 1.38/0.60  % SZS output start Proof for theBenchmark
% See solution above
% 1.46/0.61  % (32285)------------------------------
% 1.46/0.61  % (32285)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 1.46/0.61  % (32285)Termination reason: Refutation
% 1.46/0.61  
% 1.46/0.61  % (32285)Memory used [KB]: 5453
% 1.46/0.61  % (32285)Time elapsed: 0.163 s
% 1.46/0.61  % (32285)Instructions burned: 387 (million)
% 1.46/0.61  % (32285)------------------------------
% 1.46/0.61  % (32285)------------------------------
% 1.46/0.61  % (32258)Success in time 0.252 s
%------------------------------------------------------------------------------