%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SWW185+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s

% Computer : n011.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Aug 31 19:18:34 EDT 2022

% Result   : Theorem 51.23s 6.91s
% Output   : Refutation 51.90s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :  935
% Syntax   : Number of formulae    : 4119 ( 638 unt;   0 def)
%            Number of atoms       : 11096 (2257 equ)
%            Maximal formula atoms :   26 (   2 avg)
%            Number of connectives : 12130 (5153   ~;5378   |; 386   &)
%                                         ( 758 <=>; 455  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   4 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :  644 ( 642 usr; 577 prp; 0-3 aty)
%            Number of functors    :   47 (  47 usr;  10 con; 0-3 aty)
%            Number of variables   : 5421 (5354   !;  67   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f27573,plain,
    $false,
    inference(avatar_smt_refutation,[],[f6211,f6216,f6221,f6226,f6231,f6236,f6241,f6246,f6251,f6256,f6261,f6266,f6275,f6280,f6291,f6296,f6304,f6311,f6316,f6323,f6328,f6333,f6338,f6343,f6354,f6359,f6364,f6369,f6375,f6380,f6385,f6390,f6396,f6402,f6407,f6412,f6417,f6422,f6427,f6432,f6438,f6443,f6448,f6453,f6458,f6463,f6468,f6473,f6478,f6483,f6488,f6493,f6498,f6503,f6509,f6519,f6524,f6530,f6537,f6545,f6552,f6559,f6564,f6569,f6574,f6582,f6588,f6597,f6623,f6639,f6650,f6655,f6662,f6667,f6673,f6679,f6684,f6689,f6694,f6699,f6708,f6713,f6718,f6724,f6732,f6737,f6742,f6746,f6751,f6756,f6767,f6772,f6777,f6782,f6787,f6795,f6800,f6806,f6811,f6818,f6826,f6831,f6837,f6842,f6853,f6860,f6866,f6871,f6877,f6886,f6891,f6896,f6901,f6906,f6911,f6921,f6926,f6931,f6939,f6944,f6950,f6953,f6959,f6964,f6969,f6984,f6990,f6995,f7006,f7011,f7018,f7023,f7110,f7180,f7181,f7265,f7323,f7679,f7823,f7824,f7945,f7978,f9147,f9155,f9167,f9195,f9231,f9265,f9285,f9297,f9309,f9329,f9337,f9353,f9364,f9383,f9400,f9413,f9443,f9459,f9468,f9479,f9484,f9512,f9516,f9537,f9548,f9555,f9569,f9579,f9582,f9673,f9680,f9692,f9700,f9705,f9728,f9775,f9802,f9809,f9823,f9833,f9857,f9898,f9903,f9917,f9941,f9947,f9954,f9972,f9975,f9981,f9999,f10017,f10025,f10050,f10082,f10090,f10093,f10112,f10147,f10159,f10168,f10199,f10230,f10244,f10246,f10256,f10266,f10281,f10296,f10317,f10360,f10388,f10410,f10429,f10446,f10485,f10505,f10525,f10536,f10545,f10558,f10576,f10587,f10595,f10613,f10701,f10705,f10731,f10744,f10757,f10760,f10773,f10803,f10832,f10841,f10857,f10913,f10916,f10917,f11043,f11076,f11077,f11078,f11079,f11098,f11111,f11116,f11121,f11146,f11147,f11155,f11218,f11234,f11239,f11580,f11601,f11655,f11789,f11925,f11926,f11981,f11986,f12040,f12041,f12160,f12164,f12337,f12341,f12349,f12353,f12357,f12454,f12459,f12469,f12475,f12480,f12491,f12577,f12582,f12596,f12612,f12614,f12623,f12639,f12652,f12688,f12708,f12718,f12821,f12825,f12830,f12834,f12842,f12854,f12865,f12869,f12874,f12878,f12985,f12988,f12999,f13002,f13015,f13016,f13026,f13030,f13034,f13038,f13042,f13052,f13056,f13060,f13064,f13068,f13079,f13082,f13129,f13347,f13352,f13372,f13377,f13391,f13417,f13422,f13432,f13436,f13466,f13467,f13475,f13480,f13677,f13678,f13714,f13718,f13770,f13775,f13780,f13928,f13932,f13936,f14052,f14056,f14057,f14065,f14066,f14075,f14080,f14095,f14099,f14103,f14104,f14105,f14109,f14191,f14195,f14225,f14238,f14292,f14296,f14323,f14325,f14370,f14374,f14378,f14805,f14814,f14819,f14826,f15060,f15064,f15147,f15323,f15327,f15331,f15332,f15336,f15352,f15356,f15360,f15400,f15464,f15470,f15490,f15491,f15510,f15523,f15528,f15533,f15893,f15899,f15905,f15916,f15921,f15926,f15963,f16034,f16039,f16045,f16062,f16138,f16141,f16154,f16215,f16231,f16235,f16239,f16437,f16441,f16446,f16451,f16453,f16511,f16516,f16530,f16535,f16539,f16543,f16546,f17028,f17033,f17369,f17370,f17577,f17581,f17662,f17758,f17759,f18022,f18028,f18130,f18135,f18137,f18142,f18144,f18153,f18159,f18161,f18166,f18171,f18176,f18181,f18186,f18191,f18193,f18194,f18199,f18204,f18249,f18290,f18291,f18293,f18294,f18545,f18637,f18642,f18644,f18645,f18658,f18665,f18668,f18669,f18756,f18823,f18918,f18923,f18930,f18976,f20036,f20040,f20041,f20072,f20076,f20081,f20106,f20110,f20115,f20147,f20196,f20339,f20344,f20349,f20353,f20355,f20394,f20396,f20397,f20465,f20466,f20479,f20480,f20481,f20584,f20585,f20632,f20650,f20660,f20665,f20670,f20745,f20750,f20755,f20756,f20757,f20758,f20759,f20854,f20945,f20950,f20957,f20964,f20969,f20970,f21173,f21185,f21199,f21204,f21291,f21302,f21334,f21361,f21367,f21383,f21385,f21418,f21419,f21420,f21421,f21422,f21423,f21424,f21425,f21426,f21427,f21453,f21454,f21460,f21464,f21469,f21474,f21496,f21497,f21498,f21499,f21500,f21501,f21502,f21503,f21504,f21505,f21506,f21779,f21788,f21795,f21796,f21797,f21798,f21799,f21823,f21824,f21929,f21996,f22014,f22015,f22017,f22019,f22021,f22024,f22025,f22027,f22028,f22030,f22038,f22041,f22056,f22062,f22066,f22069,f22078,f22080,f22420,f22424,f22429,f23142,f23147,f23180,f23182,f23246,f23263,f24021,f24107,f24114,f24118,f24123,f24127,f24155,f24161,f24208,f24213,f24219,f24224,f24228,f24470,f24479,f24480,f24586,f24645,f24646,f24861,f24866,f24916,f24924,f24983,f25036,f25041,f25071,f25090,f25098,f25135,f25142,f25150,f25202,f25210,f25215,f25249,f25256,f25260,f25282,f25287,f25292,f25298,f25303,f25308,f25309,f25314,f25380,f25567,f25568,f25569,f25570,f25571,f25572,f25573,f25574,f25575,f25576,f25577,f25578,f25583,f25584,f25585,f25586,f25587,f25592,f25593,f25594,f25595,f25596,f25597,f25598,f25599,f25600,f25601,f25602,f25603,f25604,f25605,f25606,f25607,f25608,f25609,f25610,f25611,f25612,f25613,f25644,f25827,f25854,f25881,f25887,f25901,f26075,f26127,f26314,f26323,f26451,f26452,f26453,f26454,f26455,f26456,f26457,f26458,f26459,f26460,f26461,f26462,f26463,f26464,f26465,f26567,f26582,f26597,f26602,f26616,f26796,f26813,f26819,f27082,f27084,f27089,f27090,f27104,f27119,f27232,f27237,f27242,f27247,f27292,f27301,f27305,f27336,f27340,f27422,f27462,f27469,f27475,f27481,f27487,f27492,f27499,f27514,f27523,f27531,f27535,f27544,f27571,f27572]) ).

fof(f27572,plain,
    ( spl24_561
    | ~ spl24_13
    | ~ spl24_92
    | ~ spl24_562 ),
    inference(avatar_split_clause,[],[f27570,f27466,f6764,f6268,f27459]) ).

fof(f27459,plain,
    ( spl24_561
  <=> v_p = c_Polynomial_OpCons(t_a,v_a,v_p) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_561])]) ).

fof(f6268,plain,
    ( spl24_13
  <=> v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_13])]) ).

fof(f6764,plain,
    ( spl24_92
  <=> class_Rings_Ocomm__semiring__0(t_a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_92])]) ).

fof(f27466,plain,
    ( spl24_562
  <=> v_p = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,v_a,v_p),v_h) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_562])]) ).

fof(f27570,plain,
    ( v_p = c_Polynomial_OpCons(t_a,v_a,v_p)
    | ~ spl24_13
    | ~ spl24_92
    | ~ spl24_562 ),
    inference(superposition,[],[f27468,f27429]) ).

fof(f27429,plain,
    ( ! [X8,X7] : c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X7,v_p),X8) = c_Polynomial_OpCons(t_a,X7,v_p)
    | ~ spl24_13
    | ~ spl24_92 ),
    inference(backward_demodulation,[],[f7037,f6270]) ).

fof(f6270,plain,
    ( v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
    | ~ spl24_13 ),
    inference(avatar_component_clause,[],[f6268]) ).

fof(f7037,plain,
    ( ! [X8,X7] : c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X7,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),X8) = c_Polynomial_OpCons(t_a,X7,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))
    | ~ spl24_92 ),
    inference(resolution,[],[f4409,f6766]) ).

fof(f6766,plain,
    ( class_Rings_Ocomm__semiring__0(t_a)
    | ~ spl24_92 ),
    inference(avatar_component_clause,[],[f6764]) ).

fof(f4409,plain,
    ! [X2,X0,X1] :
      ( ~ class_Rings_Ocomm__semiring__0(X2)
      | c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,c_Polynomial_OpCons(X2,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))),X0) = c_Polynomial_OpCons(X2,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))) ),
    inference(cnf_transformation,[],[f2767]) ).

fof(f2767,plain,
    ! [X0,X1,X2] :
      ( ~ class_Rings_Ocomm__semiring__0(X2)
      | c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,c_Polynomial_OpCons(X2,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))),X0) = c_Polynomial_OpCons(X2,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))) ),
    inference(ennf_transformation,[],[f2213]) ).

fof(f2213,plain,
    ! [X2,X0,X1] :
      ( class_Rings_Ocomm__semiring__0(X2)
     => c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,c_Polynomial_OpCons(X2,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))),X0) = c_Polynomial_OpCons(X2,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))) ),
    inference(rectify,[],[f3]) ).

fof(f3,axiom,
    ! [X3,X5,X4] :
      ( class_Rings_Ocomm__semiring__0(X4)
     => c_Polynomial_OpCons(X4,X5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X4,c_Polynomial_OpCons(X4,X5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))),X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_offset__poly__single) ).

fof(f27468,plain,
    ( v_p = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,v_a,v_p),v_h)
    | ~ spl24_562 ),
    inference(avatar_component_clause,[],[f27466]) ).

fof(f27571,plain,
    ( spl24_561
    | ~ spl24_13
    | ~ spl24_92
    | ~ spl24_562 ),
    inference(avatar_split_clause,[],[f27567,f27466,f6764,f6268,f27459]) ).

fof(f27567,plain,
    ( v_p = c_Polynomial_OpCons(t_a,v_a,v_p)
    | ~ spl24_13
    | ~ spl24_92
    | ~ spl24_562 ),
    inference(superposition,[],[f27429,f27468]) ).

fof(f27544,plain,
    ( ~ spl24_575
    | ~ spl24_576
    | ~ spl24_13 ),
    inference(avatar_split_clause,[],[f27503,f6268,f27541,f27537]) ).

fof(f27537,plain,
    ( spl24_575
  <=> class_Rings_Olinordered__idom(t_a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_575])]) ).

fof(f27541,plain,
    ( spl24_576
  <=> c_Polynomial_Opos__poly(t_a,v_p) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_576])]) ).

fof(f27503,plain,
    ( ~ c_Polynomial_Opos__poly(t_a,v_p)
    | ~ class_Rings_Olinordered__idom(t_a)
    | ~ spl24_13 ),
    inference(superposition,[],[f4634,f6270]) ).

fof(f4634,plain,
    ! [X0] :
      ( ~ c_Polynomial_Opos__poly(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))
      | ~ class_Rings_Olinordered__idom(X0) ),
    inference(cnf_transformation,[],[f2441]) ).

fof(f2441,plain,
    ! [X0] :
      ( ~ class_Rings_Olinordered__idom(X0)
      | ~ c_Polynomial_Opos__poly(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) ),
    inference(ennf_transformation,[],[f1666]) ).

fof(f1666,plain,
    ! [X0] :
      ( class_Rings_Olinordered__idom(X0)
     => ~ c_Polynomial_Opos__poly(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) ),
    inference(rectify,[],[f791]) ).

fof(f791,axiom,
    ! [X4] :
      ( class_Rings_Olinordered__idom(X4)
     => ~ c_Polynomial_Opos__poly(X4,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__pos__poly__0) ).

fof(f27535,plain,
    ( ~ spl24_568
    | spl24_574
    | ~ spl24_13 ),
    inference(avatar_split_clause,[],[f27506,f6268,f27533,f27508]) ).

fof(f27508,plain,
    ( spl24_568
  <=> class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(t_a)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_568])]) ).

fof(f27533,plain,
    ( spl24_574
  <=> ! [X3] : c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(t_a),X3,v_p) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_574])]) ).

fof(f27506,plain,
    ( ! [X3] :
        ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(t_a),X3,v_p)
        | ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(t_a)) )
    | ~ spl24_13 ),
    inference(superposition,[],[f5705,f6270]) ).

fof(f5705,plain,
    ! [X0,X1] :
      ( c_Rings_Odvd__class_Odvd(X0,X1,c_Groups_Ozero__class_Ozero(X0))
      | ~ class_Rings_Ocomm__semiring__1(X0) ),
    inference(cnf_transformation,[],[f4285]) ).

fof(f4285,plain,
    ! [X0,X1] :
      ( c_Rings_Odvd__class_Odvd(X0,X1,c_Groups_Ozero__class_Ozero(X0))
      | ~ class_Rings_Ocomm__semiring__1(X0) ),
    inference(rectify,[],[f3325]) ).

fof(f3325,plain,
    ! [X1,X0] :
      ( c_Rings_Odvd__class_Odvd(X1,X0,c_Groups_Ozero__class_Ozero(X1))
      | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(ennf_transformation,[],[f1438]) ).

fof(f1438,plain,
    ! [X0,X1] :
      ( class_Rings_Ocomm__semiring__1(X1)
     => c_Rings_Odvd__class_Odvd(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(rectify,[],[f382]) ).

fof(f382,axiom,
    ! [X5,X4] :
      ( class_Rings_Ocomm__semiring__1(X4)
     => c_Rings_Odvd__class_Odvd(X4,X5,c_Groups_Ozero__class_Ozero(X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__0__right) ).

fof(f27531,plain,
    ( spl24_572
    | ~ spl24_573
    | ~ spl24_13 ),
    inference(avatar_split_clause,[],[f27502,f6268,f27528,f27525]) ).

fof(f27525,plain,
    ( spl24_572
  <=> ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(t_a) != hAPP(c_Polynomial_Opoly(t_a,X1),c_Groups_Ouminus__class_Ouminus(t_a,X0))
        | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(t_a),c_Polynomial_OpCons(t_a,X0,c_Polynomial_OpCons(t_a,c_Groups_Oone__class_Oone(t_a),v_p)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_572])]) ).

fof(f27528,plain,
    ( spl24_573
  <=> class_Rings_Oidom(t_a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_573])]) ).

fof(f27502,plain,
    ( ! [X0,X1] :
        ( ~ class_Rings_Oidom(t_a)
        | c_Groups_Ozero__class_Ozero(t_a) != hAPP(c_Polynomial_Opoly(t_a,X1),c_Groups_Ouminus__class_Ouminus(t_a,X0))
        | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(t_a),c_Polynomial_OpCons(t_a,X0,c_Polynomial_OpCons(t_a,c_Groups_Oone__class_Oone(t_a),v_p)),X1) )
    | ~ spl24_13 ),
    inference(superposition,[],[f4941,f6270]) ).

fof(f4941,plain,
    ! [X2,X0,X1] :
      ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_OpCons(X1,X0,c_Polynomial_OpCons(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))),X2)
      | c_Groups_Ozero__class_Ozero(X1) != hAPP(c_Polynomial_Opoly(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X0))
      | ~ class_Rings_Oidom(X1) ),
    inference(cnf_transformation,[],[f3810]) ).

fof(f3810,plain,
    ! [X0,X1,X2] :
      ( ( ( c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Polynomial_Opoly(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X0))
          | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_OpCons(X1,X0,c_Polynomial_OpCons(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))),X2) )
        & ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_OpCons(X1,X0,c_Polynomial_OpCons(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))),X2)
          | c_Groups_Ozero__class_Ozero(X1) != hAPP(c_Polynomial_Opoly(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X0)) ) )
      | ~ class_Rings_Oidom(X1) ),
    inference(rectify,[],[f3809]) ).

fof(f3809,plain,
    ! [X2,X0,X1] :
      ( ( ( c_Groups_Ozero__class_Ozero(X0) = hAPP(c_Polynomial_Opoly(X0,X1),c_Groups_Ouminus__class_Ouminus(X0,X2))
          | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X0),c_Polynomial_OpCons(X0,X2,c_Polynomial_OpCons(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))),X1) )
        & ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X0),c_Polynomial_OpCons(X0,X2,c_Polynomial_OpCons(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))),X1)
          | c_Groups_Ozero__class_Ozero(X0) != hAPP(c_Polynomial_Opoly(X0,X1),c_Groups_Ouminus__class_Ouminus(X0,X2)) ) )
      | ~ class_Rings_Oidom(X0) ),
    inference(nnf_transformation,[],[f3038]) ).

fof(f3038,plain,
    ! [X2,X0,X1] :
      ( ( c_Groups_Ozero__class_Ozero(X0) = hAPP(c_Polynomial_Opoly(X0,X1),c_Groups_Ouminus__class_Ouminus(X0,X2))
      <=> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X0),c_Polynomial_OpCons(X0,X2,c_Polynomial_OpCons(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))),X1) )
      | ~ class_Rings_Oidom(X0) ),
    inference(ennf_transformation,[],[f2079]) ).

fof(f2079,plain,
    ! [X2,X1,X0] :
      ( class_Rings_Oidom(X0)
     => ( c_Groups_Ozero__class_Ozero(X0) = hAPP(c_Polynomial_Opoly(X0,X1),c_Groups_Ouminus__class_Ouminus(X0,X2))
      <=> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X0),c_Polynomial_OpCons(X0,X2,c_Polynomial_OpCons(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))),X1) ) ),
    inference(rectify,[],[f377]) ).

fof(f377,axiom,
    ! [X8,X6,X30] :
      ( class_Rings_Oidom(X8)
     => ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X8),c_Polynomial_OpCons(X8,X30,c_Polynomial_OpCons(X8,c_Groups_Oone__class_Oone(X8),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)))),X6)
      <=> c_Groups_Ozero__class_Ozero(X8) = hAPP(c_Polynomial_Opoly(X8,X6),c_Groups_Ouminus__class_Ouminus(X8,X30)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__iff__poly__eq__0) ).

fof(f27523,plain,
    ( ~ spl24_570
    | ~ spl24_571
    | ~ spl24_13 ),
    inference(avatar_split_clause,[],[f27504,f6268,f27520,f27516]) ).

fof(f27516,plain,
    ( spl24_570
  <=> class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(t_a)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_570])]) ).

fof(f27520,plain,
    ( spl24_571
  <=> c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(t_a),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(t_a)),v_p) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_571])]) ).

fof(f27504,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(t_a),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(t_a)),v_p)
    | ~ class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(t_a))
    | ~ spl24_13 ),
    inference(superposition,[],[f4532,f6270]) ).

fof(f4532,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,[],[f3410]) ).

fof(f3410,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(ennf_transformation,[],[f1602]) ).

fof(f1602,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,[],[f545]) ).

fof(f545,axiom,
    ! [X4] :
      ( class_Rings_Olinordered__semidom(X4)
     => ~ c_Orderings_Oord__class_Oless(X4,c_Groups_Oone__class_Oone(X4),c_Groups_Ozero__class_Ozero(X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__one__less__zero) ).

fof(f27514,plain,
    ( ~ spl24_568
    | spl24_569
    | ~ spl24_13 ),
    inference(avatar_split_clause,[],[f27505,f6268,f27512,f27508]) ).

fof(f27512,plain,
    ( spl24_569
  <=> ! [X2] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(t_a),v_p,X2)
        | v_p = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_569])]) ).

fof(f27505,plain,
    ( ! [X2] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(t_a),v_p,X2)
        | v_p = X2
        | ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(t_a)) )
    | ~ spl24_13 ),
    inference(superposition,[],[f4832,f6270]) ).

fof(f4832,plain,
    ! [X0,X1] :
      ( ~ c_Rings_Odvd__class_Odvd(X0,c_Groups_Ozero__class_Ozero(X0),X1)
      | c_Groups_Ozero__class_Ozero(X0) = X1
      | ~ class_Rings_Ocomm__semiring__1(X0) ),
    inference(cnf_transformation,[],[f3735]) ).

fof(f3735,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X0) = X1
      | ~ class_Rings_Ocomm__semiring__1(X0)
      | ~ c_Rings_Odvd__class_Odvd(X0,c_Groups_Ozero__class_Ozero(X0),X1) ),
    inference(rectify,[],[f3389]) ).

fof(f3389,plain,
    ! [X1,X0] :
      ( c_Groups_Ozero__class_Ozero(X1) = X0
      | ~ class_Rings_Ocomm__semiring__1(X1)
      | ~ c_Rings_Odvd__class_Odvd(X1,c_Groups_Ozero__class_Ozero(X1),X0) ),
    inference(flattening,[],[f3388]) ).

fof(f3388,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X1) = X0
      | ~ c_Rings_Odvd__class_Odvd(X1,c_Groups_Ozero__class_Ozero(X1),X0)
      | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(ennf_transformation,[],[f1601]) ).

fof(f1601,plain,
    ! [X0,X1] :
      ( class_Rings_Ocomm__semiring__1(X1)
     => ( c_Rings_Odvd__class_Odvd(X1,c_Groups_Ozero__class_Ozero(X1),X0)
       => c_Groups_Ozero__class_Ozero(X1) = X0 ) ),
    inference(rectify,[],[f410]) ).

fof(f410,axiom,
    ! [X5,X4] :
      ( class_Rings_Ocomm__semiring__1(X4)
     => ( c_Rings_Odvd__class_Odvd(X4,c_Groups_Ozero__class_Ozero(X4),X5)
       => c_Groups_Ozero__class_Ozero(X4) = X5 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__0__left) ).

fof(f27499,plain,
    ( ~ spl24_567
    | ~ spl24_13
    | ~ spl24_92
    | spl24_213 ),
    inference(avatar_split_clause,[],[f27494,f10443,f6764,f6268,f27496]) ).

fof(f27496,plain,
    ( spl24_567
  <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v_p ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_567])]) ).

fof(f10443,plain,
    ( spl24_213
  <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_213])]) ).

fof(f27494,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != v_p
    | ~ spl24_13
    | ~ spl24_92
    | spl24_213 ),
    inference(backward_demodulation,[],[f10445,f27426]) ).

fof(f27426,plain,
    ( ! [X4] : v_p = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,X4)
    | ~ spl24_13
    | ~ spl24_92 ),
    inference(backward_demodulation,[],[f6999,f6270]) ).

fof(f6999,plain,
    ( ! [X4] : c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),X4)
    | ~ spl24_92 ),
    inference(resolution,[],[f5669,f6766]) ).

fof(f5669,plain,
    ! [X0,X1] :
      ( ~ class_Rings_Ocomm__semiring__0(X1)
      | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0) ),
    inference(cnf_transformation,[],[f2877]) ).

fof(f2877,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0)
      | ~ class_Rings_Ocomm__semiring__0(X1) ),
    inference(ennf_transformation,[],[f2002]) ).

fof(f2002,plain,
    ! [X1,X0] :
      ( class_Rings_Ocomm__semiring__0(X1)
     => c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0) ),
    inference(rectify,[],[f2]) ).

fof(f2,axiom,
    ! [X3,X4] :
      ( class_Rings_Ocomm__semiring__0(X4)
     => c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X4,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_offset__poly__0) ).

fof(f10445,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)
    | spl24_213 ),
    inference(avatar_component_clause,[],[f10443]) ).

fof(f27492,plain,
    ( spl24_566
    | ~ spl24_13
    | ~ spl24_371 ),
    inference(avatar_split_clause,[],[f27449,f15923,f6268,f27489]) ).

fof(f27489,plain,
    ( spl24_566
  <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(t_a,v_p) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_566])]) ).

fof(f15923,plain,
    ( spl24_371
  <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_371])]) ).

fof(f27449,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(t_a,v_p)
    | ~ spl24_13
    | ~ spl24_371 ),
    inference(backward_demodulation,[],[f15925,f6270]) ).

fof(f15925,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))
    | ~ spl24_371 ),
    inference(avatar_component_clause,[],[f15923]) ).

fof(f27487,plain,
    ( spl24_565
    | ~ spl24_13
    | ~ spl24_363 ),
    inference(avatar_split_clause,[],[f27448,f15520,f6268,f27484]) ).

fof(f27484,plain,
    ( spl24_565
  <=> v_p = c_Polynomial_OpCons(t_a,c_Groups_Ozero__class_Ozero(t_a),v_p) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_565])]) ).

fof(f15520,plain,
    ( spl24_363
  <=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = c_Polynomial_OpCons(t_a,c_Groups_Ozero__class_Ozero(t_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_363])]) ).

fof(f27448,plain,
    ( v_p = c_Polynomial_OpCons(t_a,c_Groups_Ozero__class_Ozero(t_a),v_p)
    | ~ spl24_13
    | ~ spl24_363 ),
    inference(backward_demodulation,[],[f15522,f6270]) ).

fof(f15522,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = c_Polynomial_OpCons(t_a,c_Groups_Ozero__class_Ozero(t_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))
    | ~ spl24_363 ),
    inference(avatar_component_clause,[],[f15520]) ).

fof(f27481,plain,
    ( spl24_564
    | ~ spl24_13
    | ~ spl24_14 ),
    inference(avatar_split_clause,[],[f27423,f6272,f6268,f27478]) ).

fof(f27478,plain,
    ( spl24_564
  <=> v_p = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_564])]) ).

fof(f6272,plain,
    ( spl24_14
  <=> c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_14])]) ).

fof(f27423,plain,
    ( v_p = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)
    | ~ spl24_13
    | ~ spl24_14 ),
    inference(backward_demodulation,[],[f6273,f6270]) ).

fof(f6273,plain,
    ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
    | ~ spl24_14 ),
    inference(avatar_component_clause,[],[f6272]) ).

fof(f27475,plain,
    ( spl24_563
    | ~ spl24_13
    | ~ spl24_284 ),
    inference(avatar_split_clause,[],[f27445,f12982,f6268,f27472]) ).

fof(f27472,plain,
    ( spl24_563
  <=> v_p = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),v_p,v_p) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_563])]) ).

fof(f12982,plain,
    ( spl24_284
  <=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_284])]) ).

fof(f27445,plain,
    ( v_p = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),v_p,v_p)
    | ~ spl24_13
    | ~ spl24_284 ),
    inference(backward_demodulation,[],[f12984,f6270]) ).

fof(f12984,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))
    | ~ spl24_284 ),
    inference(avatar_component_clause,[],[f12982]) ).

fof(f27469,plain,
    ( spl24_562
    | ~ spl24_13
    | ~ spl24_128 ),
    inference(avatar_split_clause,[],[f27425,f6992,f6268,f27466]) ).

fof(f6992,plain,
    ( spl24_128
  <=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,v_a,v_p),v_h) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_128])]) ).

fof(f27425,plain,
    ( v_p = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,v_a,v_p),v_h)
    | ~ spl24_13
    | ~ spl24_128 ),
    inference(backward_demodulation,[],[f6994,f6270]) ).

fof(f6994,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,v_a,v_p),v_h)
    | ~ spl24_128 ),
    inference(avatar_component_clause,[],[f6992]) ).

fof(f27462,plain,
    ( ~ spl24_561
    | ~ spl24_13
    | spl24_85 ),
    inference(avatar_split_clause,[],[f27424,f6721,f6268,f27459]) ).

fof(f6721,plain,
    ( spl24_85
  <=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = c_Polynomial_OpCons(t_a,v_a,v_p) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_85])]) ).

fof(f27424,plain,
    ( v_p != c_Polynomial_OpCons(t_a,v_a,v_p)
    | ~ spl24_13
    | spl24_85 ),
    inference(backward_demodulation,[],[f6723,f6270]) ).

fof(f6723,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) != c_Polynomial_OpCons(t_a,v_a,v_p)
    | spl24_85 ),
    inference(avatar_component_clause,[],[f6721]) ).

fof(f27422,plain,
    ( spl24_14
    | ~ spl24_128
    | ~ spl24_273 ),
    inference(avatar_split_clause,[],[f27421,f12716,f6992,f6272]) ).

fof(f12716,plain,
    ( spl24_273
  <=> ! [X2,X0,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) != c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X2,X1),X0)
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_273])]) ).

fof(f27421,plain,
    ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
    | ~ spl24_128
    | ~ spl24_273 ),
    inference(trivial_inequality_removal,[],[f27418]) ).

fof(f27418,plain,
    ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
    | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
    | ~ spl24_128
    | ~ spl24_273 ),
    inference(superposition,[],[f12717,f6994]) ).

fof(f12717,plain,
    ( ! [X2,X0,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) != c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X2,X1),X0)
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,X1,X0) )
    | ~ spl24_273 ),
    inference(avatar_component_clause,[],[f12716]) ).

fof(f27340,plain,
    ( ~ spl24_135
    | spl24_560
    | ~ spl24_9 ),
    inference(avatar_split_clause,[],[f27323,f6248,f27338,f7262]) ).

fof(f7262,plain,
    ( spl24_135
  <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_135])]) ).

fof(f27338,plain,
    ( spl24_560
  <=> ! [X2] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint))
        | c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_560])]) ).

fof(f6248,plain,
    ( spl24_9
  <=> class_Rings_Ocomm__semiring__1(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_9])]) ).

fof(f27323,plain,
    ( ! [X2] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint))
        | c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))) )
    | ~ spl24_9 ),
    inference(superposition,[],[f12886,f7701]) ).

fof(f7701,plain,
    ( ! [X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1)
    | ~ spl24_9 ),
    inference(resolution,[],[f4539,f6250]) ).

fof(f6250,plain,
    ( class_Rings_Ocomm__semiring__1(tc_Int_Oint)
    | ~ spl24_9 ),
    inference(avatar_component_clause,[],[f6248]) ).

fof(f4539,plain,
    ! [X0,X1] :
      ( ~ class_Rings_Ocomm__semiring__1(X0)
      | c_Groups_Oplus__class_Oplus(X0,X1,X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Groups_Oplus__class_Oplus(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Oone__class_Oone(X0))),X1) ),
    inference(cnf_transformation,[],[f3539]) ).

fof(f3539,plain,
    ! [X0,X1] :
      ( ~ class_Rings_Ocomm__semiring__1(X0)
      | c_Groups_Oplus__class_Oplus(X0,X1,X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Groups_Oplus__class_Oplus(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Oone__class_Oone(X0))),X1) ),
    inference(rectify,[],[f2810]) ).

fof(f2810,plain,
    ! [X1,X0] :
      ( ~ class_Rings_Ocomm__semiring__1(X1)
      | c_Groups_Oplus__class_Oplus(X1,X0,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1))),X0) ),
    inference(ennf_transformation,[],[f2019]) ).

fof(f2019,plain,
    ! [X1,X0] :
      ( class_Rings_Ocomm__semiring__1(X1)
     => c_Groups_Oplus__class_Oplus(X1,X0,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1))),X0) ),
    inference(rectify,[],[f321]) ).

fof(f321,axiom,
    ! [X23,X4] :
      ( class_Rings_Ocomm__semiring__1(X4)
     => c_Groups_Oplus__class_Oplus(X4,X23,X23) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Groups_Oplus__class_Oplus(X4,c_Groups_Oone__class_Oone(X4),c_Groups_Oone__class_Oone(X4))),X23) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).

fof(f12886,plain,
    ! [X4,X5] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X5) != X4
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    inference(forward_demodulation,[],[f12881,f4706]) ).

fof(f4706,plain,
    ! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) = X0,
    inference(cnf_transformation,[],[f1639]) ).

fof(f1639,plain,
    ! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) = X0,
    inference(rectify,[],[f804]) ).

fof(f804,axiom,
    ! [X42] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X42) = X42,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__0) ).

fof(f12881,plain,
    ! [X4,X5] :
      ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X5)) != X4
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,c_Groups_Oone__class_Oone(tc_Int_Oint))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4) ),
    inference(resolution,[],[f4875,f5775]) ).

fof(f5775,plain,
    ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X0),
    inference(cnf_transformation,[],[f1308]) ).

fof(f1308,plain,
    ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X0),
    inference(rectify,[],[f813]) ).

fof(f813,axiom,
    ! [X68] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X68,X68),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__refl) ).

fof(f4875,plain,
    ! [X2,X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
      | c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2)) != X0
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
    inference(cnf_transformation,[],[f3241]) ).

fof(f3241,plain,
    ! [X0,X1,X2] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
      | c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2)) != X0 ),
    inference(flattening,[],[f3240]) ).

fof(f3240,plain,
    ! [X0,X2,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
      | c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2)) != X0
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
    inference(ennf_transformation,[],[f1817]) ).

fof(f1817,plain,
    ! [X0,X2,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
     => ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2)) = X0
       => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
         => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ),
    inference(rectify,[],[f831]) ).

fof(f831,axiom,
    ! [X5,X28,X21] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
     => ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,X28,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5),X21)) = X5
       => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X28)
         => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X21,c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_self__quotient__aux2) ).

fof(f27336,plain,
    ( ~ spl24_58
    | spl24_559 ),
    inference(avatar_split_clause,[],[f27321,f27334,f6521]) ).

fof(f6521,plain,
    ( spl24_58
  <=> 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,[spl24_58])]) ).

fof(f27334,plain,
    ( spl24_559
  <=> ! [X0] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))
        | c_Groups_Oone__class_Oone(tc_Int_Oint) != X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_559])]) ).

fof(f27321,plain,
    ! [X0] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(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),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    inference(superposition,[],[f12886,f4730]) ).

fof(f4730,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,[],[f1416]) ).

fof(f1416,plain,
    ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X0) = X0,
    inference(rectify,[],[f784]) ).

fof(f784,axiom,
    ! [X42] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X42) = X42,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__1) ).

fof(f27305,plain,
    ( spl24_558
    | spl24_556
    | ~ spl24_554 ),
    inference(avatar_split_clause,[],[f27287,f27244,f27294,f27303]) ).

fof(f27303,plain,
    ( spl24_558
  <=> ! [X5] : c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,sK12(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X5),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_558])]) ).

fof(f27294,plain,
    ( spl24_556
  <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = sK12(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_556])]) ).

fof(f27244,plain,
    ( spl24_554
  <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK12(c_Groups_Ozero__class_Ozero(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,[spl24_554])]) ).

fof(f27287,plain,
    ( ! [X5] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = sK12(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,sK12(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X5),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5)) )
    | ~ spl24_554 ),
    inference(resolution,[],[f27246,f7381]) ).

fof(f7381,plain,
    ! [X10,X8,X9] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X8,X10)
      | X8 = X10
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X8,X9),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X10,X9)) ),
    inference(resolution,[],[f5603,f5693]) ).

fof(f5693,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
      | X0 = X1
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ),
    inference(cnf_transformation,[],[f4277]) ).

fof(f4277,plain,
    ! [X0,X1] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(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,X0)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
        | X0 = X1 ) ),
    inference(flattening,[],[f4276]) ).

fof(f4276,plain,
    ! [X0,X1] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(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,X0)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
        | X0 = X1 ) ),
    inference(nnf_transformation,[],[f1370]) ).

fof(f1370,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
        & X0 != X1 )
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
    inference(rectify,[],[f820]) ).

fof(f820,axiom,
    ! [X40,X11] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X11,X40)
        & X11 != X40 )
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X11,X40) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__le) ).

fof(f5603,plain,
    ! [X2,X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X2)) ),
    inference(cnf_transformation,[],[f4215]) ).

fof(f4215,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X2))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
    inference(rectify,[],[f3141]) ).

fof(f3141,plain,
    ! [X1,X0,X2] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1) ),
    inference(ennf_transformation,[],[f2124]) ).

fof(f2124,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1)
     => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)) ),
    inference(rectify,[],[f819]) ).

fof(f819,axiom,
    ! [X54,X52,X51] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X54,X52)
     => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X54,X51),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X52,X51)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__strict__right__mono) ).

fof(f27246,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK12(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ spl24_554 ),
    inference(avatar_component_clause,[],[f27244]) ).

fof(f27301,plain,
    ( spl24_556
    | ~ spl24_557
    | ~ spl24_554 ),
    inference(avatar_split_clause,[],[f27282,f27244,f27298,f27294]) ).

fof(f27298,plain,
    ( spl24_557
  <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),sK12(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_557])]) ).

fof(f27282,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),sK12(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = sK12(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ spl24_554 ),
    inference(resolution,[],[f27246,f5243]) ).

fof(f5243,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
      | X0 = X1 ),
    inference(cnf_transformation,[],[f3967]) ).

fof(f3967,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
      | X0 = X1 ),
    inference(rectify,[],[f3131]) ).

fof(f3131,plain,
    ! [X1,X0] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
      | X0 = X1 ),
    inference(flattening,[],[f3130]) ).

fof(f3130,plain,
    ! [X1,X0] :
      ( X0 = X1
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1) ),
    inference(ennf_transformation,[],[f2129]) ).

fof(f2129,plain,
    ! [X1,X0] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
       => X0 = X1 ) ),
    inference(rectify,[],[f809]) ).

fof(f809,axiom,
    ! [X42,X68] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X42,X68)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X68,X42)
       => X42 = X68 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__antisym) ).

fof(f27292,plain,
    ( spl24_555
    | ~ spl24_554 ),
    inference(avatar_split_clause,[],[f27285,f27244,f27289]) ).

fof(f27289,plain,
    ( spl24_555
  <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,sK12(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_555])]) ).

fof(f27285,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,sK12(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ spl24_554 ),
    inference(resolution,[],[f27246,f5678]) ).

fof(f5678,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(cnf_transformation,[],[f4266]) ).

fof(f4266,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ) ),
    inference(nnf_transformation,[],[f1685]) ).

fof(f1685,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(rectify,[],[f827]) ).

fof(f827,axiom,
    ! [X11,X40] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X40,X11)
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X40,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X11,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__add1__eq__le) ).

fof(f27247,plain,
    ( spl24_554
    | ~ spl24_9
    | ~ spl24_317 ),
    inference(avatar_split_clause,[],[f27222,f13777,f6248,f27244]) ).

fof(f13777,plain,
    ( spl24_317
  <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_317])]) ).

fof(f27222,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK12(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ spl24_9
    | ~ spl24_317 ),
    inference(resolution,[],[f25816,f23169]) ).

fof(f23169,plain,
    ( ! [X18] : c_Rings_Odvd__class_Odvd(tc_Int_Oint,sK12(X18,X18),X18)
    | ~ spl24_9 ),
    inference(superposition,[],[f7129,f22486]) ).

fof(f22486,plain,
    ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),sK12(X0,X0)) = X0,
    inference(trivial_inequality_removal,[],[f22470]) ).

fof(f22470,plain,
    ! [X0] :
      ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),sK12(X0,X0)) = X0 ),
    inference(superposition,[],[f5235,f4793]) ).

fof(f4793,plain,
    ! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X0),
    inference(cnf_transformation,[],[f1313]) ).

fof(f1313,plain,
    ! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X0),
    inference(rectify,[],[f908]) ).

fof(f908,axiom,
    ! [X5] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X5,X5),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__self) ).

fof(f5235,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),sK12(X0,X1)) = X1 ),
    inference(cnf_transformation,[],[f3963]) ).

fof(f3963,plain,
    ! [X0,X1] :
      ( ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0)
        | ! [X2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2) != X1 )
      & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),sK12(X0,X1)) = X1
        | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f3961,f3962]) ).

fof(f3962,plain,
    ! [X0,X1] :
      ( ? [X3] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3) = X1
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),sK12(X0,X1)) = X1 ),
    introduced(choice_axiom,[]) ).

fof(f3961,plain,
    ! [X0,X1] :
      ( ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0)
        | ! [X2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2) != X1 )
      & ( ? [X3] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3) = X1
        | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0) ) ),
    inference(rectify,[],[f3960]) ).

fof(f3960,plain,
    ! [X1,X0] :
      ( ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X1)
        | ! [X2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2) != X0 )
      & ( ? [X2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2) = X0
        | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X1) ) ),
    inference(nnf_transformation,[],[f1606]) ).

fof(f1606,plain,
    ! [X1,X0] :
      ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X1)
    <=> ? [X2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2) = X0 ),
    inference(rectify,[],[f913]) ).

fof(f913,axiom,
    ! [X43,X41] :
      ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X43,X41)
    <=> ? [X85] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X41),X85) = X43 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__eq__0__iff) ).

fof(f7129,plain,
    ( ! [X2,X3] : c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2))
    | ~ spl24_9 ),
    inference(resolution,[],[f4814,f6250]) ).

fof(f4814,plain,
    ! [X2,X0,X1] :
      ( ~ class_Rings_Ocomm__semiring__1(X2)
      | c_Rings_Odvd__class_Odvd(X2,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1)) ),
    inference(cnf_transformation,[],[f3726]) ).

fof(f3726,plain,
    ! [X0,X1,X2] :
      ( ~ class_Rings_Ocomm__semiring__1(X2)
      | c_Rings_Odvd__class_Odvd(X2,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1)) ),
    inference(rectify,[],[f3148]) ).

fof(f3148,plain,
    ! [X1,X0,X2] :
      ( ~ class_Rings_Ocomm__semiring__1(X2)
      | c_Rings_Odvd__class_Odvd(X2,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) ),
    inference(ennf_transformation,[],[f1993]) ).

fof(f1993,plain,
    ! [X0,X2,X1] :
      ( class_Rings_Ocomm__semiring__1(X2)
     => c_Rings_Odvd__class_Odvd(X2,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) ),
    inference(rectify,[],[f417]) ).

fof(f417,axiom,
    ! [X5,X29,X4] :
      ( class_Rings_Ocomm__semiring__1(X4)
     => c_Rings_Odvd__class_Odvd(X4,X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X29),X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__triv__right) ).

fof(f25816,plain,
    ( ! [X7] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X7,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X7,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
    | ~ spl24_317 ),
    inference(resolution,[],[f13778,f5720]) ).

fof(f5720,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X0)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ),
    inference(cnf_transformation,[],[f4299]) ).

fof(f4299,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X0)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ),
    inference(rectify,[],[f2666]) ).

fof(f2666,plain,
    ! [X1,X0] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,X1)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1) ),
    inference(flattening,[],[f2665]) ).

fof(f2665,plain,
    ! [X1,X0] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,X1) ),
    inference(ennf_transformation,[],[f2065]) ).

fof(f2065,plain,
    ! [X1,X0] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,X1)
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
       => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1) ) ),
    inference(rectify,[],[f769]) ).

fof(f769,axiom,
    ! [X42,X17] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X42,X17)
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X17)
       => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X42,X17) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__imp__le) ).

fof(f13778,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ spl24_317 ),
    inference(avatar_component_clause,[],[f13777]) ).

fof(f27242,plain,
    ( spl24_553
    | ~ spl24_9
    | ~ spl24_317 ),
    inference(avatar_split_clause,[],[f27224,f13777,f6248,f27239]) ).

fof(f27239,plain,
    ( spl24_553
  <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK12(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_553])]) ).

fof(f27224,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK12(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ spl24_9
    | ~ spl24_317 ),
    inference(resolution,[],[f25816,f23187]) ).

fof(f23187,plain,
    ( ! [X6] : c_Rings_Odvd__class_Odvd(tc_Int_Oint,sK12(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X6),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X6)),X6)
    | ~ spl24_9 ),
    inference(resolution,[],[f23169,f5494]) ).

fof(f5494,plain,
    ! [X0,X1] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1))
      | c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,X1) ),
    inference(cnf_transformation,[],[f4144]) ).

fof(f4144,plain,
    ! [X0,X1] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,X1)
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)) )
      & ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1))
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,X1) ) ),
    inference(rectify,[],[f4143]) ).

fof(f4143,plain,
    ! [X1,X0] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X0)
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) )
      & ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X0) ) ),
    inference(nnf_transformation,[],[f1327]) ).

fof(f1327,plain,
    ! [X1,X0] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X0)
    <=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) ),
    inference(rectify,[],[f767]) ).

fof(f767,axiom,
    ! [X67,X41] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X41,X67)
    <=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,X41,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X67)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_uminus__dvd__conv_I2_J) ).

fof(f27237,plain,
    ( spl24_552
    | ~ spl24_9
    | ~ spl24_317 ),
    inference(avatar_split_clause,[],[f27220,f13777,f6248,f27234]) ).

fof(f27234,plain,
    ( spl24_552
  <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,sK12(c_Groups_Ozero__class_Ozero(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,[spl24_552])]) ).

fof(f27220,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,sK12(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ spl24_9
    | ~ spl24_317 ),
    inference(resolution,[],[f25816,f23727]) ).

fof(f23727,plain,
    ( ! [X3] : c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,sK12(X3,X3)),X3)
    | ~ spl24_9 ),
    inference(resolution,[],[f23174,f13394]) ).

fof(f13394,plain,
    ( ! [X0] : c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X0)
    | ~ spl24_9 ),
    inference(superposition,[],[f13360,f4772]) ).

fof(f4772,plain,
    ! [X0] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) = X0,
    inference(cnf_transformation,[],[f2078]) ).

fof(f2078,plain,
    ! [X0] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) = X0,
    inference(rectify,[],[f812]) ).

fof(f812,axiom,
    ! [X42] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X42)) = X42,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__zminus) ).

fof(f13360,plain,
    ( ! [X6] : c_Rings_Odvd__class_Odvd(tc_Int_Oint,X6,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X6))
    | ~ spl24_9 ),
    inference(resolution,[],[f4743,f12913]) ).

fof(f12913,plain,
    ( ! [X0] : c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,X0)
    | ~ spl24_9 ),
    inference(superposition,[],[f7129,f4730]) ).

fof(f4743,plain,
    ! [X0,X1] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1)
      | c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,X1) ),
    inference(cnf_transformation,[],[f3677]) ).

fof(f3677,plain,
    ! [X0,X1] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,X1)
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1) )
      & ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1)
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,X1) ) ),
    inference(rectify,[],[f3676]) ).

fof(f3676,plain,
    ! [X1,X0] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X0)
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X0) )
      & ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X0)
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X0) ) ),
    inference(nnf_transformation,[],[f1618]) ).

fof(f1618,plain,
    ! [X1,X0] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X0)
    <=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X0) ),
    inference(rectify,[],[f766]) ).

fof(f766,axiom,
    ! [X67,X41] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X41),X67)
    <=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,X41,X67) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_uminus__dvd__conv_I1_J) ).

fof(f23174,plain,
    ( ! [X26,X27] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X27,sK12(X26,X26))
        | c_Rings_Odvd__class_Odvd(tc_Int_Oint,X27,X26) )
    | ~ spl24_9 ),
    inference(superposition,[],[f7579,f22486]) ).

fof(f7579,plain,
    ( ! [X3,X4,X5] :
        ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X5))
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X3,X5) )
    | ~ spl24_9 ),
    inference(resolution,[],[f5779,f6250]) ).

fof(f5779,plain,
    ! [X2,X3,X0,X1] :
      ( ~ class_Rings_Ocomm__semiring__1(X3)
      | c_Rings_Odvd__class_Odvd(X3,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2))
      | ~ c_Rings_Odvd__class_Odvd(X3,X1,X2) ),
    inference(cnf_transformation,[],[f4336]) ).

fof(f4336,plain,
    ! [X0,X1,X2,X3] :
      ( ~ class_Rings_Ocomm__semiring__1(X3)
      | ~ c_Rings_Odvd__class_Odvd(X3,X1,X2)
      | c_Rings_Odvd__class_Odvd(X3,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2)) ),
    inference(rectify,[],[f3174]) ).

fof(f3174,plain,
    ! [X0,X3,X2,X1] :
      ( ~ class_Rings_Ocomm__semiring__1(X1)
      | ~ c_Rings_Odvd__class_Odvd(X1,X3,X2)
      | c_Rings_Odvd__class_Odvd(X1,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X2)) ),
    inference(flattening,[],[f3173]) ).

fof(f3173,plain,
    ! [X3,X2,X1,X0] :
      ( c_Rings_Odvd__class_Odvd(X1,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X2))
      | ~ c_Rings_Odvd__class_Odvd(X1,X3,X2)
      | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(ennf_transformation,[],[f1306]) ).

fof(f1306,plain,
    ! [X3,X2,X1,X0] :
      ( class_Rings_Ocomm__semiring__1(X1)
     => ( c_Rings_Odvd__class_Odvd(X1,X3,X2)
       => c_Rings_Odvd__class_Odvd(X1,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X2)) ) ),
    inference(rectify,[],[f415]) ).

fof(f415,axiom,
    ! [X29,X4,X22,X5] :
      ( class_Rings_Ocomm__semiring__1(X4)
     => ( c_Rings_Odvd__class_Odvd(X4,X5,X22)
       => c_Rings_Odvd__class_Odvd(X4,X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X29),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult) ).

fof(f27232,plain,
    ( spl24_551
    | ~ spl24_9
    | ~ spl24_317 ),
    inference(avatar_split_clause,[],[f27225,f13777,f6248,f27229]) ).

fof(f27229,plain,
    ( spl24_551
  <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK12(sK12(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK12(c_Groups_Ozero__class_Ozero(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,[spl24_551])]) ).

fof(f27225,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK12(sK12(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK12(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ spl24_9
    | ~ spl24_317 ),
    inference(resolution,[],[f25816,f23730]) ).

fof(f23730,plain,
    ( ! [X6] : c_Rings_Odvd__class_Odvd(tc_Int_Oint,sK12(sK12(X6,X6),sK12(X6,X6)),X6)
    | ~ spl24_9 ),
    inference(resolution,[],[f23174,f23169]) ).

fof(f27119,plain,
    ( spl24_550
    | ~ spl24_548 ),
    inference(avatar_split_clause,[],[f27110,f27086,f27116]) ).

fof(f27116,plain,
    ( spl24_550
  <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_550])]) ).

fof(f27086,plain,
    ( spl24_548
  <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_548])]) ).

fof(f27110,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ spl24_548 ),
    inference(resolution,[],[f27088,f7226]) ).

fof(f7226,plain,
    ! [X2,X1] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(resolution,[],[f4660,f5695]) ).

fof(f5695,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ),
    inference(cnf_transformation,[],[f4277]) ).

fof(f4660,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1) ),
    inference(cnf_transformation,[],[f3618]) ).

fof(f3618,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1)
          & X0 != X1 ) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1)
        | X0 = X1
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(flattening,[],[f3617]) ).

fof(f3617,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1)
          & X0 != X1 ) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1)
        | X0 = X1
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(nnf_transformation,[],[f1400]) ).

fof(f1400,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)))
    <=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1)
        | X0 = X1 ) ),
    inference(rectify,[],[f826]) ).

fof(f826,axiom,
    ! [X40,X11] :
      ( ( X11 = X40
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X40,X11) )
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X40,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X11,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__add1__eq) ).

fof(f27088,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ spl24_548 ),
    inference(avatar_component_clause,[],[f27086]) ).

fof(f27104,plain,
    ( spl24_549
    | ~ spl24_547 ),
    inference(avatar_split_clause,[],[f27094,f27079,f27101]) ).

fof(f27101,plain,
    ( spl24_549
  <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_549])]) ).

fof(f27079,plain,
    ( spl24_547
  <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_547])]) ).

fof(f27094,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ spl24_547 ),
    inference(resolution,[],[f27081,f7226]) ).

fof(f27081,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ spl24_547 ),
    inference(avatar_component_clause,[],[f27079]) ).

fof(f27090,plain,
    ( spl24_547
    | ~ spl24_191
    | ~ spl24_255 ),
    inference(avatar_split_clause,[],[f27074,f12451,f9854,f27079]) ).

fof(f9854,plain,
    ( spl24_191
  <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_191])]) ).

fof(f12451,plain,
    ( spl24_255
  <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(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,[spl24_255])]) ).

fof(f27074,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ spl24_191
    | ~ spl24_255 ),
    inference(resolution,[],[f25792,f12453]) ).

fof(f12453,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_255 ),
    inference(avatar_component_clause,[],[f12451]) ).

fof(f25792,plain,
    ( ! [X5] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
    | ~ spl24_191 ),
    inference(superposition,[],[f25645,f4706]) ).

fof(f25645,plain,
    ( ! [X26,X25] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X25,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X26,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X25,X26) )
    | ~ spl24_191 ),
    inference(forward_demodulation,[],[f25630,f4958]) ).

fof(f4958,plain,
    ! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X0,
    inference(cnf_transformation,[],[f2010]) ).

fof(f2010,plain,
    ! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X0,
    inference(rectify,[],[f805]) ).

fof(f805,axiom,
    ! [X42] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X42,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X42,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__0__right) ).

fof(f25630,plain,
    ( ! [X26,X25] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X25,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X26,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X25,X26) )
    | ~ spl24_191 ),
    inference(resolution,[],[f9855,f5304]) ).

fof(f5304,plain,
    ! [X2,X3,X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X0)
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1)) ),
    inference(cnf_transformation,[],[f4004]) ).

fof(f4004,plain,
    ! [X0,X1,X2,X3] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1)
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X0) ),
    inference(rectify,[],[f3071]) ).

fof(f3071,plain,
    ! [X3,X0,X2,X1] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X0)
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X0))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X3) ),
    inference(flattening,[],[f3070]) ).

fof(f3070,plain,
    ! [X1,X0,X2,X3] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X0))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X3) ),
    inference(ennf_transformation,[],[f1768]) ).

fof(f1768,plain,
    ! [X1,X0,X2,X3] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X3)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X0)
       => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X0)) ) ),
    inference(rectify,[],[f823]) ).

fof(f823,axiom,
    ! [X42,X82,X81,X68] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X82,X68)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X81,X42)
       => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X82,X81),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X68,X42)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zless__mono) ).

fof(f9855,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ spl24_191 ),
    inference(avatar_component_clause,[],[f9854]) ).

fof(f27089,plain,
    ( spl24_548
    | ~ spl24_191
    | ~ spl24_537 ),
    inference(avatar_split_clause,[],[f27075,f26124,f9854,f27086]) ).

fof(f26124,plain,
    ( spl24_537
  <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_537])]) ).

fof(f27075,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ spl24_191
    | ~ spl24_537 ),
    inference(resolution,[],[f25792,f26126]) ).

fof(f26126,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_537 ),
    inference(avatar_component_clause,[],[f26124]) ).

fof(f27084,plain,
    ( spl24_547
    | ~ spl24_191
    | ~ spl24_255 ),
    inference(avatar_split_clause,[],[f27083,f12451,f9854,f27079]) ).

fof(f27083,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ spl24_191
    | ~ spl24_255 ),
    inference(forward_demodulation,[],[f27072,f4958]) ).

fof(f27072,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ spl24_191
    | ~ spl24_255 ),
    inference(resolution,[],[f25792,f12484]) ).

fof(f12484,plain,
    ( ! [X0] : c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),X0),X0)
    | ~ spl24_255 ),
    inference(forward_demodulation,[],[f12482,f4706]) ).

fof(f12482,plain,
    ( ! [X0] : c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),X0),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0))
    | ~ spl24_255 ),
    inference(resolution,[],[f12453,f5603]) ).

fof(f27082,plain,
    ( spl24_547
    | ~ spl24_191 ),
    inference(avatar_split_clause,[],[f27077,f9854,f27079]) ).

fof(f27077,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ spl24_191 ),
    inference(forward_demodulation,[],[f27073,f4706]) ).

fof(f27073,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ spl24_191 ),
    inference(resolution,[],[f25792,f17632]) ).

fof(f17632,plain,
    ! [X11] : c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X11,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))),X11),
    inference(forward_demodulation,[],[f17602,f4958]) ).

fof(f17602,plain,
    ! [X11] : c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X11,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X11,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(superposition,[],[f7385,f12434]) ).

fof(f12434,plain,
    ! [X6] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X6,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X6)),
    inference(superposition,[],[f5830,f5009]) ).

fof(f5009,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,[],[f1289]) ).

fof(f1289,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,[],[f817]) ).

fof(f817,axiom,
    ! [X42] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X42),X42),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zminus__inverse2) ).

fof(f5830,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,[],[f1587]) ).

fof(f1587,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,[],[f806]) ).

fof(f806,axiom,
    ! [X42,X68] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X42,X68) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X68,X42),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__commute) ).

fof(f7385,plain,
    ! [X3,X4] : c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X4),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X4))),
    inference(forward_demodulation,[],[f7379,f5810]) ).

fof(f5810,plain,
    ! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1),X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)),
    inference(cnf_transformation,[],[f4354]) ).

fof(f4354,plain,
    ! [X0,X1,X2] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1),X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)),
    inference(rectify,[],[f1837]) ).

fof(f1837,plain,
    ! [X2,X1,X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1),X2),
    inference(rectify,[],[f808]) ).

fof(f808,axiom,
    ! [X75,X74,X73] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X75,X74),X73) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X75,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X74,X73)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__assoc) ).

fof(f7379,plain,
    ! [X3,X4] : c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X4),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,c_Groups_Oone__class_Oone(tc_Int_Oint)),X4)),
    inference(resolution,[],[f5603,f6042]) ).

fof(f6042,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,[],[f4659]) ).

fof(f4659,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)))
      | X0 != X1 ),
    inference(cnf_transformation,[],[f3618]) ).

fof(f26819,plain,
    ( spl24_545
    | ~ spl24_315 ),
    inference(avatar_split_clause,[],[f26818,f13767,f26793]) ).

fof(f26793,plain,
    ( spl24_545
  <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_545])]) ).

fof(f13767,plain,
    ( spl24_315
  <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_315])]) ).

fof(f26818,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    | ~ spl24_315 ),
    inference(forward_demodulation,[],[f26764,f5388]) ).

fof(f5388,plain,
    ! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1)),
    inference(cnf_transformation,[],[f4062]) ).

fof(f4062,plain,
    ! [X0,X1,X2] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1)),
    inference(rectify,[],[f1990]) ).

fof(f1990,plain,
    ! [X2,X1,X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1)),
    inference(rectify,[],[f807]) ).

fof(f807,axiom,
    ! [X19,X42,X35] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X19,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X35,X42)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X35,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X19,X42)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__left__commute) ).

fof(f26764,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    | ~ spl24_315 ),
    inference(resolution,[],[f13768,f4618]) ).

fof(f4618,plain,
    ! [X0] :
      ( ~ c_Orderings_Oord__class_Oless__eq(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),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)) ),
    inference(cnf_transformation,[],[f2825]) ).

fof(f2825,plain,
    ! [X0] :
      ( ~ c_Orderings_Oord__class_Oless__eq(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),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)) ),
    inference(ennf_transformation,[],[f1539]) ).

fof(f1539,plain,
    ! [X0] :
      ( c_Orderings_Oord__class_Oless__eq(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),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)) ),
    inference(rectify,[],[f828]) ).

fof(f828,axiom,
    ! [X42] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X42)
     => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X42)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__0__less) ).

fof(f13768,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ spl24_315 ),
    inference(avatar_component_clause,[],[f13767]) ).

fof(f26813,plain,
    ( spl24_546
    | ~ spl24_191
    | ~ spl24_315 ),
    inference(avatar_split_clause,[],[f26808,f13767,f9854,f26810]) ).

fof(f26810,plain,
    ( spl24_546
  <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_546])]) ).

fof(f26808,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
    | ~ spl24_191
    | ~ spl24_315 ),
    inference(forward_demodulation,[],[f26807,f5830]) ).

fof(f26807,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ spl24_191
    | ~ spl24_315 ),
    inference(forward_demodulation,[],[f26806,f12551]) ).

fof(f12551,plain,
    ! [X12,X13] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X12),X13),X12) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X12),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X13,c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(superposition,[],[f4843,f4436]) ).

fof(f4436,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,[],[f1487]) ).

fof(f1487,plain,
    ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X0,
    inference(rectify,[],[f785]) ).

fof(f785,axiom,
    ! [X42] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X42),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X42,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__1__right) ).

fof(f4843,plain,
    ! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)),
    inference(cnf_transformation,[],[f3747]) ).

fof(f3747,plain,
    ! [X0,X1,X2] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)),
    inference(rectify,[],[f1573]) ).

fof(f1573,plain,
    ! [X1,X0,X2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X2)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),
    inference(rectify,[],[f783]) ).

fof(f783,axiom,
    ! [X75,X68,X74] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X68),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X75,X74)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X68),X75),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X68),X74)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zmult__distrib2) ).

fof(f26806,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    | ~ spl24_191
    | ~ spl24_315 ),
    inference(forward_demodulation,[],[f26777,f4648]) ).

fof(f4648,plain,
    ! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X1),
    inference(cnf_transformation,[],[f2094]) ).

fof(f2094,plain,
    ! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X1),
    inference(rectify,[],[f780]) ).

fof(f780,axiom,
    ! [X68,X42] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X42),X68) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X68),X42),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__commute) ).

fof(f26777,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ spl24_191
    | ~ spl24_315 ),
    inference(resolution,[],[f13768,f25617]) ).

fof(f25617,plain,
    ( ! [X6] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X6)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X6),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
    | ~ spl24_191 ),
    inference(resolution,[],[f9855,f4746]) ).

fof(f4746,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0)) ),
    inference(cnf_transformation,[],[f3680]) ).

fof(f3680,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(rectify,[],[f2622]) ).

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

fof(f2621,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X1))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
    inference(ennf_transformation,[],[f1821]) ).

fof(f1821,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
       => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X1)) ) ),
    inference(rectify,[],[f839]) ).

fof(f839,axiom,
    ! [X19,X35] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X19)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X35)
       => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19),X35)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) ).

fof(f26796,plain,
    ( spl24_545
    | ~ spl24_315 ),
    inference(avatar_split_clause,[],[f26791,f13767,f26793]) ).

fof(f26791,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    | ~ spl24_315 ),
    inference(forward_demodulation,[],[f26790,f5388]) ).

fof(f26790,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    | ~ spl24_315 ),
    inference(forward_demodulation,[],[f26783,f5830]) ).

fof(f26783,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,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_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ spl24_315 ),
    inference(resolution,[],[f13768,f5678]) ).

fof(f26616,plain,
    ( spl24_544
    | ~ spl24_271 ),
    inference(avatar_split_clause,[],[f26609,f12701,f26613]) ).

fof(f26613,plain,
    ( spl24_544
  <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_544])]) ).

fof(f12701,plain,
    ( spl24_271
  <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_271])]) ).

fof(f26609,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ spl24_271 ),
    inference(resolution,[],[f12702,f5678]) ).

fof(f12702,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ spl24_271 ),
    inference(avatar_component_clause,[],[f12701]) ).

fof(f26602,plain,
    ( spl24_543
    | ~ spl24_358 ),
    inference(avatar_split_clause,[],[f26591,f15457,f26599]) ).

fof(f26599,plain,
    ( spl24_543
  <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_543])]) ).

fof(f15457,plain,
    ( spl24_358
  <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_358])]) ).

fof(f26591,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ spl24_358 ),
    inference(resolution,[],[f15458,f5678]) ).

fof(f15458,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ spl24_358 ),
    inference(avatar_component_clause,[],[f15457]) ).

fof(f26597,plain,
    ( spl24_359
    | spl24_542
    | ~ spl24_358 ),
    inference(avatar_split_clause,[],[f26593,f15457,f26595,f15461]) ).

fof(f15461,plain,
    ( spl24_359
  <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_359])]) ).

fof(f26595,plain,
    ( spl24_542
  <=> ! [X5] : c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X5),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_542])]) ).

fof(f26593,plain,
    ( ! [X5] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X5),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5))
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
    | ~ spl24_358 ),
    inference(resolution,[],[f15458,f7381]) ).

fof(f26582,plain,
    ( spl24_541
    | ~ spl24_538 ),
    inference(avatar_split_clause,[],[f26574,f26311,f26579]) ).

fof(f26579,plain,
    ( spl24_541
  <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_541])]) ).

fof(f26311,plain,
    ( spl24_538
  <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_538])]) ).

fof(f26574,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ spl24_538 ),
    inference(resolution,[],[f26313,f7226]) ).

fof(f26313,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ spl24_538 ),
    inference(avatar_component_clause,[],[f26311]) ).

fof(f26567,plain,
    ( spl24_459
    | spl24_540
    | ~ spl24_443 ),
    inference(avatar_split_clause,[],[f26563,f20391,f26565,f20961]) ).

fof(f20961,plain,
    ( spl24_459
  <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_459])]) ).

fof(f26565,plain,
    ( spl24_540
  <=> ! [X5] : c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),X5),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_540])]) ).

fof(f20391,plain,
    ( spl24_443
  <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_443])]) ).

fof(f26563,plain,
    ( ! [X5] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),X5),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5))
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)) )
    | ~ spl24_443 ),
    inference(resolution,[],[f20393,f7381]) ).

fof(f20393,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ spl24_443 ),
    inference(avatar_component_clause,[],[f20391]) ).

fof(f26465,plain,
    ( spl24_266
    | ~ spl24_191 ),
    inference(avatar_split_clause,[],[f26174,f9854,f12616]) ).

fof(f12616,plain,
    ( spl24_266
  <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_266])]) ).

fof(f26174,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_191 ),
    inference(superposition,[],[f25681,f12434]) ).

fof(f25681,plain,
    ( ! [X1] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1))
    | ~ spl24_191 ),
    inference(superposition,[],[f25636,f5830]) ).

fof(f25636,plain,
    ( ! [X27] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X27,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X27,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ spl24_191 ),
    inference(forward_demodulation,[],[f25631,f4958]) ).

fof(f25631,plain,
    ( ! [X27] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X27,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X27,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ spl24_191 ),
    inference(resolution,[],[f9855,f5336]) ).

fof(f5336,plain,
    ! [X2,X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X2)) ),
    inference(cnf_transformation,[],[f4028]) ).

fof(f4028,plain,
    ! [X0,X1,X2] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X2)) ),
    inference(rectify,[],[f2861]) ).

fof(f2861,plain,
    ! [X2,X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X0),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1)) ),
    inference(ennf_transformation,[],[f1754]) ).

fof(f1754,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
     => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X0),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1)) ),
    inference(rectify,[],[f815]) ).

fof(f815,axiom,
    ! [X54,X52,X51] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X54,X52)
     => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X51,X54),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X51,X52)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__left__mono) ).

fof(f26464,plain,
    ( spl24_163
    | ~ spl24_256 ),
    inference(avatar_split_clause,[],[f18824,f12456,f9358]) ).

fof(f9358,plain,
    ( spl24_163
  <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_163])]) ).

fof(f12456,plain,
    ( spl24_256
  <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_256])]) ).

fof(f18824,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_256 ),
    inference(forward_demodulation,[],[f18798,f4772]) ).

fof(f18798,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_256 ),
    inference(superposition,[],[f12624,f5009]) ).

fof(f12624,plain,
    ( ! [X4] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
    | ~ spl24_256 ),
    inference(forward_demodulation,[],[f12603,f4958]) ).

fof(f12603,plain,
    ( ! [X4] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
    | ~ spl24_256 ),
    inference(resolution,[],[f12458,f5336]) ).

fof(f12458,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ spl24_256 ),
    inference(avatar_component_clause,[],[f12456]) ).

fof(f26463,plain,
    ( spl24_163
    | ~ spl24_256 ),
    inference(avatar_split_clause,[],[f23916,f12456,f9358]) ).

fof(f23916,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_256 ),
    inference(superposition,[],[f12624,f12434]) ).

fof(f26462,plain,
    ( spl24_163
    | ~ spl24_256 ),
    inference(avatar_split_clause,[],[f24354,f12456,f9358]) ).

fof(f24354,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_256 ),
    inference(superposition,[],[f18794,f5009]) ).

fof(f18794,plain,
    ( ! [X1] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
    | ~ spl24_256 ),
    inference(superposition,[],[f12624,f5830]) ).

fof(f26461,plain,
    ( spl24_266
    | ~ spl24_537 ),
    inference(avatar_split_clause,[],[f26306,f26124,f12616]) ).

fof(f26306,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_537 ),
    inference(resolution,[],[f26126,f5695]) ).

fof(f26460,plain,
    ( spl24_163
    | ~ spl24_256 ),
    inference(avatar_split_clause,[],[f18792,f12456,f9358]) ).

fof(f18792,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_256 ),
    inference(superposition,[],[f12624,f12434]) ).

fof(f26459,plain,
    ( spl24_163
    | ~ spl24_256 ),
    inference(avatar_split_clause,[],[f23960,f12456,f9358]) ).

fof(f23960,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_256 ),
    inference(forward_demodulation,[],[f23924,f4772]) ).

fof(f23924,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_256 ),
    inference(superposition,[],[f12624,f5009]) ).

fof(f26458,plain,
    ( spl24_266
    | spl24_267
    | spl24_258 ),
    inference(avatar_split_clause,[],[f26347,f12472,f12620,f12616]) ).

fof(f12620,plain,
    ( spl24_267
  <=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_267])]) ).

fof(f12472,plain,
    ( spl24_258
  <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_258])]) ).

fof(f26347,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | spl24_258 ),
    inference(resolution,[],[f12473,f7145]) ).

fof(f7145,plain,
    ! [X2,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
      | X1 = X2
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    inference(resolution,[],[f5285,f5695]) ).

fof(f5285,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1)
      | X0 = X1 ),
    inference(cnf_transformation,[],[f3994]) ).

fof(f3994,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
      | X0 = X1
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1) ),
    inference(rectify,[],[f2144]) ).

fof(f2144,plain,
    ! [X1,X0] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1)
      | X0 = X1
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
    inference(rectify,[],[f818]) ).

fof(f818,axiom,
    ! [X35,X19] :
      ( X19 = X35
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,X35,X19)
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,X19,X35) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__linear) ).

fof(f12473,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | spl24_258 ),
    inference(avatar_component_clause,[],[f12472]) ).

fof(f26457,plain,
    ( spl24_266
    | ~ spl24_191 ),
    inference(avatar_split_clause,[],[f25686,f9854,f12616]) ).

fof(f25686,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_191 ),
    inference(superposition,[],[f25636,f5009]) ).

fof(f26456,plain,
    ( spl24_267
    | ~ spl24_256
    | spl24_258 ),
    inference(avatar_split_clause,[],[f26348,f12472,f12456,f12620]) ).

fof(f26348,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | spl24_258 ),
    inference(resolution,[],[f12473,f5693]) ).

fof(f26455,plain,
    ( spl24_256
    | spl24_266 ),
    inference(avatar_split_clause,[],[f12653,f12616,f12456]) ).

fof(f12653,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | spl24_266 ),
    inference(resolution,[],[f12618,f5360]) ).

fof(f5360,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ),
    inference(cnf_transformation,[],[f1531]) ).

fof(f1531,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1) ),
    inference(rectify,[],[f811]) ).

fof(f811,axiom,
    ! [X42,X68] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X42,X68)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X68,X42) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__linear) ).

fof(f12618,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | spl24_266 ),
    inference(avatar_component_clause,[],[f12616]) ).

fof(f26454,plain,
    ( spl24_163
    | ~ spl24_256 ),
    inference(avatar_split_clause,[],[f24368,f12456,f9358]) ).

fof(f24368,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_256 ),
    inference(forward_demodulation,[],[f24363,f4772]) ).

fof(f24363,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_256 ),
    inference(superposition,[],[f18794,f12434]) ).

fof(f26453,plain,
    ( spl24_256
    | spl24_266 ),
    inference(avatar_split_clause,[],[f22388,f12616,f12456]) ).

fof(f22388,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | spl24_266 ),
    inference(resolution,[],[f12618,f5360]) ).

fof(f26452,plain,
    ( spl24_256
    | spl24_266 ),
    inference(avatar_split_clause,[],[f22387,f12616,f12456]) ).

fof(f22387,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | spl24_266 ),
    inference(resolution,[],[f12618,f5360]) ).

fof(f26451,plain,
    ( spl24_256
    | ~ spl24_191
    | ~ spl24_357 ),
    inference(avatar_split_clause,[],[f26442,f15397,f9854,f12456]) ).

fof(f15397,plain,
    ( spl24_357
  <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_357])]) ).

fof(f26442,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ spl24_191
    | ~ spl24_357 ),
    inference(resolution,[],[f15399,f25628]) ).

fof(f25628,plain,
    ( ! [X24] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X24)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X24) )
    | ~ spl24_191 ),
    inference(resolution,[],[f9855,f4403]) ).

fof(f4403,plain,
    ! [X2,X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X2)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1) ),
    inference(cnf_transformation,[],[f2500]) ).

fof(f2500,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X2) ),
    inference(flattening,[],[f2499]) ).

fof(f2499,plain,
    ! [X1,X2,X0] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X2) ),
    inference(ennf_transformation,[],[f1862]) ).

fof(f1862,plain,
    ! [X1,X2,X0] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X2)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1)
       => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1) ) ),
    inference(rectify,[],[f810]) ).

fof(f810,axiom,
    ! [X54,X51,X52] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X54,X52)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X52,X51)
       => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X54,X51) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__trans) ).

fof(f15399,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ spl24_357 ),
    inference(avatar_component_clause,[],[f15397]) ).

fof(f26323,plain,
    ( spl24_539
    | ~ spl24_537 ),
    inference(avatar_split_clause,[],[f26318,f26124,f26320]) ).

fof(f26320,plain,
    ( spl24_539
  <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_539])]) ).

fof(f26318,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_537 ),
    inference(forward_demodulation,[],[f26317,f5148]) ).

fof(f5148,plain,
    ! [X0,X1] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)),
    inference(cnf_transformation,[],[f1193]) ).

fof(f1193,plain,
    ! [X0,X1] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)),
    inference(rectify,[],[f816]) ).

fof(f816,axiom,
    ! [X68,X42] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X42,X68)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X42),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X68)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__zadd__distrib) ).

fof(f26317,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_537 ),
    inference(forward_demodulation,[],[f26298,f5388]) ).

fof(f26298,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_537 ),
    inference(resolution,[],[f26126,f6872]) ).

fof(f6872,plain,
    ! [X0] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(forward_demodulation,[],[f4747,f5830]) ).

fof(f4747,plain,
    ! [X0] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(cnf_transformation,[],[f3681]) ).

fof(f3681,plain,
    ! [X0] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
    inference(nnf_transformation,[],[f2159]) ).

fof(f2159,plain,
    ! [X0] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(rectify,[],[f829]) ).

fof(f829,axiom,
    ! [X11] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X11),X11),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X11,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_odd__less__0) ).

fof(f26314,plain,
    ( spl24_538
    | ~ spl24_537 ),
    inference(avatar_split_clause,[],[f26300,f26124,f26311]) ).

fof(f26300,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ spl24_537 ),
    inference(resolution,[],[f26126,f7228]) ).

fof(f7228,plain,
    ! [X0] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    inference(superposition,[],[f4660,f4706]) ).

fof(f26127,plain,
    ( spl24_537
    | ~ spl24_532 ),
    inference(avatar_split_clause,[],[f26109,f25642,f26124]) ).

fof(f25642,plain,
    ( spl24_532
  <=> ! [X29] : c_Orderings_Oord__class_Oless(tc_Int_Oint,X29,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X29)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_532])]) ).

fof(f26109,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_532 ),
    inference(superposition,[],[f25643,f12434]) ).

fof(f25643,plain,
    ( ! [X29] : c_Orderings_Oord__class_Oless(tc_Int_Oint,X29,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X29))
    | ~ spl24_532 ),
    inference(avatar_component_clause,[],[f25642]) ).

fof(f26075,plain,
    ( spl24_237
    | spl24_536
    | ~ spl24_236 ),
    inference(avatar_split_clause,[],[f26071,f11227,f26073,f11231]) ).

fof(f11231,plain,
    ( spl24_237
  <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_237])]) ).

fof(f26073,plain,
    ( spl24_536
  <=> ! [X6] : c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X6),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_536])]) ).

fof(f11227,plain,
    ( spl24_236
  <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_236])]) ).

fof(f26071,plain,
    ( ! [X6] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X6),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6))
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oone__class_Oone(tc_Int_Oint) )
    | ~ spl24_236 ),
    inference(resolution,[],[f11228,f7381]) ).

fof(f11228,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ spl24_236 ),
    inference(avatar_component_clause,[],[f11227]) ).

fof(f25901,plain,
    ( spl24_534
    | ~ spl24_191 ),
    inference(avatar_split_clause,[],[f25900,f9854,f25878]) ).

fof(f25878,plain,
    ( spl24_534
  <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_534])]) ).

fof(f25900,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ spl24_191 ),
    inference(forward_demodulation,[],[f25899,f4958]) ).

fof(f25899,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))
    | ~ spl24_191 ),
    inference(forward_demodulation,[],[f25898,f5830]) ).

fof(f25898,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
    | ~ spl24_191 ),
    inference(forward_demodulation,[],[f25873,f4648]) ).

fof(f25873,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ spl24_191 ),
    inference(resolution,[],[f25617,f25636]) ).

fof(f25887,plain,
    ( spl24_535
    | ~ spl24_191
    | ~ spl24_454 ),
    inference(avatar_split_clause,[],[f25882,f20747,f9854,f25884]) ).

fof(f25884,plain,
    ( spl24_535
  <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_535])]) ).

fof(f20747,plain,
    ( spl24_454
  <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_454])]) ).

fof(f25882,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
    | ~ spl24_191
    | ~ spl24_454 ),
    inference(forward_demodulation,[],[f25867,f4648]) ).

fof(f25867,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ spl24_191
    | ~ spl24_454 ),
    inference(resolution,[],[f25617,f20749]) ).

fof(f20749,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ spl24_454 ),
    inference(avatar_component_clause,[],[f20747]) ).

fof(f25881,plain,
    ( spl24_534
    | ~ spl24_191 ),
    inference(avatar_split_clause,[],[f25865,f9854,f25878]) ).

fof(f25865,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ spl24_191 ),
    inference(resolution,[],[f25617,f9855]) ).

fof(f25854,plain,
    ( spl24_533
    | ~ spl24_191
    | ~ spl24_454 ),
    inference(avatar_split_clause,[],[f25849,f20747,f9854,f25851]) ).

fof(f25851,plain,
    ( spl24_533
  <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_533])]) ).

fof(f25849,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
    | ~ spl24_191
    | ~ spl24_454 ),
    inference(forward_demodulation,[],[f25836,f5830]) ).

fof(f25836,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ spl24_191
    | ~ spl24_454 ),
    inference(resolution,[],[f25623,f20749]) ).

fof(f25623,plain,
    ( ! [X20] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X20)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X20,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
    | ~ spl24_191 ),
    inference(resolution,[],[f9855,f5761]) ).

fof(f5761,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1)) ),
    inference(cnf_transformation,[],[f2926]) ).

fof(f2926,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1)) ),
    inference(flattening,[],[f2925]) ).

fof(f2925,plain,
    ! [X1,X0] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
    inference(ennf_transformation,[],[f1580]) ).

fof(f1580,plain,
    ! [X1,X0] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
       => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1)) ) ),
    inference(rectify,[],[f842]) ).

fof(f842,axiom,
    ! [X19,X35] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X19)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X35)
       => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X19,X35)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).

fof(f25827,plain,
    ( spl24_438
    | ~ spl24_317 ),
    inference(avatar_split_clause,[],[f25811,f13777,f20194]) ).

fof(f20194,plain,
    ( spl24_438
  <=> ! [X7] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X7,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_438])]) ).

fof(f25811,plain,
    ( ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ spl24_317 ),
    inference(resolution,[],[f13778,f4859]) ).

fof(f4859,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0)) ),
    inference(cnf_transformation,[],[f2393]) ).

fof(f2393,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0),X0)
        & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0)) )
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
    inference(ennf_transformation,[],[f1927]) ).

fof(f1927,plain,
    ! [X0,X1] :
      ( 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_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0),X0)
        & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0)) ) ),
    inference(rectify,[],[f920]) ).

fof(f920,axiom,
    ! [X29,X5] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X29)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X5,X29))
        & c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X5,X29),X29) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__mod__conj) ).

fof(f25644,plain,
    ( spl24_532
    | spl24_172
    | ~ spl24_191 ),
    inference(avatar_split_clause,[],[f25640,f9854,f9476,f25642]) ).

fof(f9476,plain,
    ( spl24_172
  <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_172])]) ).

fof(f25640,plain,
    ( ! [X29] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X29,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X29)) )
    | ~ spl24_191 ),
    inference(forward_demodulation,[],[f25634,f4706]) ).

fof(f25634,plain,
    ( ! [X29] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X29),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X29)) )
    | ~ spl24_191 ),
    inference(resolution,[],[f9855,f7381]) ).

fof(f25613,plain,
    ( spl24_153
    | ~ spl24_311 ),
    inference(avatar_split_clause,[],[f18840,f13674,f9279]) ).

fof(f9279,plain,
    ( spl24_153
  <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_153])]) ).

fof(f13674,plain,
    ( spl24_311
  <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_311])]) ).

fof(f18840,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_311 ),
    inference(resolution,[],[f13676,f5134]) ).

fof(f5134,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1) ),
    inference(cnf_transformation,[],[f3928]) ).

fof(f3928,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)),X1) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1) ) ),
    inference(rectify,[],[f3927]) ).

fof(f3927,plain,
    ! [X1,X0] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X0) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ) ),
    inference(nnf_transformation,[],[f2186]) ).

fof(f2186,plain,
    ! [X1,X0] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X0) ),
    inference(rectify,[],[f825]) ).

fof(f825,axiom,
    ! [X11,X40] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X40,X11)
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X40,c_Groups_Oone__class_Oone(tc_Int_Oint)),X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add1__zle__eq) ).

fof(f13676,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_311 ),
    inference(avatar_component_clause,[],[f13674]) ).

fof(f25612,plain,
    ( spl24_256
    | spl24_266 ),
    inference(avatar_split_clause,[],[f22388,f12616,f12456]) ).

fof(f25611,plain,
    ( spl24_530
    | ~ spl24_311 ),
    inference(avatar_split_clause,[],[f18853,f13674,f25580]) ).

fof(f25580,plain,
    ( spl24_530
  <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_530])]) ).

fof(f18853,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ spl24_311 ),
    inference(forward_demodulation,[],[f18846,f4706]) ).

fof(f18846,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ spl24_311 ),
    inference(resolution,[],[f13676,f5678]) ).

fof(f25610,plain,
    ( spl24_530
    | ~ spl24_402 ),
    inference(avatar_split_clause,[],[f20563,f17755,f25580]) ).

fof(f17755,plain,
    ( spl24_402
  <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_402])]) ).

fof(f20563,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ spl24_402 ),
    inference(resolution,[],[f17757,f7228]) ).

fof(f17757,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_402 ),
    inference(avatar_component_clause,[],[f17755]) ).

fof(f25609,plain,
    ( spl24_235
    | spl24_236 ),
    inference(avatar_split_clause,[],[f11241,f11227,f11215]) ).

fof(f11215,plain,
    ( spl24_235
  <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_235])]) ).

fof(f11241,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | spl24_236 ),
    inference(resolution,[],[f11229,f5360]) ).

fof(f11229,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | spl24_236 ),
    inference(avatar_component_clause,[],[f11227]) ).

fof(f25608,plain,
    ( spl24_500
    | spl24_517 ),
    inference(avatar_split_clause,[],[f25565,f25212,f24583]) ).

fof(f24583,plain,
    ( spl24_500
  <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_500])]) ).

fof(f25212,plain,
    ( spl24_517
  <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(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,[spl24_517])]) ).

fof(f25565,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | spl24_517 ),
    inference(resolution,[],[f25214,f5360]) ).

fof(f25214,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | spl24_517 ),
    inference(avatar_component_clause,[],[f25212]) ).

fof(f25607,plain,
    ( spl24_256
    | spl24_266 ),
    inference(avatar_split_clause,[],[f22387,f12616,f12456]) ).

fof(f25606,plain,
    ( spl24_153
    | spl24_315 ),
    inference(avatar_split_clause,[],[f23130,f13767,f9279]) ).

fof(f23130,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | spl24_315 ),
    inference(resolution,[],[f13769,f7246]) ).

fof(f7246,plain,
    ! [X6,X5] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X6,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5,c_Groups_Oone__class_Oone(tc_Int_Oint)))
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X6) ),
    inference(resolution,[],[f5134,f5360]) ).

fof(f13769,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | spl24_315 ),
    inference(avatar_component_clause,[],[f13767]) ).

fof(f25605,plain,
    ( spl24_530
    | ~ spl24_402 ),
    inference(avatar_split_clause,[],[f20022,f17755,f25580]) ).

fof(f20022,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ spl24_402 ),
    inference(resolution,[],[f17757,f7228]) ).

fof(f25604,plain,
    ( spl24_530
    | ~ spl24_311 ),
    inference(avatar_split_clause,[],[f20561,f13674,f25580]) ).

fof(f20561,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ spl24_311 ),
    inference(forward_demodulation,[],[f20554,f4706]) ).

fof(f20554,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ spl24_311 ),
    inference(resolution,[],[f13676,f5678]) ).

fof(f25603,plain,
    ( spl24_153
    | spl24_315 ),
    inference(avatar_split_clause,[],[f18695,f13767,f9279]) ).

fof(f18695,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | spl24_315 ),
    inference(resolution,[],[f13769,f7246]) ).

fof(f25602,plain,
    ( spl24_531
    | ~ spl24_402 ),
    inference(avatar_split_clause,[],[f20037,f17755,f25589]) ).

fof(f25589,plain,
    ( spl24_531
  <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_531])]) ).

fof(f20037,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ spl24_402 ),
    inference(forward_demodulation,[],[f20024,f4706]) ).

fof(f20024,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ spl24_402 ),
    inference(resolution,[],[f17757,f7226]) ).

fof(f25601,plain,
    ( spl24_530
    | ~ spl24_311 ),
    inference(avatar_split_clause,[],[f24025,f13674,f25580]) ).

fof(f24025,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ spl24_311 ),
    inference(forward_demodulation,[],[f24013,f4706]) ).

fof(f24013,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ spl24_311 ),
    inference(resolution,[],[f13676,f5678]) ).

fof(f25600,plain,
    ( spl24_342
    | spl24_403 ),
    inference(avatar_split_clause,[],[f20578,f18015,f14802]) ).

fof(f14802,plain,
    ( spl24_342
  <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_342])]) ).

fof(f18015,plain,
    ( spl24_403
  <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_403])]) ).

fof(f20578,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | spl24_403 ),
    inference(resolution,[],[f18017,f5360]) ).

fof(f18017,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | spl24_403 ),
    inference(avatar_component_clause,[],[f18015]) ).

fof(f25599,plain,
    ( spl24_237
    | spl24_233
    | spl24_446 ),
    inference(avatar_split_clause,[],[f20635,f20581,f11143,f11231]) ).

fof(f11143,plain,
    ( spl24_233
  <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_233])]) ).

fof(f20581,plain,
    ( spl24_446
  <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_446])]) ).

fof(f20635,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | spl24_446 ),
    inference(resolution,[],[f20583,f5285]) ).

fof(f20583,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | spl24_446 ),
    inference(avatar_component_clause,[],[f20581]) ).

fof(f25598,plain,
    ( spl24_153
    | ~ spl24_311 ),
    inference(avatar_split_clause,[],[f20548,f13674,f9279]) ).

fof(f20548,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_311 ),
    inference(resolution,[],[f13676,f5134]) ).

fof(f25597,plain,
    ( spl24_357
    | spl24_358 ),
    inference(avatar_split_clause,[],[f22408,f15457,f15397]) ).

fof(f22408,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | spl24_358 ),
    inference(resolution,[],[f15459,f5360]) ).

fof(f15459,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | spl24_358 ),
    inference(avatar_component_clause,[],[f15457]) ).

fof(f25596,plain,
    ( spl24_531
    | ~ spl24_402 ),
    inference(avatar_split_clause,[],[f20573,f17755,f25589]) ).

fof(f20573,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ spl24_402 ),
    inference(forward_demodulation,[],[f20565,f4706]) ).

fof(f20565,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ spl24_402 ),
    inference(resolution,[],[f17757,f7226]) ).

fof(f25595,plain,
    ( spl24_153
    | ~ spl24_444 ),
    inference(avatar_split_clause,[],[f20491,f20462,f9279]) ).

fof(f20462,plain,
    ( spl24_444
  <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_444])]) ).

fof(f20491,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_444 ),
    inference(forward_demodulation,[],[f20490,f12434]) ).

fof(f20490,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))))
    | ~ spl24_444 ),
    inference(forward_demodulation,[],[f20487,f5830]) ).

fof(f20487,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ spl24_444 ),
    inference(resolution,[],[f20464,f5678]) ).

fof(f20464,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ spl24_444 ),
    inference(avatar_component_clause,[],[f20462]) ).

fof(f25594,plain,
    ( spl24_342
    | spl24_403 ),
    inference(avatar_split_clause,[],[f20579,f18015,f14802]) ).

fof(f20579,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | spl24_403 ),
    inference(resolution,[],[f18017,f5360]) ).

fof(f25593,plain,
    ( spl24_315
    | ~ spl24_234 ),
    inference(avatar_split_clause,[],[f18657,f11152,f13767]) ).

fof(f11152,plain,
    ( spl24_234
  <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_234])]) ).

fof(f18657,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ spl24_234 ),
    inference(resolution,[],[f11154,f5695]) ).

fof(f11154,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ spl24_234 ),
    inference(avatar_component_clause,[],[f11152]) ).

fof(f25592,plain,
    ( spl24_531
    | ~ spl24_402 ),
    inference(avatar_split_clause,[],[f24084,f17755,f25589]) ).

fof(f24084,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ spl24_402 ),
    inference(forward_demodulation,[],[f24074,f4706]) ).

fof(f24074,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ spl24_402 ),
    inference(resolution,[],[f17757,f7226]) ).

fof(f25587,plain,
    ( spl24_357
    | spl24_358 ),
    inference(avatar_split_clause,[],[f15535,f15457,f15397]) ).

fof(f15535,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | spl24_358 ),
    inference(resolution,[],[f15459,f5360]) ).

fof(f25586,plain,
    ( spl24_357
    | spl24_358 ),
    inference(avatar_split_clause,[],[f15534,f15457,f15397]) ).

fof(f15534,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | spl24_358 ),
    inference(resolution,[],[f15459,f5360]) ).

fof(f25585,plain,
    ( spl24_233
    | spl24_237
    | spl24_446 ),
    inference(avatar_split_clause,[],[f20636,f20581,f11231,f11143]) ).

fof(f20636,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | spl24_446 ),
    inference(resolution,[],[f20583,f5285]) ).

fof(f25584,plain,
    ( spl24_256
    | spl24_266 ),
    inference(avatar_split_clause,[],[f12654,f12616,f12456]) ).

fof(f12654,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | spl24_266 ),
    inference(resolution,[],[f12618,f5360]) ).

fof(f25583,plain,
    ( spl24_530
    | ~ spl24_402 ),
    inference(avatar_split_clause,[],[f24072,f17755,f25580]) ).

fof(f24072,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ spl24_402 ),
    inference(resolution,[],[f17757,f7228]) ).

fof(f25578,plain,
    ( spl24_235
    | spl24_236 ),
    inference(avatar_split_clause,[],[f11240,f11227,f11215]) ).

fof(f11240,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | spl24_236 ),
    inference(resolution,[],[f11229,f5360]) ).

fof(f25577,plain,
    ( spl24_500
    | spl24_517 ),
    inference(avatar_split_clause,[],[f25566,f25212,f24583]) ).

fof(f25566,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | spl24_517 ),
    inference(resolution,[],[f25214,f5360]) ).

fof(f25576,plain,
    ( spl24_357
    | spl24_358 ),
    inference(avatar_split_clause,[],[f22407,f15457,f15397]) ).

fof(f22407,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | spl24_358 ),
    inference(resolution,[],[f15459,f5360]) ).

fof(f25575,plain,
    ( spl24_153
    | spl24_315 ),
    inference(avatar_split_clause,[],[f16160,f13767,f9279]) ).

fof(f16160,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | spl24_315 ),
    inference(resolution,[],[f13769,f7246]) ).

fof(f25574,plain,
    ( spl24_237
    | spl24_235
    | spl24_446 ),
    inference(avatar_split_clause,[],[f20633,f20581,f11215,f11231]) ).

fof(f20633,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | spl24_446 ),
    inference(resolution,[],[f20583,f7145]) ).

fof(f25573,plain,
    ( spl24_256
    | spl24_266 ),
    inference(avatar_split_clause,[],[f12653,f12616,f12456]) ).

fof(f25572,plain,
    ( spl24_153
    | spl24_315 ),
    inference(avatar_split_clause,[],[f20541,f13767,f9279]) ).

fof(f20541,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | spl24_315 ),
    inference(resolution,[],[f13769,f7246]) ).

fof(f25571,plain,
    ( spl24_342
    | spl24_403 ),
    inference(avatar_split_clause,[],[f24132,f18015,f14802]) ).

fof(f24132,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | spl24_403 ),
    inference(resolution,[],[f18017,f5360]) ).

fof(f25570,plain,
    ( spl24_153
    | ~ spl24_311 ),
    inference(avatar_split_clause,[],[f24006,f13674,f9279]) ).

fof(f24006,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_311 ),
    inference(resolution,[],[f13676,f5134]) ).

fof(f25569,plain,
    ( spl24_342
    | spl24_403 ),
    inference(avatar_split_clause,[],[f24131,f18015,f14802]) ).

fof(f24131,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | spl24_403 ),
    inference(resolution,[],[f18017,f5360]) ).

fof(f25568,plain,
    ( ~ spl24_163
    | spl24_517 ),
    inference(avatar_contradiction_clause,[],[f25563]) ).

fof(f25563,plain,
    ( $false
    | ~ spl24_163
    | spl24_517 ),
    inference(resolution,[],[f25214,f12049]) ).

fof(f12049,plain,
    ( ! [X1] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1),X1)
    | ~ spl24_163 ),
    inference(superposition,[],[f11274,f5830]) ).

fof(f11274,plain,
    ( ! [X10] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X10,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10)
    | ~ spl24_163 ),
    inference(forward_demodulation,[],[f11272,f4958]) ).

fof(f11272,plain,
    ( ! [X10] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X10,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X10,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ spl24_163 ),
    inference(resolution,[],[f5336,f9360]) ).

fof(f9360,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_163 ),
    inference(avatar_component_clause,[],[f9358]) ).

fof(f25567,plain,
    ( ~ spl24_163
    | spl24_517 ),
    inference(avatar_contradiction_clause,[],[f25564]) ).

fof(f25564,plain,
    ( $false
    | ~ spl24_163
    | spl24_517 ),
    inference(resolution,[],[f25214,f11274]) ).

fof(f25380,plain,
    ( spl24_528
    | spl24_529
    | spl24_461 ),
    inference(avatar_split_clause,[],[f25365,f21167,f25377,f25373]) ).

fof(f25373,plain,
    ( spl24_528
  <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = sK2(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_528])]) ).

fof(f25377,plain,
    ( spl24_529
  <=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = sK2(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_529])]) ).

fof(f21167,plain,
    ( spl24_461
  <=> 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_Oone__class_Oone(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_461])]) ).

fof(f25365,plain,
    ( 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_Oone__class_Oone(tc_Nat_Onat))
    | c_Groups_Oone__class_Oone(tc_Nat_Onat) = sK2(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = sK2(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(resolution,[],[f25228,f6762]) ).

fof(f6762,plain,
    ! [X0] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
      | c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
    inference(forward_demodulation,[],[f6761,f5628]) ).

fof(f5628,plain,
    ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) = X0,
    inference(cnf_transformation,[],[f1956]) ).

fof(f1956,plain,
    ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) = X0,
    inference(rectify,[],[f114]) ).

fof(f114,axiom,
    ! [X17] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X17) = X17,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).

fof(f6761,plain,
    ! [X0] :
      ( 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)) = X0
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(forward_demodulation,[],[f6760,f4806]) ).

fof(f4806,plain,
    ! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),
    inference(cnf_transformation,[],[f2142]) ).

fof(f2142,plain,
    ! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),
    inference(rectify,[],[f166]) ).

fof(f166,axiom,
    ! [X23,X17] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X23,X17) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X23),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__commute) ).

fof(f6760,plain,
    ! [X0] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
      | c_Groups_Ozero__class_Ozero(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,[],[f6759,f5628]) ).

fof(f6759,plain,
    ! [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_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
    inference(forward_demodulation,[],[f6758,f5867]) ).

fof(f5867,plain,
    ! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(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(definition_unfolding,[],[f4414,f4877,f4877]) ).

fof(f4877,plain,
    ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) = c_Nat_OSuc(X0),
    inference(cnf_transformation,[],[f1210]) ).

fof(f1210,plain,
    ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) = c_Nat_OSuc(X0),
    inference(rectify,[],[f326]) ).

fof(f326,axiom,
    ! [X17] : c_Nat_OSuc(X17) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X17),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).

fof(f4414,plain,
    ! [X0,X1] : c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Nat_OSuc(X1)),
    inference(cnf_transformation,[],[f3462]) ).

fof(f3462,plain,
    ! [X0,X1] : c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Nat_OSuc(X1)),
    inference(rectify,[],[f1328]) ).

fof(f1328,plain,
    ! [X1,X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)),
    inference(rectify,[],[f125]) ).

fof(f125,axiom,
    ! [X17,X23] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X23,c_Nat_OSuc(X17)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X23,X17)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc__right) ).

fof(f6758,plain,
    ! [X0] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
      | c_Groups_Ozero__class_Ozero(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,[],[f5945,f4806]) ).

fof(f5945,plain,
    ! [X0] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
      | c_Groups_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 ),
    inference(definition_unfolding,[],[f5248,f4877,f4877,f4877]) ).

fof(f5248,plain,
    ! [X0] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
      | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0 ),
    inference(cnf_transformation,[],[f2532]) ).

fof(f2532,plain,
    ! [X0] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
      | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0 ),
    inference(flattening,[],[f2531]) ).

fof(f2531,plain,
    ! [X0] :
      ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
    inference(ennf_transformation,[],[f2185]) ).

fof(f2185,plain,
    ! [X0] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
     => ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) ),
    inference(rectify,[],[f654]) ).

fof(f654,axiom,
    ! [X19] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
     => ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X19
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X19 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__lt__two__imp__zero__or__one) ).

fof(f25228,plain,
    ! [X6] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK2(X6,X6),X6)
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X6 ),
    inference(resolution,[],[f5892,f6091]) ).

fof(f6091,plain,
    ! [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),X1)),
    inference(equality_resolution,[],[f5937]) ).

fof(f5937,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),X0))
      | X0 != X1 ),
    inference(definition_unfolding,[],[f5096,f4877]) ).

fof(f5096,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
      | X0 != X1 ),
    inference(cnf_transformation,[],[f3905]) ).

fof(f3905,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
        | X0 = X1
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
        | ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
          & X0 != X1 ) ) ),
    inference(flattening,[],[f3904]) ).

fof(f3904,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
        | X0 = X1
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
        | ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
          & X0 != X1 ) ) ),
    inference(nnf_transformation,[],[f2184]) ).

fof(f2184,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
        | X0 = X1 )
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) ),
    inference(rectify,[],[f491]) ).

fof(f491,axiom,
    ! [X18,X43] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X43,X18)
        | X18 = X43 )
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X43,c_Nat_OSuc(X18)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq) ).

fof(f5892,plain,
    ! [X0,X1] :
      ( ~ 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),X1))
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK2(X0,X1),X1)
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
    inference(definition_unfolding,[],[f4698,f4877]) ).

fof(f4698,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK2(X0,X1),X1)
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1)) ),
    inference(cnf_transformation,[],[f3651]) ).

fof(f3651,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1))
        | ( ! [X2] :
              ( c_Nat_OSuc(X2) != X0
              | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) )
          & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) )
      & ( ( c_Nat_OSuc(sK2(X0,X1)) = X0
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK2(X0,X1),X1) )
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f3649,f3650]) ).

fof(f3650,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( c_Nat_OSuc(X3) = X0
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X1) )
     => ( c_Nat_OSuc(sK2(X0,X1)) = X0
        & c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK2(X0,X1),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f3649,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1))
        | ( ! [X2] :
              ( c_Nat_OSuc(X2) != X0
              | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) )
          & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) )
      & ( ? [X3] :
            ( c_Nat_OSuc(X3) = X0
            & c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X1) )
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1)) ) ),
    inference(rectify,[],[f3648]) ).

fof(f3648,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1))
        | ( ! [X2] :
              ( c_Nat_OSuc(X2) != X0
              | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) )
          & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) )
      & ( ? [X2] :
            ( c_Nat_OSuc(X2) = X0
            & c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) )
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1)) ) ),
    inference(flattening,[],[f3647]) ).

fof(f3647,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1))
        | ( ! [X2] :
              ( c_Nat_OSuc(X2) != X0
              | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) )
          & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) )
      & ( ? [X2] :
            ( c_Nat_OSuc(X2) = X0
            & c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) )
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1)) ) ),
    inference(nnf_transformation,[],[f2194]) ).

fof(f2194,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1))
    <=> ( ? [X2] :
            ( c_Nat_OSuc(X2) = X0
            & c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) )
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) ),
    inference(rectify,[],[f555]) ).

fof(f555,axiom,
    ! [X43,X18] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X43,c_Nat_OSuc(X18))
    <=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X43
        | ? [X64] :
            ( c_Nat_OSuc(X64) = X43
            & c_Orderings_Oord__class_Oless(tc_Nat_Onat,X64,X18) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq__0__disj) ).

fof(f25314,plain,
    ( spl24_527
    | ~ spl24_518 ),
    inference(avatar_split_clause,[],[f25262,f25246,f25311]) ).

fof(f25311,plain,
    ( spl24_527
  <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK2(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_527])]) ).

fof(f25246,plain,
    ( spl24_518
  <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK2(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_518])]) ).

fof(f25262,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK2(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ spl24_518 ),
    inference(resolution,[],[f25248,f14552]) ).

fof(f14552,plain,
    ! [X4] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,c_Groups_Oone__class_Oone(tc_Nat_Onat))
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(superposition,[],[f5991,f4540]) ).

fof(f4540,plain,
    ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
    inference(cnf_transformation,[],[f2216]) ).

fof(f2216,plain,
    ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
    inference(rectify,[],[f115]) ).

fof(f115,axiom,
    ! [X23] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X23,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X23,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).

fof(f5991,plain,
    ! [X0,X1] :
      ( ~ 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),X1))
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
    inference(definition_unfolding,[],[f5685,f4877]) ).

fof(f5685,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1)) ),
    inference(cnf_transformation,[],[f4269]) ).

fof(f4269,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
        | ~ 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__eq(tc_Nat_Onat,X0,X1) ) ),
    inference(nnf_transformation,[],[f1384]) ).

fof(f1384,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1)) ),
    inference(rectify,[],[f566]) ).

fof(f566,axiom,
    ! [X43,X18] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X43,X18)
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X43,c_Nat_OSuc(X18)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq__le) ).

fof(f25248,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK2(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ spl24_518 ),
    inference(avatar_component_clause,[],[f25246]) ).

fof(f25309,plain,
    ( spl24_524
    | ~ spl24_518 ),
    inference(avatar_split_clause,[],[f25264,f25246,f25295]) ).

fof(f25295,plain,
    ( spl24_524
  <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = sK2(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_524])]) ).

fof(f25264,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = sK2(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ spl24_518 ),
    inference(resolution,[],[f25248,f6605]) ).

fof(f6605,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(backward_demodulation,[],[f6397,f5628]) ).

fof(f6397,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(forward_demodulation,[],[f5942,f4806]) ).

fof(f5942,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_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(definition_unfolding,[],[f5143,f4877]) ).

fof(f5143,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,[],[f3933]) ).

fof(f3933,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))) )
      & ( 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(nnf_transformation,[],[f2076]) ).

fof(f2076,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(rectify,[],[f554]) ).

fof(f554,axiom,
    ! [X18] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X18 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc0) ).

fof(f25308,plain,
    ( spl24_526
    | ~ spl24_518 ),
    inference(avatar_split_clause,[],[f25266,f25246,f25305]) ).

fof(f25305,plain,
    ( spl24_526
  <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK2(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_526])]) ).

fof(f25266,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK2(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ spl24_518 ),
    inference(resolution,[],[f25248,f4632]) ).

fof(f4632,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
    inference(cnf_transformation,[],[f3601]) ).

fof(f3601,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
        | X0 = X1
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
        | ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
          & X0 != X1 ) ) ),
    inference(rectify,[],[f3600]) ).

fof(f3600,plain,
    ! [X1,X0] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
        | X0 = X1
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
        | ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
          & X0 != X1 ) ) ),
    inference(flattening,[],[f3599]) ).

fof(f3599,plain,
    ! [X1,X0] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
        | X0 = X1
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
        | ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
          & X0 != X1 ) ) ),
    inference(nnf_transformation,[],[f2052]) ).

fof(f2052,plain,
    ! [X1,X0] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
        | X0 = X1 )
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
    inference(rectify,[],[f505]) ).

fof(f505,axiom,
    ! [X18,X43] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X43,X18)
        | X18 = X43 )
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X43,X18) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__eq__less__or__eq) ).

fof(f25303,plain,
    ( ~ spl24_525
    | ~ spl24_351
    | ~ spl24_518 ),
    inference(avatar_split_clause,[],[f25261,f25246,f15325,f25300]) ).

fof(f25300,plain,
    ( spl24_525
  <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),sK2(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_525])]) ).

fof(f15325,plain,
    ( spl24_351
  <=> ! [X11] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X11)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X11,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_351])]) ).

fof(f25261,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),sK2(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | ~ spl24_351
    | ~ spl24_518 ),
    inference(resolution,[],[f25248,f15326]) ).

fof(f15326,plain,
    ( ! [X11] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X11,c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X11) )
    | ~ spl24_351 ),
    inference(avatar_component_clause,[],[f15325]) ).

fof(f25298,plain,
    ( spl24_524
    | ~ spl24_518 ),
    inference(avatar_split_clause,[],[f25293,f25246,f25295]) ).

fof(f25293,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = sK2(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ spl24_518 ),
    inference(forward_demodulation,[],[f25269,f6813]) ).

fof(f6813,plain,
    ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(forward_demodulation,[],[f6812,f5628]) ).

fof(f6812,plain,
    ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
    inference(forward_demodulation,[],[f5923,f4806]) ).

fof(f5923,plain,
    ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definition_unfolding,[],[f5018,f4877]) ).

fof(f5018,plain,
    ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(cnf_transformation,[],[f1307]) ).

fof(f1307,plain,
    ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(rectify,[],[f909]) ).

fof(f909,axiom,
    ! [X23] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X23,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__1) ).

fof(f25269,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,sK2(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = sK2(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ spl24_518 ),
    inference(resolution,[],[f25248,f5322]) ).

fof(f5322,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
      | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,X1) = X0 ),
    inference(cnf_transformation,[],[f4016]) ).

fof(f4016,plain,
    ! [X0,X1] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,X1) = X0
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
    inference(rectify,[],[f2565]) ).

fof(f2565,plain,
    ! [X1,X0] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0) = X1
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
    inference(ennf_transformation,[],[f1926]) ).

fof(f1926,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
     => c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0) = X1 ),
    inference(rectify,[],[f895]) ).

fof(f895,axiom,
    ! [X17,X23] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X23,X17)
     => c_Divides_Odiv__class_Omod(tc_Nat_Onat,X23,X17) = X23 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__less) ).

fof(f25292,plain,
    ( spl24_523
    | ~ spl24_518 ),
    inference(avatar_split_clause,[],[f25276,f25246,f25289]) ).

fof(f25289,plain,
    ( spl24_523
  <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK2(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_523])]) ).

fof(f25276,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK2(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ spl24_518 ),
    inference(resolution,[],[f25248,f5982]) ).

fof(f5982,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1),X0) ),
    inference(definition_unfolding,[],[f5574,f4877]) ).

fof(f5574,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
    inference(cnf_transformation,[],[f3159]) ).

fof(f3159,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
    inference(ennf_transformation,[],[f1425]) ).

fof(f1425,plain,
    ! [X1,X0] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X0) ),
    inference(rectify,[],[f563]) ).

fof(f563,axiom,
    ! [X17,X23] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X23,X17)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X23),X17) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__leI) ).

fof(f25287,plain,
    ( ~ spl24_522
    | ~ spl24_518 ),
    inference(avatar_split_clause,[],[f25274,f25246,f25284]) ).

fof(f25284,plain,
    ( spl24_522
  <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK2(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_522])]) ).

fof(f25274,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK2(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | ~ spl24_518 ),
    inference(resolution,[],[f25248,f5956]) ).

fof(f5956,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,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)) ),
    inference(definition_unfolding,[],[f5364,f4877]) ).

fof(f5364,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,[],[f4043]) ).

fof(f4043,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(rectify,[],[f4042]) ).

fof(f4042,plain,
    ! [X1,X0] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ) ),
    inference(nnf_transformation,[],[f1865]) ).

fof(f1865,plain,
    ! [X1,X0] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) ),
    inference(rectify,[],[f492]) ).

fof(f492,axiom,
    ! [X43,X18] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,c_Nat_OSuc(X43))
    <=> ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X43,X18) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__eq) ).

fof(f25282,plain,
    ( spl24_521
    | ~ spl24_518 ),
    inference(avatar_split_clause,[],[f25275,f25246,f25279]) ).

fof(f25279,plain,
    ( spl24_521
  <=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK2(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),sK14(sK2(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_521])]) ).

fof(f25275,plain,
    ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK2(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),sK14(sK2(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | ~ spl24_518 ),
    inference(resolution,[],[f25248,f5962]) ).

fof(f5962,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,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,sK14(X0,X1))) = X1 ),
    inference(definition_unfolding,[],[f5387,f4877]) ).

fof(f5387,plain,
    ! [X0,X1] :
      ( c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,sK14(X0,X1))) = X1
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
    inference(cnf_transformation,[],[f4061]) ).

fof(f4061,plain,
    ! [X0,X1] :
      ( ( c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,sK14(X0,X1))) = X1
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
        | ! [X3] : c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3)) != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f4059,f4060]) ).

fof(f4060,plain,
    ! [X0,X1] :
      ( ? [X2] : c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2)) = X1
     => c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,sK14(X0,X1))) = X1 ),
    introduced(choice_axiom,[]) ).

fof(f4059,plain,
    ! [X0,X1] :
      ( ( ? [X2] : c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2)) = X1
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
        | ! [X3] : c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3)) != X1 ) ),
    inference(rectify,[],[f4058]) ).

fof(f4058,plain,
    ! [X0,X1] :
      ( ( ? [X2] : c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2)) = X1
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
        | ! [X2] : c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2)) != X1 ) ),
    inference(nnf_transformation,[],[f1742]) ).

fof(f1742,plain,
    ! [X0,X1] :
      ( ? [X2] : c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2)) = X1
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
    inference(rectify,[],[f560]) ).

fof(f560,axiom,
    ! [X43,X18] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X43,X18)
    <=> ? [X57] : c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X43,X57)) = X18 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__iff__Suc__add) ).

fof(f25260,plain,
    ( spl24_520
    | ~ spl24_114
    | ~ spl24_112 ),
    inference(avatar_split_clause,[],[f25250,f6888,f6898,f25258]) ).

fof(f25258,plain,
    ( spl24_520
  <=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_520])]) ).

fof(f6898,plain,
    ( spl24_114
  <=> class_Rings_Osemiring__0(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_114])]) ).

fof(f6888,plain,
    ( spl24_112
  <=> class_Power_Opower(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_112])]) ).

fof(f25250,plain,
    ( ! [X0] :
        ( ~ class_Rings_Osemiring__0(tc_Int_Oint)
        | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)) )
    | ~ spl24_112 ),
    inference(resolution,[],[f5901,f6890]) ).

fof(f6890,plain,
    ( class_Power_Opower(tc_Int_Oint)
    | ~ spl24_112 ),
    inference(avatar_component_clause,[],[f6888]) ).

fof(f5901,plain,
    ! [X0,X1] :
      ( ~ class_Power_Opower(X0)
      | ~ class_Rings_Osemiring__0(X0)
      | c_Groups_Ozero__class_Ozero(X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_Groups_Ozero__class_Ozero(X0)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)) ),
    inference(definition_unfolding,[],[f4787,f4877]) ).

fof(f4787,plain,
    ! [X0,X1] :
      ( ~ class_Power_Opower(X0)
      | c_Groups_Ozero__class_Ozero(X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_Groups_Ozero__class_Ozero(X0)),c_Nat_OSuc(X1))
      | ~ class_Rings_Osemiring__0(X0) ),
    inference(cnf_transformation,[],[f3704]) ).

fof(f3704,plain,
    ! [X0,X1] :
      ( ~ class_Power_Opower(X0)
      | c_Groups_Ozero__class_Ozero(X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_Groups_Ozero__class_Ozero(X0)),c_Nat_OSuc(X1))
      | ~ class_Rings_Osemiring__0(X0) ),
    inference(rectify,[],[f3223]) ).

fof(f3223,plain,
    ! [X1,X0] :
      ( ~ class_Power_Opower(X1)
      | c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),c_Nat_OSuc(X0))
      | ~ class_Rings_Osemiring__0(X1) ),
    inference(flattening,[],[f3222]) ).

fof(f3222,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),c_Nat_OSuc(X0))
      | ~ class_Power_Opower(X1)
      | ~ class_Rings_Osemiring__0(X1) ),
    inference(ennf_transformation,[],[f1863]) ).

fof(f1863,plain,
    ! [X0,X1] :
      ( ( class_Power_Opower(X1)
        & class_Rings_Osemiring__0(X1) )
     => c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),c_Nat_OSuc(X0)) ),
    inference(rectify,[],[f734]) ).

fof(f734,axiom,
    ! [X17,X4] :
      ( ( class_Power_Opower(X4)
        & class_Rings_Osemiring__0(X4) )
     => c_Groups_Ozero__class_Ozero(X4) = hAPP(hAPP(c_Power_Opower__class_Opower(X4),c_Groups_Ozero__class_Ozero(X4)),c_Nat_OSuc(X17)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__0__Suc) ).

fof(f25256,plain,
    ( ~ spl24_25
    | spl24_519
    | ~ spl24_120 ),
    inference(avatar_split_clause,[],[f25251,f6936,f25254,f6340]) ).

fof(f6340,plain,
    ( spl24_25
  <=> class_Rings_Osemiring__0(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_25])]) ).

fof(f25254,plain,
    ( spl24_519
  <=> ! [X1] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_519])]) ).

fof(f6936,plain,
    ( spl24_120
  <=> class_Power_Opower(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_120])]) ).

fof(f25251,plain,
    ( ! [X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1))
        | ~ class_Rings_Osemiring__0(tc_Nat_Onat) )
    | ~ spl24_120 ),
    inference(resolution,[],[f5901,f6938]) ).

fof(f6938,plain,
    ( class_Power_Opower(tc_Nat_Onat)
    | ~ spl24_120 ),
    inference(avatar_component_clause,[],[f6936]) ).

fof(f25249,plain,
    ( spl24_518
    | spl24_137
    | ~ spl24_111 ),
    inference(avatar_split_clause,[],[f25232,f6883,f7320,f25246]) ).

fof(f7320,plain,
    ( spl24_137
  <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_137])]) ).

fof(f6883,plain,
    ( spl24_111
  <=> 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,[spl24_111])]) ).

fof(f25232,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK2(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ spl24_111 ),
    inference(resolution,[],[f5892,f11292]) ).

fof(f11292,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)))
    | ~ spl24_111 ),
    inference(forward_demodulation,[],[f11291,f4540]) ).

fof(f11291,plain,
    ( ! [X0] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,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)))
    | ~ spl24_111 ),
    inference(resolution,[],[f5489,f6885]) ).

fof(f6885,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))
    | ~ spl24_111 ),
    inference(avatar_component_clause,[],[f6883]) ).

fof(f5489,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,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) ),
    inference(cnf_transformation,[],[f4140]) ).

fof(f4140,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,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0) ) ),
    inference(rectify,[],[f4139]) ).

fof(f4139,plain,
    ! [X2,X1,X0] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X2)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X2) ) ),
    inference(nnf_transformation,[],[f1960]) ).

fof(f1960,plain,
    ! [X2,X1,X0] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X2)
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) ),
    inference(rectify,[],[f499]) ).

fof(f499,axiom,
    ! [X43,X44,X18] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X43,X18)
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X44,X43),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X44,X18)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel__less) ).

fof(f25215,plain,
    ( spl24_514
    | ~ spl24_517
    | ~ spl24_500 ),
    inference(avatar_split_clause,[],[f25188,f24583,f25212,f25196]) ).

fof(f25196,plain,
    ( spl24_514
  <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_514])]) ).

fof(f25188,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ spl24_500 ),
    inference(resolution,[],[f24585,f5243]) ).

fof(f24585,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ spl24_500 ),
    inference(avatar_component_clause,[],[f24583]) ).

fof(f25210,plain,
    ( spl24_516
    | ~ spl24_500 ),
    inference(avatar_split_clause,[],[f25205,f24583,f25207]) ).

fof(f25207,plain,
    ( spl24_516
  <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_516])]) ).

fof(f25205,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    | ~ spl24_500 ),
    inference(forward_demodulation,[],[f25204,f7545]) ).

fof(f7545,plain,
    ! [X6,X4,X5] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X6,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5,X4)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X6,X5)),
    inference(superposition,[],[f5388,f5830]) ).

fof(f25204,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
    | ~ spl24_500 ),
    inference(forward_demodulation,[],[f25203,f5388]) ).

fof(f25203,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
    | ~ spl24_500 ),
    inference(forward_demodulation,[],[f25191,f5830]) ).

fof(f25191,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ spl24_500 ),
    inference(resolution,[],[f24585,f5678]) ).

fof(f25202,plain,
    ( spl24_514
    | spl24_515
    | ~ spl24_500 ),
    inference(avatar_split_clause,[],[f25194,f24583,f25200,f25196]) ).

fof(f25200,plain,
    ( spl24_515
  <=> ! [X5] : c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_515])]) ).

fof(f25194,plain,
    ( ! [X5] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5)))
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
    | ~ spl24_500 ),
    inference(forward_demodulation,[],[f25193,f5810]) ).

fof(f25193,plain,
    ( ! [X5] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X5)) )
    | ~ spl24_500 ),
    inference(resolution,[],[f24585,f7381]) ).

fof(f25150,plain,
    ( ~ spl24_5
    | spl24_513 ),
    inference(avatar_split_clause,[],[f25146,f25148,f6228]) ).

fof(f6228,plain,
    ( spl24_5
  <=> class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_5])]) ).

fof(f25148,plain,
    ( spl24_513
  <=> ! [X35,X34,X33,X32] :
        ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(c_Polynomial_Opoly(tc_Nat_Onat,c_Polynomial_Omonom(tc_Nat_Onat,X32,X34)),X33),hAPP(c_Polynomial_Opoly(tc_Nat_Onat,c_Polynomial_Omonom(tc_Nat_Onat,X32,X35)),X33))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X35) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_513])]) ).

fof(f25146,plain,
    ! [X34,X35,X32,X33] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(c_Polynomial_Opoly(tc_Nat_Onat,c_Polynomial_Omonom(tc_Nat_Onat,X32,X34)),X33),hAPP(c_Polynomial_Opoly(tc_Nat_Onat,c_Polynomial_Omonom(tc_Nat_Onat,X32,X35)),X33))
      | ~ class_Rings_Ocomm__semiring__1(tc_Nat_Onat)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X35) ),
    inference(forward_subsumption_demodulation,[],[f25145,f5620]) ).

fof(f5620,plain,
    ! [X2,X3,X0,X1] :
      ( hAPP(c_Polynomial_Opoly(X1,c_Polynomial_Omonom(X1,X0,X2)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X2))
      | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(cnf_transformation,[],[f4226]) ).

fof(f4226,plain,
    ! [X0,X1,X2,X3] :
      ( ~ class_Rings_Ocomm__semiring__1(X1)
      | hAPP(c_Polynomial_Opoly(X1,c_Polynomial_Omonom(X1,X0,X2)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X2)) ),
    inference(rectify,[],[f3386]) ).

fof(f3386,plain,
    ! [X0,X2,X3,X1] :
      ( ~ class_Rings_Ocomm__semiring__1(X2)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X3)) = hAPP(c_Polynomial_Opoly(X2,c_Polynomial_Omonom(X2,X0,X3)),X1) ),
    inference(ennf_transformation,[],[f1292]) ).

fof(f1292,plain,
    ! [X1,X2,X0,X3] :
      ( class_Rings_Ocomm__semiring__1(X2)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X3)) = hAPP(c_Polynomial_Opoly(X2,c_Polynomial_Omonom(X2,X0,X3)),X1) ),
    inference(rectify,[],[f697]) ).

fof(f697,axiom,
    ! [X5,X19,X4,X17] :
      ( class_Rings_Ocomm__semiring__1(X4)
     => hAPP(c_Polynomial_Opoly(X4,c_Polynomial_Omonom(X4,X5,X17)),X19) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X19),X17)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__monom) ).

fof(f25145,plain,
    ! [X34,X35,X32,X33] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X35)
      | ~ class_Rings_Ocomm__semiring__1(tc_Nat_Onat)
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X32),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X33),X34)),hAPP(c_Polynomial_Opoly(tc_Nat_Onat,c_Polynomial_Omonom(tc_Nat_Onat,X32,X35)),X33)) ),
    inference(forward_subsumption_demodulation,[],[f25128,f5620]) ).

fof(f25128,plain,
    ! [X34,X35,X32,X33] :
      ( ~ class_Rings_Ocomm__semiring__1(tc_Nat_Onat)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X35)
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X32),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X33),X34)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X32),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X33),X35))) ),
    inference(resolution,[],[f5259,f5448]) ).

fof(f5448,plain,
    ! [X2,X3,X0,X1] :
      ( c_Rings_Odvd__class_Odvd(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X3))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X3)
      | ~ class_Rings_Ocomm__semiring__1(X2) ),
    inference(cnf_transformation,[],[f4108]) ).

fof(f4108,plain,
    ! [X0,X1,X2,X3] :
      ( c_Rings_Odvd__class_Odvd(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X3))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X3)
      | ~ class_Rings_Ocomm__semiring__1(X2) ),
    inference(rectify,[],[f2464]) ).

fof(f2464,plain,
    ! [X0,X2,X3,X1] :
      ( c_Rings_Odvd__class_Odvd(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
      | ~ class_Rings_Ocomm__semiring__1(X3) ),
    inference(flattening,[],[f2463]) ).

fof(f2463,plain,
    ! [X2,X1,X3,X0] :
      ( c_Rings_Odvd__class_Odvd(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
      | ~ class_Rings_Ocomm__semiring__1(X3) ),
    inference(ennf_transformation,[],[f1467]) ).

fof(f1467,plain,
    ! [X2,X1,X3,X0] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
       => c_Rings_Odvd__class_Odvd(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1)) ) ),
    inference(rectify,[],[f742]) ).

fof(f742,axiom,
    ! [X23,X17,X5,X4] :
      ( class_Rings_Ocomm__semiring__1(X4)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X23,X17)
       => c_Rings_Odvd__class_Odvd(X4,hAPP(hAPP(c_Power_Opower__class_Opower(X4),X5),X23),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X5),X17)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__power__dvd) ).

fof(f5259,plain,
    ! [X2,X0,X1] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,X1)
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)) ),
    inference(cnf_transformation,[],[f3979]) ).

fof(f3979,plain,
    ! [X0,X1,X2] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1))
        | ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,X1)
          & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2 ) )
      & ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,X1)
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)) ) ),
    inference(rectify,[],[f3978]) ).

fof(f3978,plain,
    ! [X2,X1,X0] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
        | ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
          & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) )
      & ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)) ) ),
    inference(flattening,[],[f3977]) ).

fof(f3977,plain,
    ! [X2,X1,X0] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
        | ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
          & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) )
      & ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)) ) ),
    inference(nnf_transformation,[],[f1915]) ).

fof(f1915,plain,
    ! [X2,X1,X0] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
    <=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) ),
    inference(rectify,[],[f625]) ).

fof(f625,axiom,
    ! [X44,X18,X43] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X44),X43),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X44),X18))
    <=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X44
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X43,X18) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__dvd__cancel__disj) ).

fof(f25142,plain,
    ( ~ spl24_5
    | spl24_512 ),
    inference(avatar_split_clause,[],[f25138,f25140,f6228]) ).

fof(f25140,plain,
    ( spl24_512
  <=> ! [X31,X29,X27,X28,X30] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X28,X30)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29,X31)
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(c_Polynomial_Opoly(tc_Nat_Onat,c_Polynomial_Omonom(tc_Nat_Onat,X27,X29)),X28),hAPP(c_Polynomial_Opoly(tc_Nat_Onat,c_Polynomial_Omonom(tc_Nat_Onat,X27,X31)),X30)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_512])]) ).

fof(f25138,plain,
    ! [X31,X28,X29,X27,X30] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X28,X30)
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(c_Polynomial_Opoly(tc_Nat_Onat,c_Polynomial_Omonom(tc_Nat_Onat,X27,X29)),X28),hAPP(c_Polynomial_Opoly(tc_Nat_Onat,c_Polynomial_Omonom(tc_Nat_Onat,X27,X31)),X30))
      | ~ class_Rings_Ocomm__semiring__1(tc_Nat_Onat)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29,X31) ),
    inference(forward_subsumption_demodulation,[],[f25137,f5620]) ).

fof(f25137,plain,
    ! [X31,X28,X29,X27,X30] :
      ( ~ class_Rings_Ocomm__semiring__1(tc_Nat_Onat)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X28,X30)
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X27),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X28),X29)),hAPP(c_Polynomial_Opoly(tc_Nat_Onat,c_Polynomial_Omonom(tc_Nat_Onat,X27,X31)),X30))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29,X31) ),
    inference(forward_subsumption_demodulation,[],[f25127,f5620]) ).

fof(f25127,plain,
    ! [X31,X28,X29,X27,X30] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29,X31)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X28,X30)
      | ~ class_Rings_Ocomm__semiring__1(tc_Nat_Onat)
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X27),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X28),X29)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X27),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X30),X31))) ),
    inference(resolution,[],[f5259,f5752]) ).

fof(f5752,plain,
    ! [X2,X3,X0,X1,X4] :
      ( c_Rings_Odvd__class_Odvd(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X1))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
      | ~ class_Rings_Ocomm__semiring__1(X3)
      | ~ c_Rings_Odvd__class_Odvd(X3,X0,X4) ),
    inference(cnf_transformation,[],[f4319]) ).

fof(f4319,plain,
    ! [X0,X1,X2,X3,X4] :
      ( c_Rings_Odvd__class_Odvd(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X1))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
      | ~ c_Rings_Odvd__class_Odvd(X3,X0,X4)
      | ~ class_Rings_Ocomm__semiring__1(X3) ),
    inference(rectify,[],[f2709]) ).

fof(f2709,plain,
    ! [X2,X3,X4,X1,X0] :
      ( c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),X3))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
      | ~ c_Rings_Odvd__class_Odvd(X1,X2,X0)
      | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(flattening,[],[f2708]) ).

fof(f2708,plain,
    ! [X1,X2,X3,X0,X4] :
      ( c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),X3))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
      | ~ c_Rings_Odvd__class_Odvd(X1,X2,X0)
      | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(ennf_transformation,[],[f2219]) ).

fof(f2219,plain,
    ! [X1,X2,X3,X0,X4] :
      ( class_Rings_Ocomm__semiring__1(X1)
     => ( c_Rings_Odvd__class_Odvd(X1,X2,X0)
       => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
         => c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),X3)) ) ) ),
    inference(rectify,[],[f741]) ).

fof(f741,axiom,
    ! [X35,X4,X19,X23,X17] :
      ( class_Rings_Ocomm__semiring__1(X4)
     => ( c_Rings_Odvd__class_Odvd(X4,X19,X35)
       => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X23)
         => c_Rings_Odvd__class_Odvd(X4,hAPP(hAPP(c_Power_Opower__class_Opower(X4),X19),X17),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X35),X23)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__power__le) ).

fof(f25135,plain,
    ( ~ spl24_5
    | spl24_511 ),
    inference(avatar_split_clause,[],[f25131,f25133,f6228]) ).

fof(f25133,plain,
    ( spl24_511
  <=> ! [X24,X23,X25,X26] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X24,X26)
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(c_Polynomial_Opoly(tc_Nat_Onat,c_Polynomial_Omonom(tc_Nat_Onat,X23,X25)),X24),hAPP(c_Polynomial_Opoly(tc_Nat_Onat,c_Polynomial_Omonom(tc_Nat_Onat,X23,X25)),X26)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_511])]) ).

fof(f25131,plain,
    ! [X26,X24,X25,X23] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X24,X26)
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(c_Polynomial_Opoly(tc_Nat_Onat,c_Polynomial_Omonom(tc_Nat_Onat,X23,X25)),X24),hAPP(c_Polynomial_Opoly(tc_Nat_Onat,c_Polynomial_Omonom(tc_Nat_Onat,X23,X25)),X26))
      | ~ class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ),
    inference(forward_subsumption_demodulation,[],[f25130,f5620]) ).

fof(f25130,plain,
    ! [X26,X24,X25,X23] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X24,X26)
      | ~ class_Rings_Ocomm__semiring__1(tc_Nat_Onat)
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X24),X25)),hAPP(c_Polynomial_Opoly(tc_Nat_Onat,c_Polynomial_Omonom(tc_Nat_Onat,X23,X25)),X26)) ),
    inference(forward_subsumption_demodulation,[],[f25126,f5620]) ).

fof(f25126,plain,
    ! [X26,X24,X25,X23] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X24,X26)
      | ~ class_Rings_Ocomm__semiring__1(tc_Nat_Onat)
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X24),X25)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X26),X25))) ),
    inference(resolution,[],[f5259,f4750]) ).

fof(f4750,plain,
    ! [X2,X3,X0,X1] :
      ( c_Rings_Odvd__class_Odvd(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0))
      | ~ class_Rings_Ocomm__semiring__1(X2)
      | ~ c_Rings_Odvd__class_Odvd(X2,X3,X1) ),
    inference(cnf_transformation,[],[f3683]) ).

fof(f3683,plain,
    ! [X0,X1,X2,X3] :
      ( ~ c_Rings_Odvd__class_Odvd(X2,X3,X1)
      | ~ class_Rings_Ocomm__semiring__1(X2)
      | c_Rings_Odvd__class_Odvd(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) ),
    inference(rectify,[],[f2618]) ).

fof(f2618,plain,
    ! [X1,X2,X3,X0] :
      ( ~ c_Rings_Odvd__class_Odvd(X3,X0,X2)
      | ~ class_Rings_Ocomm__semiring__1(X3)
      | c_Rings_Odvd__class_Odvd(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1)) ),
    inference(flattening,[],[f2617]) ).

fof(f2617,plain,
    ! [X1,X3,X2,X0] :
      ( c_Rings_Odvd__class_Odvd(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1))
      | ~ c_Rings_Odvd__class_Odvd(X3,X0,X2)
      | ~ class_Rings_Ocomm__semiring__1(X3) ),
    inference(ennf_transformation,[],[f1529]) ).

fof(f1529,plain,
    ! [X1,X3,X2,X0] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => ( c_Rings_Odvd__class_Odvd(X3,X0,X2)
       => c_Rings_Odvd__class_Odvd(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1)) ) ),
    inference(rectify,[],[f724]) ).

fof(f724,axiom,
    ! [X19,X17,X35,X4] :
      ( class_Rings_Ocomm__semiring__1(X4)
     => ( c_Rings_Odvd__class_Odvd(X4,X19,X35)
       => c_Rings_Odvd__class_Odvd(X4,hAPP(hAPP(c_Power_Opower__class_Opower(X4),X19),X17),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X35),X17)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__power__same) ).

fof(f25098,plain,
    ( spl24_510
    | ~ spl24_1
    | ~ spl24_454 ),
    inference(avatar_split_clause,[],[f25093,f20747,f6208,f25095]) ).

fof(f25095,plain,
    ( spl24_510
  <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_510])]) ).

fof(f6208,plain,
    ( spl24_1
  <=> 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,[spl24_1])]) ).

fof(f25093,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    | ~ spl24_1
    | ~ spl24_454 ),
    inference(forward_demodulation,[],[f25092,f7545]) ).

fof(f25092,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
    | ~ spl24_1
    | ~ spl24_454 ),
    inference(forward_demodulation,[],[f25091,f5388]) ).

fof(f25091,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
    | ~ spl24_1
    | ~ spl24_454 ),
    inference(forward_demodulation,[],[f25055,f5830]) ).

fof(f25055,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ spl24_1
    | ~ spl24_454 ),
    inference(resolution,[],[f20749,f7754]) ).

fof(f7754,plain,
    ( ! [X0] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))) )
    | ~ spl24_1 ),
    inference(resolution,[],[f5761,f6210]) ).

fof(f6210,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ spl24_1 ),
    inference(avatar_component_clause,[],[f6208]) ).

fof(f25090,plain,
    ( spl24_509
    | ~ spl24_454 ),
    inference(avatar_split_clause,[],[f25089,f20747,f25068]) ).

fof(f25068,plain,
    ( spl24_509
  <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_509])]) ).

fof(f25089,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    | ~ spl24_454 ),
    inference(forward_demodulation,[],[f25088,f7545]) ).

fof(f25088,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
    | ~ spl24_454 ),
    inference(forward_demodulation,[],[f25087,f5388]) ).

fof(f25087,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
    | ~ spl24_454 ),
    inference(forward_demodulation,[],[f25062,f5830]) ).

fof(f25062,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,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_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ spl24_454 ),
    inference(resolution,[],[f20749,f5678]) ).

fof(f25071,plain,
    ( spl24_509
    | ~ spl24_454 ),
    inference(avatar_split_clause,[],[f25066,f20747,f25068]) ).

fof(f25066,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    | ~ spl24_454 ),
    inference(forward_demodulation,[],[f25065,f7545]) ).

fof(f25065,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
    | ~ spl24_454 ),
    inference(forward_demodulation,[],[f25044,f5388]) ).

fof(f25044,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
    | ~ spl24_454 ),
    inference(resolution,[],[f20749,f4618]) ).

fof(f25041,plain,
    ( spl24_498
    | spl24_508
    | ~ spl24_453 ),
    inference(avatar_split_clause,[],[f25037,f20742,f25039,f24473]) ).

fof(f24473,plain,
    ( spl24_498
  <=> c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_498])]) ).

fof(f25039,plain,
    ( spl24_508
  <=> ! [X6] : c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X6),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_508])]) ).

fof(f20742,plain,
    ( spl24_453
  <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_453])]) ).

fof(f25037,plain,
    ( ! [X6] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X6),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6)))
        | c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
    | ~ spl24_453 ),
    inference(forward_demodulation,[],[f25028,f5810]) ).

fof(f25028,plain,
    ( ! [X6] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X6),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X6))
        | c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
    | ~ spl24_453 ),
    inference(resolution,[],[f20744,f7381]) ).

fof(f20744,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ spl24_453 ),
    inference(avatar_component_clause,[],[f20742]) ).

fof(f25036,plain,
    ( spl24_507
    | ~ spl24_453 ),
    inference(avatar_split_clause,[],[f25031,f20742,f25033]) ).

fof(f25033,plain,
    ( spl24_507
  <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_507])]) ).

fof(f25031,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    | ~ spl24_453 ),
    inference(forward_demodulation,[],[f25030,f7545]) ).

fof(f25030,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
    | ~ spl24_453 ),
    inference(forward_demodulation,[],[f25029,f5388]) ).

fof(f25029,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
    | ~ spl24_453 ),
    inference(forward_demodulation,[],[f25026,f5830]) ).

fof(f25026,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ spl24_453 ),
    inference(resolution,[],[f20744,f5678]) ).

fof(f24983,plain,
    ( spl24_463
    | spl24_506
    | ~ spl24_5 ),
    inference(avatar_split_clause,[],[f24974,f6228,f24981,f21179]) ).

fof(f21179,plain,
    ( spl24_463
  <=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_463])]) ).

fof(f24981,plain,
    ( spl24_506
  <=> ! [X2] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X2),X2)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_506])]) ).

fof(f24974,plain,
    ( ! [X2] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X2),X2)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
    | ~ spl24_5 ),
    inference(superposition,[],[f4911,f7700]) ).

fof(f7700,plain,
    ( ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X0)
    | ~ spl24_5 ),
    inference(resolution,[],[f4539,f6230]) ).

fof(f6230,plain,
    ( class_Rings_Ocomm__semiring__1(tc_Nat_Onat)
    | ~ spl24_5 ),
    inference(avatar_component_clause,[],[f6228]) ).

fof(f4911,plain,
    ! [X0,X1] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1),X1)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
      | c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0 ),
    inference(cnf_transformation,[],[f3789]) ).

fof(f3789,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
      | ( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
          | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1),X1) )
        & ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1),X1)
          | c_Groups_Oone__class_Oone(tc_Nat_Onat) != X0 ) ) ),
    inference(nnf_transformation,[],[f3202]) ).

fof(f3202,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
      | ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
      <=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1),X1) ) ),
    inference(ennf_transformation,[],[f1424]) ).

fof(f1424,plain,
    ! [X1,X0] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
     => ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
      <=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1),X1) ) ),
    inference(rectify,[],[f629]) ).

fof(f629,axiom,
    ! [X18,X43] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X43)
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18),X43),X43)
      <=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = X18 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__cancel2) ).

fof(f24924,plain,
    ( ~ spl24_504
    | spl24_505
    | ~ spl24_5 ),
    inference(avatar_split_clause,[],[f24910,f6228,f24922,f24918]) ).

fof(f24918,plain,
    ( spl24_504
  <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,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_Oone__class_Oone(tc_Nat_Onat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_504])]) ).

fof(f24922,plain,
    ( spl24_505
  <=> ! [X2] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X2
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_505])]) ).

fof(f24910,plain,
    ( ! [X2] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X2
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,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_Oone__class_Oone(tc_Nat_Onat))) )
    | ~ spl24_5 ),
    inference(superposition,[],[f4418,f7700]) ).

fof(f4418,plain,
    ! [X0,X1] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0),X1)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
      | c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0 ),
    inference(cnf_transformation,[],[f3465]) ).

fof(f3465,plain,
    ! [X0,X1] :
      ( ( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
          | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0),X1) )
        & ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0),X1)
          | c_Groups_Oone__class_Oone(tc_Nat_Onat) != X0 ) )
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(rectify,[],[f3464]) ).

fof(f3464,plain,
    ! [X1,X0] :
      ( ( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
          | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1),X0) )
        & ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1),X0)
          | c_Groups_Oone__class_Oone(tc_Nat_Onat) != X1 ) )
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
    inference(nnf_transformation,[],[f2705]) ).

fof(f2705,plain,
    ! [X1,X0] :
      ( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
      <=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1),X0) )
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
    inference(ennf_transformation,[],[f1346]) ).

fof(f1346,plain,
    ! [X1,X0] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
     => ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
      <=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1),X0) ) ),
    inference(rectify,[],[f630]) ).

fof(f630,axiom,
    ! [X43,X18] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X43)
     => ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X18
      <=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X43),X18),X43) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__cancel1) ).

fof(f24916,plain,
    ( spl24_137
    | spl24_162 ),
    inference(avatar_split_clause,[],[f24914,f9335,f7320]) ).

fof(f9335,plain,
    ( spl24_162
  <=> ! [X1] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_162])]) ).

fof(f24914,plain,
    ! [X10] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X10)
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X10) ),
    inference(superposition,[],[f4418,f6045]) ).

fof(f6045,plain,
    ! [X1] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(equality_resolution,[],[f4694]) ).

fof(f4694,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ),
    inference(cnf_transformation,[],[f3645]) ).

fof(f3645,plain,
    ! [X0,X1] :
      ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) )
      & ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)
        | ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
          & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ) ) ),
    inference(flattening,[],[f3644]) ).

fof(f3644,plain,
    ! [X0,X1] :
      ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) )
      & ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)
        | ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
          & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ) ) ),
    inference(nnf_transformation,[],[f2177]) ).

fof(f2177,plain,
    ! [X0,X1] :
      ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
    <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) ),
    inference(rectify,[],[f120]) ).

fof(f120,axiom,
    ! [X18,X43] :
      ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X43
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X18 )
    <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X43),X18) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__is__0) ).

fof(f24866,plain,
    ( ~ spl24_503
    | ~ spl24_58
    | spl24_316 ),
    inference(avatar_split_clause,[],[f24846,f13772,f6521,f24863]) ).

fof(f24863,plain,
    ( spl24_503
  <=> c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_503])]) ).

fof(f13772,plain,
    ( spl24_316
  <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_316])]) ).

fof(f24846,plain,
    ( c_Groups_Oone__class_Oone(tc_Int_Oint) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ spl24_58
    | spl24_316 ),
    inference(resolution,[],[f24829,f13774]) ).

fof(f13774,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | spl24_316 ),
    inference(avatar_component_clause,[],[f13772]) ).

fof(f24829,plain,
    ( ! [X12] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X12)
        | c_Groups_Oone__class_Oone(tc_Int_Oint) != X12 )
    | ~ spl24_58 ),
    inference(forward_demodulation,[],[f24818,f4706]) ).

fof(f24818,plain,
    ( ! [X12] :
        ( c_Groups_Oone__class_Oone(tc_Int_Oint) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X12)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X12) )
    | ~ spl24_58 ),
    inference(resolution,[],[f12773,f6523]) ).

fof(f6523,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))
    | ~ spl24_58 ),
    inference(avatar_component_clause,[],[f6521]) ).

fof(f12773,plain,
    ! [X16,X17] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X17,c_Groups_Oone__class_Oone(tc_Int_Oint))
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X16)
      | c_Groups_Oone__class_Oone(tc_Int_Oint) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,X17,X16) ),
    inference(forward_demodulation,[],[f12772,f4706]) ).

fof(f12772,plain,
    ! [X16,X17] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X17,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X16)
      | c_Groups_Oone__class_Oone(tc_Int_Oint) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,X17,X16) ),
    inference(forward_demodulation,[],[f12771,f4730]) ).

fof(f12771,plain,
    ! [X16,X17] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X16)
      | c_Groups_Oone__class_Oone(tc_Int_Oint) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,X17,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X16))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X17,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(forward_demodulation,[],[f12768,f4706]) ).

fof(f12768,plain,
    ! [X16,X17] :
      ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,X17,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),X16)) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X17,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X16) ),
    inference(resolution,[],[f5485,f6042]) ).

fof(f5485,plain,
    ! [X2,X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
      | c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2)) != X0 ),
    inference(cnf_transformation,[],[f4135]) ).

fof(f4135,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
      | c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2)) != X0
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
    inference(rectify,[],[f2615]) ).

fof(f2615,plain,
    ! [X2,X1,X0] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
      | c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0)) != X2
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(flattening,[],[f2614]) ).

fof(f2614,plain,
    ! [X2,X1,X0] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
      | c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0)) != X2
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
    inference(ennf_transformation,[],[f1594]) ).

fof(f1594,plain,
    ! [X2,X1,X0] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
     => ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0)) = X2
       => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
         => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0) ) ) ),
    inference(rectify,[],[f830]) ).

fof(f830,axiom,
    ! [X21,X28,X5] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
     => ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,X28,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5),X21)) = X5
       => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X28,X5)
         => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X21) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_self__quotient__aux1) ).

fof(f24861,plain,
    ( ~ spl24_502
    | ~ spl24_58
    | spl24_263 ),
    inference(avatar_split_clause,[],[f24847,f12579,f6521,f24858]) ).

fof(f24858,plain,
    ( spl24_502
  <=> c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_502])]) ).

fof(f12579,plain,
    ( spl24_263
  <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_263])]) ).

fof(f24847,plain,
    ( c_Groups_Oone__class_Oone(tc_Int_Oint) != c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ spl24_58
    | spl24_263 ),
    inference(resolution,[],[f24829,f12581]) ).

fof(f12581,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | spl24_263 ),
    inference(avatar_component_clause,[],[f12579]) ).

fof(f24646,plain,
    ( spl24_498
    | spl24_501
    | spl24_451 ),
    inference(avatar_split_clause,[],[f24639,f20667,f24642,f24473]) ).

fof(f24642,plain,
    ( spl24_501
  <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_501])]) ).

fof(f20667,plain,
    ( spl24_451
  <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_451])]) ).

fof(f24639,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | spl24_451 ),
    inference(resolution,[],[f20668,f5285]) ).

fof(f20668,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | spl24_451 ),
    inference(avatar_component_clause,[],[f20667]) ).

fof(f24645,plain,
    ( spl24_498
    | spl24_501
    | spl24_451 ),
    inference(avatar_split_clause,[],[f24640,f20667,f24642,f24473]) ).

fof(f24640,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | spl24_451 ),
    inference(resolution,[],[f20668,f5285]) ).

fof(f24586,plain,
    ( spl24_500
    | ~ spl24_235
    | spl24_448 ),
    inference(avatar_split_clause,[],[f24578,f20647,f11215,f24583]) ).

fof(f20647,plain,
    ( spl24_448
  <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_448])]) ).

fof(f24578,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ spl24_235
    | spl24_448 ),
    inference(resolution,[],[f20648,f14751]) ).

fof(f14751,plain,
    ( ! [X13] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X13,c_Groups_Oone__class_Oone(tc_Int_Oint))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X13) )
    | ~ spl24_235 ),
    inference(resolution,[],[f7200,f11217]) ).

fof(f11217,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ spl24_235 ),
    inference(avatar_component_clause,[],[f11215]) ).

fof(f7200,plain,
    ! [X2,X3,X4] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,X3)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X3)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,X2) ),
    inference(resolution,[],[f4403,f5360]) ).

fof(f20648,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | spl24_448 ),
    inference(avatar_component_clause,[],[f20647]) ).

fof(f24480,plain,
    ( spl24_498
    | ~ spl24_453
    | ~ spl24_448 ),
    inference(avatar_split_clause,[],[f24460,f20647,f20742,f24473]) ).

fof(f24460,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ spl24_448 ),
    inference(resolution,[],[f20649,f5243]) ).

fof(f20649,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ spl24_448 ),
    inference(avatar_component_clause,[],[f20647]) ).

fof(f24479,plain,
    ( spl24_498
    | spl24_499
    | ~ spl24_448 ),
    inference(avatar_split_clause,[],[f24471,f20647,f24477,f24473]) ).

fof(f24477,plain,
    ( spl24_499
  <=> ! [X5] : c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X5)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_499])]) ).

fof(f24471,plain,
    ( ! [X5] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X5))
        | c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
    | ~ spl24_448 ),
    inference(forward_demodulation,[],[f24465,f5810]) ).

fof(f24465,plain,
    ( ! [X5] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X5),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X5))
        | c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
    | ~ spl24_448 ),
    inference(resolution,[],[f20649,f7381]) ).

fof(f24470,plain,
    ( spl24_497
    | ~ spl24_448 ),
    inference(avatar_split_clause,[],[f24463,f20647,f24467]) ).

fof(f24467,plain,
    ( spl24_497
  <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_497])]) ).

fof(f24463,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ spl24_448 ),
    inference(resolution,[],[f20649,f5678]) ).

fof(f24228,plain,
    ( ~ spl24_9
    | spl24_496
    | ~ spl24_121 ),
    inference(avatar_split_clause,[],[f24202,f6941,f24226,f6248]) ).

fof(f24226,plain,
    ( spl24_496
  <=> ! [X18,X20,X17,X19] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Int_Oint),X20,X19)
        | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Int_Oint),X20,c_Polynomial_Osmult(tc_Int_Oint,X17,c_Polynomial_Osmult(tc_Int_Oint,X18,X19))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_496])]) ).

fof(f6941,plain,
    ( spl24_121
  <=> class_Rings_Ocomm__semiring__0(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_121])]) ).

fof(f24202,plain,
    ( ! [X18,X19,X17,X20] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Int_Oint),X20,X19)
        | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Int_Oint),X20,c_Polynomial_Osmult(tc_Int_Oint,X17,c_Polynomial_Osmult(tc_Int_Oint,X18,X19)))
        | ~ class_Rings_Ocomm__semiring__1(tc_Int_Oint) )
    | ~ spl24_121 ),
    inference(superposition,[],[f5403,f7799]) ).

fof(f7799,plain,
    ( ! [X8,X9,X7] : c_Polynomial_Osmult(tc_Int_Oint,X7,c_Polynomial_Osmult(tc_Int_Oint,X8,X9)) = c_Polynomial_Osmult(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X7),X8),X9)
    | ~ spl24_121 ),
    inference(resolution,[],[f5706,f6943]) ).

fof(f6943,plain,
    ( class_Rings_Ocomm__semiring__0(tc_Int_Oint)
    | ~ spl24_121 ),
    inference(avatar_component_clause,[],[f6941]) ).

fof(f5706,plain,
    ! [X2,X3,X0,X1] :
      ( ~ class_Rings_Ocomm__semiring__0(X1)
      | c_Polynomial_Osmult(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X0),X3) = c_Polynomial_Osmult(X1,X2,c_Polynomial_Osmult(X1,X0,X3)) ),
    inference(cnf_transformation,[],[f4286]) ).

fof(f4286,plain,
    ! [X0,X1,X2,X3] :
      ( c_Polynomial_Osmult(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X0),X3) = c_Polynomial_Osmult(X1,X2,c_Polynomial_Osmult(X1,X0,X3))
      | ~ class_Rings_Ocomm__semiring__0(X1) ),
    inference(rectify,[],[f2732]) ).

fof(f2732,plain,
    ! [X1,X2,X0,X3] :
      ( c_Polynomial_Osmult(X2,X0,c_Polynomial_Osmult(X2,X1,X3)) = c_Polynomial_Osmult(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1),X3)
      | ~ class_Rings_Ocomm__semiring__0(X2) ),
    inference(ennf_transformation,[],[f1503]) ).

fof(f1503,plain,
    ! [X1,X3,X2,X0] :
      ( class_Rings_Ocomm__semiring__0(X2)
     => c_Polynomial_Osmult(X2,X0,c_Polynomial_Osmult(X2,X1,X3)) = c_Polynomial_Osmult(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1),X3) ),
    inference(rectify,[],[f129]) ).

fof(f129,axiom,
    ! [X5,X29,X4,X24] :
      ( class_Rings_Ocomm__semiring__0(X4)
     => c_Polynomial_Osmult(X4,X5,c_Polynomial_Osmult(X4,X29,X24)) = c_Polynomial_Osmult(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X5),X29),X24) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__smult) ).

fof(f5403,plain,
    ! [X2,X3,X0,X1] :
      ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),X0,c_Polynomial_Osmult(X3,X2,X1))
      | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),X0,X1)
      | ~ class_Rings_Ocomm__semiring__1(X3) ),
    inference(cnf_transformation,[],[f4073]) ).

fof(f4073,plain,
    ! [X0,X1,X2,X3] :
      ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),X0,c_Polynomial_Osmult(X3,X2,X1))
      | ~ class_Rings_Ocomm__semiring__1(X3)
      | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),X0,X1) ),
    inference(rectify,[],[f2480]) ).

fof(f2480,plain,
    ! [X3,X0,X2,X1] :
      ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X3,c_Polynomial_Osmult(X1,X2,X0))
      | ~ class_Rings_Ocomm__semiring__1(X1)
      | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X3,X0) ),
    inference(flattening,[],[f2479]) ).

fof(f2479,plain,
    ! [X3,X1,X0,X2] :
      ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X3,c_Polynomial_Osmult(X1,X2,X0))
      | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X3,X0)
      | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(ennf_transformation,[],[f1277]) ).

fof(f1277,plain,
    ! [X3,X1,X0,X2] :
      ( class_Rings_Ocomm__semiring__1(X1)
     => ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X3,X0)
       => c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X3,c_Polynomial_Osmult(X1,X2,X0)) ) ),
    inference(rectify,[],[f480]) ).

fof(f480,axiom,
    ! [X21,X4,X5,X24] :
      ( class_Rings_Ocomm__semiring__1(X4)
     => ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4),X24,X21)
       => c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4),X24,c_Polynomial_Osmult(X4,X5,X21)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__smult) ).

fof(f24224,plain,
    ( spl24_495
    | ~ spl24_9
    | ~ spl24_121 ),
    inference(avatar_split_clause,[],[f24203,f6941,f6248,f24222]) ).

fof(f24222,plain,
    ( spl24_495
  <=> ! [X24,X21,X23,X22] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Int_Oint),c_Polynomial_Osmult(tc_Int_Oint,X21,c_Polynomial_Osmult(tc_Int_Oint,X22,X23)),X24)
        | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Int_Oint),X23,X24) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_495])]) ).

fof(f24203,plain,
    ( ! [X21,X24,X22,X23] :
        ( ~ class_Rings_Ocomm__semiring__1(tc_Int_Oint)
        | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Int_Oint),c_Polynomial_Osmult(tc_Int_Oint,X21,c_Polynomial_Osmult(tc_Int_Oint,X22,X23)),X24)
        | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Int_Oint),X23,X24) )
    | ~ spl24_121 ),
    inference(superposition,[],[f4770,f7799]) ).

fof(f4770,plain,
    ! [X2,X3,X0,X1] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2),c_Polynomial_Osmult(X2,X3,X1),X0)
      | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2),X1,X0)
      | ~ class_Rings_Ocomm__semiring__1(X2) ),
    inference(cnf_transformation,[],[f3696]) ).

fof(f3696,plain,
    ! [X0,X1,X2,X3] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2),c_Polynomial_Osmult(X2,X3,X1),X0)
      | ~ class_Rings_Ocomm__semiring__1(X2)
      | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2),X1,X0) ),
    inference(rectify,[],[f2888]) ).

fof(f2888,plain,
    ! [X0,X2,X1,X3] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X3,X2),X0)
      | ~ class_Rings_Ocomm__semiring__1(X1)
      | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X2,X0) ),
    inference(flattening,[],[f2887]) ).

fof(f2887,plain,
    ! [X0,X1,X3,X2] :
      ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X2,X0)
      | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X3,X2),X0)
      | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(ennf_transformation,[],[f1375]) ).

fof(f1375,plain,
    ! [X0,X1,X3,X2] :
      ( class_Rings_Ocomm__semiring__1(X1)
     => ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X3,X2),X0)
       => c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X2,X0) ) ),
    inference(rectify,[],[f481]) ).

fof(f481,axiom,
    ! [X21,X4,X24,X5] :
      ( class_Rings_Ocomm__semiring__1(X4)
     => ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4),c_Polynomial_Osmult(X4,X5,X24),X21)
       => c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4),X24,X21) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__dvd__cancel) ).

fof(f24219,plain,
    ( spl24_494
    | ~ spl24_121
    | ~ spl24_121 ),
    inference(avatar_split_clause,[],[f24204,f6941,f6941,f24217]) ).

fof(f24217,plain,
    ( spl24_494
  <=> ! [X25,X27,X26] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Int_Oint,c_Polynomial_Osmult(tc_Int_Oint,X25,c_Polynomial_Osmult(tc_Int_Oint,X26,X27))),c_Polynomial_Odegree(tc_Int_Oint,X27)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_494])]) ).

fof(f24204,plain,
    ( ! [X26,X27,X25] :
        ( ~ class_Rings_Ocomm__semiring__0(tc_Int_Oint)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Int_Oint,c_Polynomial_Osmult(tc_Int_Oint,X25,c_Polynomial_Osmult(tc_Int_Oint,X26,X27))),c_Polynomial_Odegree(tc_Int_Oint,X27)) )
    | ~ spl24_121 ),
    inference(superposition,[],[f5260,f7799]) ).

fof(f5260,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X0,c_Polynomial_Osmult(X0,X2,X1)),c_Polynomial_Odegree(X0,X1))
      | ~ class_Rings_Ocomm__semiring__0(X0) ),
    inference(cnf_transformation,[],[f3980]) ).

fof(f3980,plain,
    ! [X0,X1,X2] :
      ( ~ class_Rings_Ocomm__semiring__0(X0)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X0,c_Polynomial_Osmult(X0,X2,X1)),c_Polynomial_Odegree(X0,X1)) ),
    inference(rectify,[],[f3076]) ).

fof(f3076,plain,
    ! [X2,X0,X1] :
      ( ~ class_Rings_Ocomm__semiring__0(X2)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,c_Polynomial_Osmult(X2,X1,X0)),c_Polynomial_Odegree(X2,X0)) ),
    inference(ennf_transformation,[],[f1944]) ).

fof(f1944,plain,
    ! [X0,X1,X2] :
      ( class_Rings_Ocomm__semiring__0(X2)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,c_Polynomial_Osmult(X2,X1,X0)),c_Polynomial_Odegree(X2,X0)) ),
    inference(rectify,[],[f330]) ).

fof(f330,axiom,
    ! [X24,X5,X4] :
      ( class_Rings_Ocomm__semiring__0(X4)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X4,c_Polynomial_Osmult(X4,X5,X24)),c_Polynomial_Odegree(X4,X24)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__smult__le) ).

fof(f24213,plain,
    ( ~ spl24_121
    | spl24_493
    | ~ spl24_121 ),
    inference(avatar_split_clause,[],[f24200,f6941,f24211,f6941]) ).

fof(f24211,plain,
    ( spl24_493
  <=> ! [X10,X9,X11,X12] :
        ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Int_Oint),c_Polynomial_Osmult(tc_Int_Oint,X9,c_Polynomial_Osmult(tc_Int_Oint,X10,X11)),c_Polynomial_OpCons(tc_Int_Oint,X12,X11)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint))
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)) = X11 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_493])]) ).

fof(f24200,plain,
    ( ! [X10,X11,X9,X12] :
        ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Int_Oint),c_Polynomial_Osmult(tc_Int_Oint,X9,c_Polynomial_Osmult(tc_Int_Oint,X10,X11)),c_Polynomial_OpCons(tc_Int_Oint,X12,X11)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint))
        | ~ class_Rings_Ocomm__semiring__0(tc_Int_Oint)
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)) = X11 )
    | ~ spl24_121 ),
    inference(superposition,[],[f4606,f7799]) ).

fof(f4606,plain,
    ! [X2,X3,X0,X1] :
      ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X0,X1),c_Polynomial_OpCons(X3,X2,X1)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
      | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X1
      | ~ class_Rings_Ocomm__semiring__0(X3) ),
    inference(cnf_transformation,[],[f3582]) ).

fof(f3582,plain,
    ! [X0,X1,X2,X3] :
      ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X0,X1),c_Polynomial_OpCons(X3,X2,X1)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
      | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X1
      | ~ class_Rings_Ocomm__semiring__0(X3) ),
    inference(rectify,[],[f2930]) ).

fof(f2930,plain,
    ! [X3,X0,X1,X2] :
      ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),c_Polynomial_Osmult(X2,X3,X0),c_Polynomial_OpCons(X2,X1,X0)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
      | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
      | ~ class_Rings_Ocomm__semiring__0(X2) ),
    inference(flattening,[],[f2929]) ).

fof(f2929,plain,
    ! [X2,X1,X3,X0] :
      ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
      | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),c_Polynomial_Osmult(X2,X3,X0),c_Polynomial_OpCons(X2,X1,X0)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
      | ~ class_Rings_Ocomm__semiring__0(X2) ),
    inference(ennf_transformation,[],[f2009]) ).

fof(f2009,plain,
    ! [X2,X1,X3,X0] :
      ( class_Rings_Ocomm__semiring__0(X2)
     => ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),c_Polynomial_Osmult(X2,X3,X0),c_Polynomial_OpCons(X2,X1,X0)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
       => c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0 ) ),
    inference(rectify,[],[f75]) ).

fof(f75,axiom,
    ! [X24,X5,X4,X22] :
      ( class_Rings_Ocomm__semiring__0(X4)
     => ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),c_Polynomial_Osmult(X4,X22,X24),c_Polynomial_OpCons(X4,X5,X24))
       => c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X24 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_offset__poly__eq__0__lemma) ).

fof(f24208,plain,
    ( spl24_492
    | ~ spl24_121
    | ~ spl24_121 ),
    inference(avatar_split_clause,[],[f24201,f6941,f6941,f24206]) ).

fof(f24206,plain,
    ( spl24_492
  <=> ! [X13,X14,X16,X15] :
        ( c_Polynomial_OpCons(tc_Int_Oint,X16,X15) != c_Polynomial_Osmult(tc_Int_Oint,X13,c_Polynomial_Osmult(tc_Int_Oint,X14,X15))
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)) = X15 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_492])]) ).

fof(f24201,plain,
    ( ! [X16,X14,X15,X13] :
        ( ~ class_Rings_Ocomm__semiring__0(tc_Int_Oint)
        | c_Polynomial_OpCons(tc_Int_Oint,X16,X15) != c_Polynomial_Osmult(tc_Int_Oint,X13,c_Polynomial_Osmult(tc_Int_Oint,X14,X15))
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)) = X15 )
    | ~ spl24_121 ),
    inference(superposition,[],[f4596,f7799]) ).

fof(f4596,plain,
    ! [X2,X3,X0,X1] :
      ( c_Polynomial_OpCons(X2,X1,X3) != c_Polynomial_Osmult(X2,X0,X3)
      | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X3
      | ~ class_Rings_Ocomm__semiring__0(X2) ),
    inference(cnf_transformation,[],[f2959]) ).

fof(f2959,plain,
    ! [X0,X1,X2,X3] :
      ( ~ class_Rings_Ocomm__semiring__0(X2)
      | c_Polynomial_OpCons(X2,X1,X3) != c_Polynomial_Osmult(X2,X0,X3)
      | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X3 ),
    inference(flattening,[],[f2958]) ).

fof(f2958,plain,
    ! [X3,X1,X0,X2] :
      ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X3
      | c_Polynomial_OpCons(X2,X1,X3) != c_Polynomial_Osmult(X2,X0,X3)
      | ~ class_Rings_Ocomm__semiring__0(X2) ),
    inference(ennf_transformation,[],[f1977]) ).

fof(f1977,plain,
    ! [X3,X1,X0,X2] :
      ( class_Rings_Ocomm__semiring__0(X2)
     => ( c_Polynomial_OpCons(X2,X1,X3) = c_Polynomial_Osmult(X2,X0,X3)
       => c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X3 ) ),
    inference(rectify,[],[f30]) ).

fof(f30,axiom,
    ! [X22,X5,X4,X24] :
      ( class_Rings_Ocomm__semiring__0(X4)
     => ( c_Polynomial_Osmult(X4,X22,X24) = c_Polynomial_OpCons(X4,X5,X24)
       => c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X24 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_synthetic__div__unique__lemma) ).

fof(f24161,plain,
    ( spl24_491
    | ~ spl24_9 ),
    inference(avatar_split_clause,[],[f24143,f6248,f24158]) ).

fof(f24158,plain,
    ( spl24_491
  <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK12(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_491])]) ).

fof(f24143,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK12(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ spl24_9 ),
    inference(resolution,[],[f23187,f15429]) ).

fof(f15429,plain,
    ! [X13] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X13,c_Groups_Oone__class_Oone(tc_Int_Oint))
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X13,c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    inference(forward_demodulation,[],[f15428,f4706]) ).

fof(f15428,plain,
    ! [X13] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X13,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X13,c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    inference(forward_demodulation,[],[f15422,f4706]) ).

fof(f15422,plain,
    ! [X13] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X13,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X13,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(resolution,[],[f5720,f6042]) ).

fof(f24155,plain,
    ( ~ spl24_490
    | ~ spl24_9 ),
    inference(avatar_split_clause,[],[f24142,f6248,f24152]) ).

fof(f24152,plain,
    ( spl24_490
  <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),sK12(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_490])]) ).

fof(f24142,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),sK12(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))))
    | ~ spl24_9 ),
    inference(resolution,[],[f23187,f15447]) ).

fof(f15447,plain,
    ! [X13] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X13,c_Groups_Oone__class_Oone(tc_Int_Oint))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X13) ),
    inference(forward_demodulation,[],[f15446,f4706]) ).

fof(f15446,plain,
    ! [X13] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X13,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X13) ),
    inference(forward_demodulation,[],[f15440,f4706]) ).

fof(f15440,plain,
    ! [X13] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X13)
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X13,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(resolution,[],[f5776,f6042]) ).

fof(f5776,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,X1) ),
    inference(cnf_transformation,[],[f4333]) ).

fof(f4333,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,X1)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(rectify,[],[f3198]) ).

fof(f3198,plain,
    ! [X1,X0] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1)
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
    inference(flattening,[],[f3197]) ).

fof(f3197,plain,
    ! [X0,X1] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
    inference(ennf_transformation,[],[f1687]) ).

fof(f1687,plain,
    ! [X0,X1] :
      ( 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,X0,X1)
       => ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X0) ) ),
    inference(rectify,[],[f775]) ).

fof(f775,axiom,
    ! [X23,X17] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X23)
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X23,X17)
       => ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X17,X23) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__not__zless) ).

fof(f24127,plain,
    ( ~ spl24_5
    | spl24_489
    | ~ spl24_15 ),
    inference(avatar_split_clause,[],[f24101,f6277,f24125,f6228]) ).

fof(f24125,plain,
    ( spl24_489
  <=> ! [X18,X20,X17,X19] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Nat_Onat),X20,X19)
        | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Nat_Onat),X20,c_Polynomial_Osmult(tc_Nat_Onat,X17,c_Polynomial_Osmult(tc_Nat_Onat,X18,X19))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_489])]) ).

fof(f6277,plain,
    ( spl24_15
  <=> class_Rings_Ocomm__semiring__0(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_15])]) ).

fof(f24101,plain,
    ( ! [X18,X19,X17,X20] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Nat_Onat),X20,X19)
        | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Nat_Onat),X20,c_Polynomial_Osmult(tc_Nat_Onat,X17,c_Polynomial_Osmult(tc_Nat_Onat,X18,X19)))
        | ~ class_Rings_Ocomm__semiring__1(tc_Nat_Onat) )
    | ~ spl24_15 ),
    inference(superposition,[],[f5403,f7798]) ).

fof(f7798,plain,
    ( ! [X6,X4,X5] : c_Polynomial_Osmult(tc_Nat_Onat,X4,c_Polynomial_Osmult(tc_Nat_Onat,X5,X6)) = c_Polynomial_Osmult(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X5),X6)
    | ~ spl24_15 ),
    inference(resolution,[],[f5706,f6279]) ).

fof(f6279,plain,
    ( class_Rings_Ocomm__semiring__0(tc_Nat_Onat)
    | ~ spl24_15 ),
    inference(avatar_component_clause,[],[f6277]) ).

fof(f24123,plain,
    ( ~ spl24_15
    | spl24_488
    | ~ spl24_15 ),
    inference(avatar_split_clause,[],[f24103,f6277,f24121,f6277]) ).

fof(f24121,plain,
    ( spl24_488
  <=> ! [X25,X27,X26] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Nat_Onat,c_Polynomial_Osmult(tc_Nat_Onat,X25,c_Polynomial_Osmult(tc_Nat_Onat,X26,X27))),c_Polynomial_Odegree(tc_Nat_Onat,X27)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_488])]) ).

fof(f24103,plain,
    ( ! [X26,X27,X25] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Nat_Onat,c_Polynomial_Osmult(tc_Nat_Onat,X25,c_Polynomial_Osmult(tc_Nat_Onat,X26,X27))),c_Polynomial_Odegree(tc_Nat_Onat,X27))
        | ~ class_Rings_Ocomm__semiring__0(tc_Nat_Onat) )
    | ~ spl24_15 ),
    inference(superposition,[],[f5260,f7798]) ).

fof(f24118,plain,
    ( spl24_487
    | ~ spl24_15
    | ~ spl24_15 ),
    inference(avatar_split_clause,[],[f24100,f6277,f6277,f24116]) ).

fof(f24116,plain,
    ( spl24_487
  <=> ! [X13,X14,X16,X15] :
        ( c_Polynomial_Osmult(tc_Nat_Onat,X13,c_Polynomial_Osmult(tc_Nat_Onat,X14,X15)) != c_Polynomial_OpCons(tc_Nat_Onat,X16,X15)
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)) = X15 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_487])]) ).

fof(f24100,plain,
    ( ! [X16,X14,X15,X13] :
        ( ~ class_Rings_Ocomm__semiring__0(tc_Nat_Onat)
        | c_Polynomial_Osmult(tc_Nat_Onat,X13,c_Polynomial_Osmult(tc_Nat_Onat,X14,X15)) != c_Polynomial_OpCons(tc_Nat_Onat,X16,X15)
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)) = X15 )
    | ~ spl24_15 ),
    inference(superposition,[],[f4596,f7798]) ).

fof(f24114,plain,
    ( ~ spl24_5
    | spl24_486
    | ~ spl24_15 ),
    inference(avatar_split_clause,[],[f24102,f6277,f24112,f6228]) ).

fof(f24112,plain,
    ( spl24_486
  <=> ! [X22,X21,X24,X23] :
        ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Nat_Onat),X23,X24)
        | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Nat_Onat),c_Polynomial_Osmult(tc_Nat_Onat,X21,c_Polynomial_Osmult(tc_Nat_Onat,X22,X23)),X24) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_486])]) ).

fof(f24102,plain,
    ( ! [X21,X24,X22,X23] :
        ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Nat_Onat),X23,X24)
        | ~ class_Rings_Ocomm__semiring__1(tc_Nat_Onat)
        | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Nat_Onat),c_Polynomial_Osmult(tc_Nat_Onat,X21,c_Polynomial_Osmult(tc_Nat_Onat,X22,X23)),X24) )
    | ~ spl24_15 ),
    inference(superposition,[],[f4770,f7798]) ).

fof(f24107,plain,
    ( spl24_485
    | ~ spl24_15
    | ~ spl24_15 ),
    inference(avatar_split_clause,[],[f24099,f6277,f6277,f24105]) ).

fof(f24105,plain,
    ( spl24_485
  <=> ! [X12,X11,X9,X10] :
        ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)) = X11
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Nat_Onat),c_Polynomial_Osmult(tc_Nat_Onat,X9,c_Polynomial_Osmult(tc_Nat_Onat,X10,X11)),c_Polynomial_OpCons(tc_Nat_Onat,X12,X11)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_485])]) ).

fof(f24099,plain,
    ( ! [X10,X11,X9,X12] :
        ( ~ class_Rings_Ocomm__semiring__0(tc_Nat_Onat)
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)) = X11
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Nat_Onat),c_Polynomial_Osmult(tc_Nat_Onat,X9,c_Polynomial_Osmult(tc_Nat_Onat,X10,X11)),c_Polynomial_OpCons(tc_Nat_Onat,X12,X11)) )
    | ~ spl24_15 ),
    inference(superposition,[],[f4606,f7798]) ).

fof(f24021,plain,
    ( spl24_484
    | spl24_314
    | ~ spl24_311 ),
    inference(avatar_split_clause,[],[f24017,f13674,f13763,f24019]) ).

fof(f24019,plain,
    ( spl24_484
  <=> ! [X10] : c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X10)),X10) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_484])]) ).

fof(f13763,plain,
    ( spl24_314
  <=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_314])]) ).

fof(f24017,plain,
    ( ! [X10] :
        ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X10)),X10) )
    | ~ spl24_311 ),
    inference(forward_demodulation,[],[f24016,f5810]) ).

fof(f24016,plain,
    ( ! [X10] :
        ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)),X10),X10) )
    | ~ spl24_311 ),
    inference(forward_demodulation,[],[f24015,f4706]) ).

fof(f24015,plain,
    ( ! [X10] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)),X10),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X10))
        | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
    | ~ spl24_311 ),
    inference(resolution,[],[f13676,f7381]) ).

fof(f23263,plain,
    ( spl24_483
    | spl24_459
    | ~ spl24_444 ),
    inference(avatar_split_clause,[],[f23216,f20462,f20961,f23261]) ).

fof(f23261,plain,
    ( spl24_483
  <=> ! [X29] : c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X29),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),X29)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_483])]) ).

fof(f23216,plain,
    ( ! [X29] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X29),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),X29)) )
    | ~ spl24_444 ),
    inference(resolution,[],[f7381,f20464]) ).

fof(f23246,plain,
    ( spl24_482
    | spl24_359
    | ~ spl24_357 ),
    inference(avatar_split_clause,[],[f23217,f15397,f15461,f23244]) ).

fof(f23244,plain,
    ( spl24_482
  <=> ! [X30] : c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X30),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X30)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_482])]) ).

fof(f23217,plain,
    ( ! [X30] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X30),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X30)) )
    | ~ spl24_357 ),
    inference(resolution,[],[f7381,f15399]) ).

fof(f23182,plain,
    spl24_481,
    inference(avatar_split_clause,[],[f23158,f23177]) ).

fof(f23177,plain,
    ( spl24_481
  <=> c_Groups_Oone__class_Oone(tc_Int_Oint) = sK12(c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_481])]) ).

fof(f23158,plain,
    c_Groups_Oone__class_Oone(tc_Int_Oint) = sK12(c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(superposition,[],[f4730,f22486]) ).

fof(f23180,plain,
    spl24_481,
    inference(avatar_split_clause,[],[f23156,f23177]) ).

fof(f23156,plain,
    c_Groups_Oone__class_Oone(tc_Int_Oint) = sK12(c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(superposition,[],[f22486,f4730]) ).

fof(f23147,plain,
    ( spl24_480
    | ~ spl24_391 ),
    inference(avatar_split_clause,[],[f23137,f16524,f23144]) ).

fof(f23144,plain,
    ( spl24_480
  <=> c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Int_Oint)))) = c_Polynomial_OpCons(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Int_Oint))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_480])]) ).

fof(f16524,plain,
    ( spl24_391
  <=> class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_391])]) ).

fof(f23137,plain,
    ( c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Int_Oint)))) = c_Polynomial_OpCons(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Int_Oint)))))
    | ~ spl24_391 ),
    inference(resolution,[],[f7051,f16525]) ).

fof(f16525,plain,
    ( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Int_Oint))
    | ~ spl24_391 ),
    inference(avatar_component_clause,[],[f16524]) ).

fof(f7051,plain,
    ! [X0] :
      ( ~ class_Rings_Ocomm__semiring__1(X0)
      | c_Polynomial_OpCons(tc_Polynomial_Opoly(X0),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X0)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0)))) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))) ),
    inference(resolution,[],[f4828,f4567]) ).

fof(f4567,plain,
    ! [X0] :
      ( ~ class_Rings_Ocomm__semiring__1(X0)
      | c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) ),
    inference(cnf_transformation,[],[f2486]) ).

fof(f2486,plain,
    ! [X0] :
      ( c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))
      | ~ class_Rings_Ocomm__semiring__1(X0) ),
    inference(ennf_transformation,[],[f1925]) ).

fof(f1925,plain,
    ! [X0] :
      ( class_Rings_Ocomm__semiring__1(X0)
     => c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) ),
    inference(rectify,[],[f226]) ).

fof(f226,axiom,
    ! [X4] :
      ( class_Rings_Ocomm__semiring__1(X4)
     => c_Polynomial_OpCons(X4,c_Groups_Oone__class_Oone(X4),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__poly__def) ).

fof(f4828,plain,
    ! [X0] :
      ( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__semiring__1(X0) ),
    inference(cnf_transformation,[],[f2797]) ).

fof(f2797,plain,
    ! [X0] :
      ( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__semiring__1(X0) ),
    inference(ennf_transformation,[],[f2190]) ).

fof(f2190,plain,
    ! [X0] :
      ( class_Rings_Ocomm__semiring__1(X0)
     => class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1146]) ).

fof(f1146,axiom,
    ! [X94] :
      ( class_Rings_Ocomm__semiring__1(X94)
     => class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X94)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__1) ).

fof(f23142,plain,
    ( spl24_479
    | ~ spl24_384 ),
    inference(avatar_split_clause,[],[f23136,f16431,f23139]) ).

fof(f23139,plain,
    ( spl24_479
  <=> c_Polynomial_OpCons(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Nat_Onat))))) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Nat_Onat)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_479])]) ).

fof(f16431,plain,
    ( spl24_384
  <=> class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_384])]) ).

fof(f23136,plain,
    ( c_Polynomial_OpCons(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Nat_Onat))))) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Nat_Onat))))
    | ~ spl24_384 ),
    inference(resolution,[],[f7051,f16432]) ).

fof(f16432,plain,
    ( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Nat_Onat))
    | ~ spl24_384 ),
    inference(avatar_component_clause,[],[f16431]) ).

fof(f22429,plain,
    ( ~ spl24_92
    | spl24_478
    | ~ spl24_92 ),
    inference(avatar_split_clause,[],[f22412,f6764,f22427,f6764]) ).

fof(f22427,plain,
    ( spl24_478
  <=> ! [X9,X7,X6,X8] :
        ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,X6,c_Polynomial_Osmult(t_a,X7,X8)),c_Polynomial_OpCons(t_a,X9,X8))
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = X8 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_478])]) ).

fof(f22412,plain,
    ( ! [X8,X6,X9,X7] :
        ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,X6,c_Polynomial_Osmult(t_a,X7,X8)),c_Polynomial_OpCons(t_a,X9,X8))
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = X8
        | ~ class_Rings_Ocomm__semiring__0(t_a) )
    | ~ spl24_92 ),
    inference(superposition,[],[f4606,f7800]) ).

fof(f7800,plain,
    ( ! [X10,X11,X12] : c_Polynomial_Osmult(t_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),X10),X11),X12) = c_Polynomial_Osmult(t_a,X10,c_Polynomial_Osmult(t_a,X11,X12))
    | ~ spl24_92 ),
    inference(resolution,[],[f5706,f6766]) ).

fof(f22424,plain,
    ( spl24_477
    | ~ spl24_92
    | ~ spl24_92 ),
    inference(avatar_split_clause,[],[f22413,f6764,f6764,f22422]) ).

fof(f22422,plain,
    ( spl24_477
  <=> ! [X10,X11,X13,X12] :
        ( c_Polynomial_Osmult(t_a,X10,c_Polynomial_Osmult(t_a,X11,X12)) != c_Polynomial_OpCons(t_a,X13,X12)
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = X12 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_477])]) ).

fof(f22413,plain,
    ( ! [X10,X11,X12,X13] :
        ( ~ class_Rings_Ocomm__semiring__0(t_a)
        | c_Polynomial_Osmult(t_a,X10,c_Polynomial_Osmult(t_a,X11,X12)) != c_Polynomial_OpCons(t_a,X13,X12)
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = X12 )
    | ~ spl24_92 ),
    inference(superposition,[],[f4596,f7800]) ).

fof(f22420,plain,
    ( spl24_476
    | ~ spl24_92
    | ~ spl24_92 ),
    inference(avatar_split_clause,[],[f22416,f6764,f6764,f22418]) ).

fof(f22418,plain,
    ( spl24_476
  <=> ! [X22,X24,X23] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,X22,c_Polynomial_Osmult(t_a,X23,X24))),c_Polynomial_Odegree(t_a,X24)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_476])]) ).

fof(f22416,plain,
    ( ! [X24,X22,X23] :
        ( ~ class_Rings_Ocomm__semiring__0(t_a)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,X22,c_Polynomial_Osmult(t_a,X23,X24))),c_Polynomial_Odegree(t_a,X24)) )
    | ~ spl24_92 ),
    inference(superposition,[],[f5260,f7800]) ).

fof(f22080,plain,
    ( spl24_156
    | ~ spl24_38
    | ~ spl24_138 ),
    inference(avatar_split_clause,[],[f22079,f7672,f6414,f9292]) ).

fof(f9292,plain,
    ( spl24_156
  <=> ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_156])]) ).

fof(f6414,plain,
    ( spl24_38
  <=> class_Divides_Osemiring__div(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_38])]) ).

fof(f7672,plain,
    ( spl24_138
  <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_138])]) ).

fof(f22079,plain,
    ( ! [X9] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X9,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_38
    | ~ spl24_138 ),
    inference(forward_demodulation,[],[f22049,f13482]) ).

fof(f13482,plain,
    ( ! [X1] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X1
    | ~ spl24_38 ),
    inference(resolution,[],[f4827,f6416]) ).

fof(f6416,plain,
    ( class_Divides_Osemiring__div(tc_Int_Oint)
    | ~ spl24_38 ),
    inference(avatar_component_clause,[],[f6414]) ).

fof(f4827,plain,
    ! [X0,X1] :
      ( ~ class_Divides_Osemiring__div(X1)
      | c_Divides_Odiv__class_Omod(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0 ),
    inference(cnf_transformation,[],[f2598]) ).

fof(f2598,plain,
    ! [X0,X1] :
      ( ~ class_Divides_Osemiring__div(X1)
      | c_Divides_Odiv__class_Omod(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0 ),
    inference(ennf_transformation,[],[f1214]) ).

fof(f1214,plain,
    ! [X0,X1] :
      ( class_Divides_Osemiring__div(X1)
     => c_Divides_Odiv__class_Omod(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0 ),
    inference(rectify,[],[f867]) ).

fof(f867,axiom,
    ! [X5,X4] :
      ( class_Divides_Osemiring__div(X4)
     => c_Divides_Odiv__class_Omod(X4,X5,c_Groups_Ozero__class_Ozero(X4)) = X5 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__by__0) ).

fof(f22049,plain,
    ( ! [X9] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X9,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_138 ),
    inference(resolution,[],[f7674,f5410]) ).

fof(f5410,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(cnf_transformation,[],[f3129]) ).

fof(f3129,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(ennf_transformation,[],[f2030]) ).

fof(f2030,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
     => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(rectify,[],[f918]) ).

fof(f918,axiom,
    ! [X5,X29] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X29,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
     => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X5,X29),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__mod__sign) ).

fof(f7674,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_138 ),
    inference(avatar_component_clause,[],[f7672]) ).

fof(f22078,plain,
    ( spl24_474
    | spl24_475
    | ~ spl24_9
    | ~ spl24_138 ),
    inference(avatar_split_clause,[],[f22071,f7672,f6248,f22076,f22073]) ).

fof(f22073,plain,
    ( spl24_474
  <=> ! [X5] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X5) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_474])]) ).

fof(f22076,plain,
    ( spl24_475
  <=> ! [X6] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X6 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_475])]) ).

fof(f22071,plain,
    ( ! [X6,X5] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X5)
        | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X6 )
    | ~ spl24_9
    | ~ spl24_138 ),
    inference(forward_demodulation,[],[f22070,f4958]) ).

fof(f22070,plain,
    ( ! [X6,X5] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,X6,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X5) )
    | ~ spl24_9
    | ~ spl24_138 ),
    inference(forward_demodulation,[],[f22046,f7254]) ).

fof(f7254,plain,
    ( ! [X1] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)
    | ~ spl24_9 ),
    inference(resolution,[],[f5604,f6250]) ).

fof(f5604,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(cnf_transformation,[],[f2538]) ).

fof(f2538,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(ennf_transformation,[],[f1852]) ).

fof(f1852,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,[],[f106]) ).

fof(f106,axiom,
    ! [X5,X4] :
      ( class_Rings_Ocomm__semiring__1(X4)
     => c_Groups_Ozero__class_Ozero(X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Groups_Ozero__class_Ozero(X4)),X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).

fof(f22046,plain,
    ( ! [X6,X5] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X5) )
    | ~ spl24_138 ),
    inference(resolution,[],[f7674,f5485]) ).

fof(f22069,plain,
    ( spl24_189
    | ~ spl24_38
    | ~ spl24_138 ),
    inference(avatar_split_clause,[],[f22068,f7672,f6414,f9848]) ).

fof(f9848,plain,
    ( spl24_189
  <=> ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_189])]) ).

fof(f22068,plain,
    ( ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
    | ~ spl24_38
    | ~ spl24_138 ),
    inference(forward_demodulation,[],[f22042,f13482]) ).

fof(f22042,plain,
    ( ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ spl24_138 ),
    inference(resolution,[],[f7674,f4859]) ).

fof(f22066,plain,
    ( spl24_133
    | ~ spl24_138 ),
    inference(avatar_split_clause,[],[f22044,f7672,f7107]) ).

fof(f7107,plain,
    ( spl24_133
  <=> c_Orderings_Oord__class_Oless__eq(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,[spl24_133])]) ).

fof(f22044,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_138 ),
    inference(resolution,[],[f7674,f5095]) ).

fof(f5095,plain,
    ! [X0] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0) ),
    inference(cnf_transformation,[],[f3903]) ).

fof(f3903,plain,
    ! [X0] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0) ) ),
    inference(nnf_transformation,[],[f1843]) ).

fof(f1843,plain,
    ! [X0] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
    inference(rectify,[],[f821]) ).

fof(f821,axiom,
    ! [X11] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X11)
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__one__le__iff__zero__less) ).

fof(f22062,plain,
    ( spl24_473
    | spl24_189
    | ~ spl24_9
    | ~ spl24_138 ),
    inference(avatar_split_clause,[],[f22058,f7672,f6248,f9848,f22060]) ).

fof(f22060,plain,
    ( spl24_473
  <=> ! [X2] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_473])]) ).

fof(f22058,plain,
    ( ! [X2,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) )
    | ~ spl24_9
    | ~ spl24_138 ),
    inference(forward_demodulation,[],[f22057,f4706]) ).

fof(f22057,plain,
    ( ! [X2,X1] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
    | ~ spl24_9
    | ~ spl24_138 ),
    inference(forward_demodulation,[],[f22043,f7254]) ).

fof(f22043,plain,
    ( ! [X2,X1] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1),X2))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) )
    | ~ spl24_138 ),
    inference(resolution,[],[f7674,f4892]) ).

fof(f4892,plain,
    ! [X2,X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0),X1))
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(cnf_transformation,[],[f2429]) ).

fof(f2429,plain,
    ! [X0,X1,X2] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0),X1))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
    inference(flattening,[],[f2428]) ).

fof(f2428,plain,
    ! [X1,X0,X2] :
      ( c_Orderings_Oord__class_Oless__eq(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),X2)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0),X1)) ),
    inference(ennf_transformation,[],[f1722]) ).

fof(f1722,plain,
    ! [X1,X0,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0),X1))
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
       => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
         => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ) ) ),
    inference(rectify,[],[f832]) ).

fof(f832,axiom,
    ! [X79,X78,X50] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X50),X79),X78))
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X78,X50)
       => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X50)
         => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X79) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_q__pos__lemma) ).

fof(f22056,plain,
    ~ spl24_138,
    inference(avatar_contradiction_clause,[],[f22051]) ).

fof(f22051,plain,
    ( $false
    | ~ spl24_138 ),
    inference(resolution,[],[f7674,f6166]) ).

fof(f6166,plain,
    ! [X1] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X1),
    inference(equality_resolution,[],[f5694]) ).

fof(f5694,plain,
    ! [X0,X1] :
      ( X0 != X1
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
    inference(cnf_transformation,[],[f4277]) ).

fof(f22041,plain,
    ( spl24_236
    | ~ spl24_9
    | ~ spl24_453
    | ~ spl24_469 ),
    inference(avatar_split_clause,[],[f22040,f21773,f20742,f6248,f11227]) ).

fof(f21773,plain,
    ( spl24_469
  <=> c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_469])]) ).

fof(f22040,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ spl24_9
    | ~ spl24_453
    | ~ spl24_469 ),
    inference(forward_demodulation,[],[f20744,f21939]) ).

fof(f21939,plain,
    ( ! [X2] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2) = X2
    | ~ spl24_9
    | ~ spl24_469 ),
    inference(forward_demodulation,[],[f21866,f4436]) ).

fof(f21866,plain,
    ( ! [X2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2)
    | ~ spl24_9
    | ~ spl24_469 ),
    inference(backward_demodulation,[],[f21717,f21775]) ).

fof(f21775,plain,
    ( c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ spl24_469 ),
    inference(avatar_component_clause,[],[f21773]) ).

fof(f21717,plain,
    ( ! [X2] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ spl24_9 ),
    inference(superposition,[],[f7701,f4648]) ).

fof(f22038,plain,
    ( ~ spl24_402
    | ~ spl24_9
    | spl24_449
    | ~ spl24_469 ),
    inference(avatar_split_clause,[],[f22037,f21773,f20657,f6248,f17755]) ).

fof(f20657,plain,
    ( spl24_449
  <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_449])]) ).

fof(f22037,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_9
    | spl24_449
    | ~ spl24_469 ),
    inference(forward_demodulation,[],[f22036,f5830]) ).

fof(f22036,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_9
    | spl24_449
    | ~ spl24_469 ),
    inference(forward_demodulation,[],[f22035,f21895]) ).

fof(f21895,plain,
    ( ! [X14,X15] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X15,X14) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X14,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X14,X15))
    | ~ spl24_9
    | ~ spl24_469 ),
    inference(forward_demodulation,[],[f21881,f4730]) ).

fof(f21881,plain,
    ( ! [X14,X15] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X15,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X14)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X14,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X14,X15))
    | ~ spl24_9
    | ~ spl24_469 ),
    inference(backward_demodulation,[],[f21754,f21775]) ).

fof(f21754,plain,
    ( ! [X14,X15] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X15,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),X14)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X14,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X14,X15))
    | ~ spl24_9 ),
    inference(superposition,[],[f7545,f7701]) ).

fof(f22035,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_9
    | spl24_449
    | ~ spl24_469 ),
    inference(forward_demodulation,[],[f22034,f5830]) ).

fof(f22034,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_9
    | spl24_449
    | ~ spl24_469 ),
    inference(forward_demodulation,[],[f22033,f21895]) ).

fof(f22033,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_9
    | spl24_449
    | ~ spl24_469 ),
    inference(forward_demodulation,[],[f22032,f5830]) ).

fof(f22032,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_9
    | spl24_449
    | ~ spl24_469 ),
    inference(forward_demodulation,[],[f20658,f21895]) ).

fof(f20658,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | spl24_449 ),
    inference(avatar_component_clause,[],[f20657]) ).

fof(f22030,plain,
    ( spl24_317
    | ~ spl24_9
    | ~ spl24_455
    | ~ spl24_469 ),
    inference(avatar_split_clause,[],[f22029,f21773,f20752,f6248,f13777]) ).

fof(f20752,plain,
    ( spl24_455
  <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_455])]) ).

fof(f22029,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ spl24_9
    | ~ spl24_455
    | ~ spl24_469 ),
    inference(forward_demodulation,[],[f20754,f21939]) ).

fof(f20754,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ spl24_455 ),
    inference(avatar_component_clause,[],[f20752]) ).

fof(f22028,plain,
    ( spl24_311
    | ~ spl24_402 ),
    inference(avatar_split_clause,[],[f20026,f17755,f13674]) ).

fof(f20026,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_402 ),
    inference(resolution,[],[f17757,f5695]) ).

fof(f22027,plain,
    ( ~ spl24_153
    | ~ spl24_9
    | spl24_423
    | ~ spl24_469 ),
    inference(avatar_split_clause,[],[f22026,f21773,f18639,f6248,f9279]) ).

fof(f18639,plain,
    ( spl24_423
  <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_423])]) ).

fof(f22026,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_9
    | spl24_423
    | ~ spl24_469 ),
    inference(forward_demodulation,[],[f18640,f21939]) ).

fof(f18640,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | spl24_423 ),
    inference(avatar_component_clause,[],[f18639]) ).

fof(f22025,plain,
    ( spl24_311
    | ~ spl24_402 ),
    inference(avatar_split_clause,[],[f20567,f17755,f13674]) ).

fof(f20567,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_402 ),
    inference(resolution,[],[f17757,f5695]) ).

fof(f22024,plain,
    ( spl24_402
    | ~ spl24_9
    | ~ spl24_241
    | ~ spl24_469 ),
    inference(avatar_split_clause,[],[f22023,f21773,f11652,f6248,f17755]) ).

fof(f11652,plain,
    ( spl24_241
  <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_241])]) ).

fof(f22023,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_9
    | ~ spl24_241
    | ~ spl24_469 ),
    inference(forward_demodulation,[],[f22022,f5830]) ).

fof(f22022,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_9
    | ~ spl24_241
    | ~ spl24_469 ),
    inference(forward_demodulation,[],[f11654,f21895]) ).

fof(f11654,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_241 ),
    inference(avatar_component_clause,[],[f11652]) ).

fof(f22021,plain,
    ( ~ spl24_233
    | ~ spl24_9
    | spl24_451
    | ~ spl24_469 ),
    inference(avatar_split_clause,[],[f22020,f21773,f20667,f6248,f11143]) ).

fof(f22020,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ spl24_9
    | spl24_451
    | ~ spl24_469 ),
    inference(forward_demodulation,[],[f20668,f21939]) ).

fof(f22019,plain,
    ( ~ spl24_163
    | ~ spl24_9
    | spl24_450
    | ~ spl24_469 ),
    inference(avatar_split_clause,[],[f22018,f21773,f20662,f6248,f9358]) ).

fof(f20662,plain,
    ( spl24_450
  <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_450])]) ).

fof(f22018,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_9
    | spl24_450
    | ~ spl24_469 ),
    inference(forward_demodulation,[],[f20663,f21939]) ).

fof(f20663,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | spl24_450 ),
    inference(avatar_component_clause,[],[f20662]) ).

fof(f22017,plain,
    ( spl24_191
    | ~ spl24_9
    | ~ spl24_454
    | ~ spl24_469 ),
    inference(avatar_split_clause,[],[f22016,f21773,f20747,f6248,f9854]) ).

fof(f22016,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ spl24_9
    | ~ spl24_454
    | ~ spl24_469 ),
    inference(forward_demodulation,[],[f20749,f21939]) ).

fof(f22015,plain,
    ( spl24_402
    | ~ spl24_9
    | ~ spl24_431
    | ~ spl24_469 ),
    inference(avatar_split_clause,[],[f21994,f21773,f20033,f6248,f17755]) ).

fof(f20033,plain,
    ( spl24_431
  <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(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,[spl24_431])]) ).

fof(f21994,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_9
    | ~ spl24_431
    | ~ spl24_469 ),
    inference(forward_demodulation,[],[f21993,f21939]) ).

fof(f21993,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_9
    | ~ spl24_431
    | ~ spl24_469 ),
    inference(forward_demodulation,[],[f21992,f5830]) ).

fof(f21992,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_9
    | ~ spl24_431
    | ~ spl24_469 ),
    inference(forward_demodulation,[],[f21865,f21895]) ).

fof(f21865,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_431
    | ~ spl24_469 ),
    inference(backward_demodulation,[],[f20035,f21775]) ).

fof(f20035,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_431 ),
    inference(avatar_component_clause,[],[f20033]) ).

fof(f22014,plain,
    ( ~ spl24_153
    | ~ spl24_9
    | ~ spl24_469
    | spl24_472 ),
    inference(avatar_split_clause,[],[f22013,f21820,f21773,f6248,f9279]) ).

fof(f21820,plain,
    ( spl24_472
  <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_472])]) ).

fof(f22013,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_9
    | ~ spl24_469
    | spl24_472 ),
    inference(forward_demodulation,[],[f22012,f21939]) ).

fof(f22012,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_9
    | ~ spl24_469
    | spl24_472 ),
    inference(forward_demodulation,[],[f21821,f21965]) ).

fof(f21965,plain,
    ( ! [X2,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1)
    | ~ spl24_9
    | ~ spl24_469 ),
    inference(forward_demodulation,[],[f21877,f4730]) ).

fof(f21877,plain,
    ( ! [X2,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1))
    | ~ spl24_9
    | ~ spl24_469 ),
    inference(backward_demodulation,[],[f21748,f21775]) ).

fof(f21748,plain,
    ( ! [X2,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1))
    | ~ spl24_9 ),
    inference(superposition,[],[f5388,f7701]) ).

fof(f21821,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | spl24_472 ),
    inference(avatar_component_clause,[],[f21820]) ).

fof(f21996,plain,
    ( spl24_138
    | ~ spl24_9
    | ~ spl24_314
    | ~ spl24_431
    | ~ spl24_469 ),
    inference(avatar_split_clause,[],[f21995,f21773,f20033,f13763,f6248,f7672]) ).

fof(f21995,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_9
    | ~ spl24_314
    | ~ spl24_431
    | ~ spl24_469 ),
    inference(forward_demodulation,[],[f21994,f13765]) ).

fof(f13765,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ spl24_314 ),
    inference(avatar_component_clause,[],[f13763]) ).

fof(f21929,plain,
    ( spl24_138
    | ~ spl24_260
    | ~ spl24_469 ),
    inference(avatar_split_clause,[],[f21928,f21773,f12488,f7672]) ).

fof(f12488,plain,
    ( spl24_260
  <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(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,[spl24_260])]) ).

fof(f21928,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_260
    | ~ spl24_469 ),
    inference(forward_demodulation,[],[f21828,f12434]) ).

fof(f21828,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_260
    | ~ spl24_469 ),
    inference(backward_demodulation,[],[f12490,f21775]) ).

fof(f12490,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_260 ),
    inference(avatar_component_clause,[],[f12488]) ).

fof(f21824,plain,
    ( ~ spl24_443
    | spl24_459
    | ~ spl24_444 ),
    inference(avatar_split_clause,[],[f20489,f20462,f20961,f20391]) ).

fof(f20489,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ spl24_444 ),
    inference(resolution,[],[f20464,f5243]) ).

fof(f21823,plain,
    ( spl24_472
    | ~ spl24_314
    | ~ spl24_449 ),
    inference(avatar_split_clause,[],[f21818,f20657,f13763,f21820]) ).

fof(f21818,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_314
    | ~ spl24_449 ),
    inference(forward_demodulation,[],[f21813,f4958]) ).

fof(f21813,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_314
    | ~ spl24_449 ),
    inference(backward_demodulation,[],[f20659,f13765]) ).

fof(f20659,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_449 ),
    inference(avatar_component_clause,[],[f20657]) ).

fof(f21799,plain,
    ( spl24_314
    | ~ spl24_315
    | ~ spl24_311 ),
    inference(avatar_split_clause,[],[f20556,f13674,f13767,f13763]) ).

fof(f20556,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ spl24_311 ),
    inference(resolution,[],[f13676,f5243]) ).

fof(f21798,plain,
    ( spl24_443
    | ~ spl24_255
    | ~ spl24_314 ),
    inference(avatar_split_clause,[],[f20386,f13763,f12451,f20391]) ).

fof(f20386,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ spl24_255
    | ~ spl24_314 ),
    inference(resolution,[],[f20122,f12453]) ).

fof(f20122,plain,
    ( ! [X4] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
    | ~ spl24_314 ),
    inference(superposition,[],[f5679,f13765]) ).

fof(f5679,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ),
    inference(cnf_transformation,[],[f4266]) ).

fof(f21797,plain,
    ( spl24_443
    | ~ spl24_255
    | ~ spl24_314 ),
    inference(avatar_split_clause,[],[f20389,f13763,f12451,f20391]) ).

fof(f20389,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ spl24_255
    | ~ spl24_314 ),
    inference(forward_demodulation,[],[f20385,f4958]) ).

fof(f20385,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ spl24_255
    | ~ spl24_314 ),
    inference(resolution,[],[f20122,f12484]) ).

fof(f21796,plain,
    ( spl24_314
    | ~ spl24_315
    | spl24_234 ),
    inference(avatar_split_clause,[],[f20405,f11152,f13767,f13763]) ).

fof(f20405,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | spl24_234 ),
    inference(resolution,[],[f11153,f5693]) ).

fof(f11153,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | spl24_234 ),
    inference(avatar_component_clause,[],[f11152]) ).

fof(f21795,plain,
    ( spl24_443
    | ~ spl24_314 ),
    inference(avatar_split_clause,[],[f20395,f13763,f20391]) ).

fof(f20395,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ spl24_314 ),
    inference(forward_demodulation,[],[f20384,f4706]) ).

fof(f20384,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ spl24_314 ),
    inference(resolution,[],[f20122,f17632]) ).

fof(f21788,plain,
    ( spl24_471
    | ~ spl24_135
    | ~ spl24_9 ),
    inference(avatar_split_clause,[],[f21736,f6248,f7262,f21786]) ).

fof(f21786,plain,
    ( spl24_471
  <=> ! [X11] :
        ( c_Groups_Oone__class_Oone(tc_Int_Oint) = X11
        | c_Groups_Oone__class_Oone(tc_Int_Oint) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,X11,X11) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_471])]) ).

fof(f21736,plain,
    ( ! [X11] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | c_Groups_Oone__class_Oone(tc_Int_Oint) = X11
        | c_Groups_Oone__class_Oone(tc_Int_Oint) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,X11,X11) )
    | ~ spl24_9 ),
    inference(superposition,[],[f4973,f7701]) ).

fof(f4973,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(tc_Int_Oint) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0)
      | c_Groups_Oone__class_Oone(tc_Int_Oint) = X0
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(cnf_transformation,[],[f3830]) ).

fof(f3830,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
      | ( ( c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0)
          | c_Groups_Oone__class_Oone(tc_Int_Oint) != X0
          | c_Groups_Oone__class_Oone(tc_Int_Oint) != X1 )
        & ( ( c_Groups_Oone__class_Oone(tc_Int_Oint) = X0
            & c_Groups_Oone__class_Oone(tc_Int_Oint) = X1 )
          | c_Groups_Oone__class_Oone(tc_Int_Oint) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0) ) ) ),
    inference(rectify,[],[f3829]) ).

fof(f3829,plain,
    ! [X1,X0] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
      | ( ( c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X1)
          | c_Groups_Oone__class_Oone(tc_Int_Oint) != X1
          | c_Groups_Oone__class_Oone(tc_Int_Oint) != X0 )
        & ( ( c_Groups_Oone__class_Oone(tc_Int_Oint) = X1
            & c_Groups_Oone__class_Oone(tc_Int_Oint) = X0 )
          | c_Groups_Oone__class_Oone(tc_Int_Oint) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X1) ) ) ),
    inference(flattening,[],[f3828]) ).

fof(f3828,plain,
    ! [X1,X0] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
      | ( ( c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X1)
          | c_Groups_Oone__class_Oone(tc_Int_Oint) != X1
          | c_Groups_Oone__class_Oone(tc_Int_Oint) != X0 )
        & ( ( c_Groups_Oone__class_Oone(tc_Int_Oint) = X1
            & c_Groups_Oone__class_Oone(tc_Int_Oint) = X0 )
          | c_Groups_Oone__class_Oone(tc_Int_Oint) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X1) ) ) ),
    inference(nnf_transformation,[],[f3073]) ).

fof(f3073,plain,
    ! [X1,X0] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
      | ( c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X1)
      <=> ( c_Groups_Oone__class_Oone(tc_Int_Oint) = X1
          & c_Groups_Oone__class_Oone(tc_Int_Oint) = X0 ) ) ),
    inference(ennf_transformation,[],[f1534]) ).

fof(f1534,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
     => ( c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X1)
      <=> ( c_Groups_Oone__class_Oone(tc_Int_Oint) = X1
          & c_Groups_Oone__class_Oone(tc_Int_Oint) = X0 ) ) ),
    inference(rectify,[],[f765]) ).

fof(f765,axiom,
    ! [X43,X18] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X43)
     => ( ( c_Groups_Oone__class_Oone(tc_Int_Oint) = X18
          & c_Groups_Oone__class_Oone(tc_Int_Oint) = X43 )
      <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X43),X18) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__zmult__eq__1__iff) ).

fof(f21779,plain,
    ( ~ spl24_135
    | spl24_469
    | spl24_470
    | ~ spl24_9 ),
    inference(avatar_split_clause,[],[f21735,f6248,f21777,f21773,f7262]) ).

fof(f21777,plain,
    ( spl24_470
  <=> ! [X10] : c_Groups_Oone__class_Oone(tc_Int_Oint) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,X10,X10) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_470])]) ).

fof(f21735,plain,
    ( ! [X10] :
        ( c_Groups_Oone__class_Oone(tc_Int_Oint) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,X10,X10)
        | c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))) )
    | ~ spl24_9 ),
    inference(superposition,[],[f4972,f7701]) ).

fof(f4972,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(tc_Int_Oint) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
      | c_Groups_Oone__class_Oone(tc_Int_Oint) = X1 ),
    inference(cnf_transformation,[],[f3830]) ).

fof(f21506,plain,
    ( spl24_141
    | ~ spl24_144 ),
    inference(avatar_split_clause,[],[f21495,f9145,f7942]) ).

fof(f7942,plain,
    ( spl24_141
  <=> c_Orderings_Oord__class_Oless(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,[spl24_141])]) ).

fof(f9145,plain,
    ( spl24_144
  <=> ! [X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_144])]) ).

fof(f21495,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ spl24_144 ),
    inference(resolution,[],[f9146,f14500]) ).

fof(f14500,plain,
    ! [X4] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,c_Groups_Oone__class_Oone(tc_Nat_Onat))
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4) ),
    inference(superposition,[],[f5957,f4540]) ).

fof(f5957,plain,
    ! [X0,X1] :
      ( 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),X1))
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
    inference(definition_unfolding,[],[f5363,f4877]) ).

fof(f5363,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,[],[f4043]) ).

fof(f9146,plain,
    ( ! [X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | ~ spl24_144 ),
    inference(avatar_component_clause,[],[f9145]) ).

fof(f21505,plain,
    ( spl24_143
    | ~ spl24_144 ),
    inference(avatar_split_clause,[],[f21490,f9145,f9142]) ).

fof(f9142,plain,
    ( spl24_143
  <=> ! [X0] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_143])]) ).

fof(f21490,plain,
    ( ! [X4] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ spl24_144 ),
    inference(resolution,[],[f9146,f5957]) ).

fof(f21504,plain,
    ( spl24_161
    | ~ spl24_144 ),
    inference(avatar_split_clause,[],[f21482,f9145,f9332]) ).

fof(f9332,plain,
    ( spl24_161
  <=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_161])]) ).

fof(f21482,plain,
    ( ! [X3] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X3
    | ~ spl24_144 ),
    inference(resolution,[],[f9146,f5082]) ).

fof(f5082,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,[],[f2873]) ).

fof(f2873,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(ennf_transformation,[],[f1880]) ).

fof(f1880,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,[],[f479]) ).

fof(f479,axiom,
    ! [X17] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X17
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X17) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr0I) ).

fof(f21503,plain,
    ( spl24_141
    | ~ spl24_144 ),
    inference(avatar_split_clause,[],[f21486,f9145,f7942]) ).

fof(f21486,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ spl24_144 ),
    inference(resolution,[],[f9146,f6121]) ).

fof(f6121,plain,
    ! [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),X1))
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1) ),
    inference(equality_resolution,[],[f5955]) ).

fof(f5955,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
      | 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),X1))
      | X0 != X1 ),
    inference(definition_unfolding,[],[f5358,f4877]) ).

fof(f5358,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1))
      | X0 != X1 ),
    inference(cnf_transformation,[],[f4039]) ).

fof(f4039,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
      | ( ( X0 = X1
          | ~ 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))
          | X0 != X1 ) ) ),
    inference(nnf_transformation,[],[f2734]) ).

fof(f2734,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
      | ( X0 = X1
      <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1)) ) ),
    inference(ennf_transformation,[],[f1647]) ).

fof(f1647,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
     => ( X0 = X1
      <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1)) ) ),
    inference(rectify,[],[f489]) ).

fof(f489,axiom,
    ! [X18,X43] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X43)
     => ( X18 = X43
      <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,c_Nat_OSuc(X43)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__less__Suc__eq) ).

fof(f21502,plain,
    ~ spl24_144,
    inference(avatar_contradiction_clause,[],[f21489]) ).

fof(f21489,plain,
    ( $false
    | ~ spl24_144 ),
    inference(resolution,[],[f9146,f5993]) ).

fof(f5993,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(definition_unfolding,[],[f5714,f4877]) ).

fof(f5714,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,[],[f4293]) ).

fof(f4293,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,[],[f2085]) ).

fof(f2085,plain,
    ! [X1,X0] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))),
    inference(rectify,[],[f558]) ).

fof(f558,axiom,
    ! [X54,X23] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X54,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X54,X23))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__Suc1) ).

fof(f21501,plain,
    ( ~ spl24_111
    | ~ spl24_144 ),
    inference(avatar_contradiction_clause,[],[f21491]) ).

fof(f21491,plain,
    ( $false
    | ~ spl24_111
    | ~ spl24_144 ),
    inference(resolution,[],[f9146,f11292]) ).

fof(f21500,plain,
    ~ spl24_144,
    inference(avatar_contradiction_clause,[],[f21483]) ).

fof(f21483,plain,
    ( $false
    | ~ spl24_144 ),
    inference(resolution,[],[f9146,f6048]) ).

fof(f6048,plain,
    ! [X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)),
    inference(equality_resolution,[],[f5890]) ).

fof(f5890,plain,
    ! [X0,X1] :
      ( 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),X1))
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ),
    inference(definition_unfolding,[],[f4700,f4877]) ).

fof(f4700,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1))
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ),
    inference(cnf_transformation,[],[f3651]) ).

fof(f21499,plain,
    ( ~ spl24_111
    | ~ spl24_144 ),
    inference(avatar_contradiction_clause,[],[f21484]) ).

fof(f21484,plain,
    ( $false
    | ~ spl24_111
    | ~ spl24_144 ),
    inference(resolution,[],[f9146,f11012]) ).

fof(f11012,plain,
    ( ! [X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | ~ spl24_111 ),
    inference(resolution,[],[f6885,f5224]) ).

fof(f5224,plain,
    ! [X2,X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2)) ),
    inference(cnf_transformation,[],[f3950]) ).

fof(f3950,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(rectify,[],[f2704]) ).

fof(f2704,plain,
    ! [X1,X2,X0] :
      ( 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,X0) ),
    inference(ennf_transformation,[],[f1496]) ).

fof(f1496,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) ),
    inference(rectify,[],[f497]) ).

fof(f497,axiom,
    ! [X52,X23,X54] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X54,X52)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X54,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X23,X52)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__less__add2) ).

fof(f21498,plain,
    ~ spl24_144,
    inference(avatar_contradiction_clause,[],[f21488]) ).

fof(f21488,plain,
    ( $false
    | ~ spl24_144 ),
    inference(resolution,[],[f9146,f5984]) ).

fof(f5984,plain,
    ! [X0,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))),
    inference(definition_unfolding,[],[f5653,f4877]) ).

fof(f5653,plain,
    ! [X0,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))),
    inference(cnf_transformation,[],[f4251]) ).

fof(f4251,plain,
    ! [X0,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))),
    inference(rectify,[],[f1301]) ).

fof(f1301,plain,
    ! [X1,X0] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))),
    inference(rectify,[],[f559]) ).

fof(f559,axiom,
    ! [X23,X54] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X54,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X23,X54))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__Suc2) ).

fof(f21497,plain,
    ~ spl24_144,
    inference(avatar_contradiction_clause,[],[f21487]) ).

fof(f21487,plain,
    ( $false
    | ~ spl24_144 ),
    inference(resolution,[],[f9146,f6091]) ).

fof(f21496,plain,
    ( ~ spl24_111
    | ~ spl24_144 ),
    inference(avatar_contradiction_clause,[],[f21485]) ).

fof(f21485,plain,
    ( $false
    | ~ spl24_111
    | ~ spl24_144 ),
    inference(resolution,[],[f9146,f6885]) ).

fof(f21474,plain,
    ( spl24_242
    | ~ spl24_141 ),
    inference(avatar_split_clause,[],[f21437,f7942,f11786]) ).

fof(f11786,plain,
    ( spl24_242
  <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_242])]) ).

fof(f21437,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ spl24_141 ),
    inference(resolution,[],[f7944,f15338]) ).

fof(f15338,plain,
    ! [X1] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1) ),
    inference(resolution,[],[f4640,f4894]) ).

fof(f4894,plain,
    ! [X0] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),
    inference(cnf_transformation,[],[f2114]) ).

fof(f2114,plain,
    ! [X0] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),
    inference(rectify,[],[f703]) ).

fof(f703,axiom,
    ! [X19] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X19),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gcd__lcm__complete__lattice__nat_Obot__least) ).

fof(f4640,plain,
    ! [X0,X1] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
    inference(cnf_transformation,[],[f3606]) ).

fof(f3606,plain,
    ! [X0,X1] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
    inference(rectify,[],[f2902]) ).

fof(f2902,plain,
    ! [X1,X0] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,X1)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(flattening,[],[f2901]) ).

fof(f2901,plain,
    ! [X1,X0] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,X1) ),
    inference(ennf_transformation,[],[f1953]) ).

fof(f1953,plain,
    ! [X1,X0] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,X1)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
       => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ) ),
    inference(rectify,[],[f626]) ).

fof(f626,axiom,
    ! [X51,X17] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X51,X17)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X17)
       => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X51,X17) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__imp__le) ).

fof(f7944,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ spl24_141 ),
    inference(avatar_component_clause,[],[f7942]) ).

fof(f21469,plain,
    ( spl24_468
    | ~ spl24_141 ),
    inference(avatar_split_clause,[],[f21436,f7942,f21466]) ).

fof(f21466,plain,
    ( spl24_468
  <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK20(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_468])]) ).

fof(f21436,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK20(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ spl24_141 ),
    inference(resolution,[],[f7944,f5987]) ).

fof(f5987,plain,
    ! [X0] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK20(X0)) = X0 ),
    inference(definition_unfolding,[],[f5672,f4877]) ).

fof(f5672,plain,
    ! [X0] :
      ( c_Nat_OSuc(sK20(X0)) = X0
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
    inference(cnf_transformation,[],[f4263]) ).

fof(f4263,plain,
    ! [X0] :
      ( ( c_Nat_OSuc(sK20(X0)) = X0
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
        | ! [X2] : c_Nat_OSuc(X2) != X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK20])],[f4261,f4262]) ).

fof(f4262,plain,
    ! [X0] :
      ( ? [X1] : c_Nat_OSuc(X1) = X0
     => c_Nat_OSuc(sK20(X0)) = X0 ),
    introduced(choice_axiom,[]) ).

fof(f4261,plain,
    ! [X0] :
      ( ( ? [X1] : c_Nat_OSuc(X1) = X0
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
        | ! [X2] : c_Nat_OSuc(X2) != X0 ) ),
    inference(rectify,[],[f4260]) ).

fof(f4260,plain,
    ! [X0] :
      ( ( ? [X1] : c_Nat_OSuc(X1) = X0
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
        | ! [X1] : c_Nat_OSuc(X1) != X0 ) ),
    inference(nnf_transformation,[],[f1634]) ).

fof(f1634,plain,
    ! [X0] :
      ( ? [X1] : c_Nat_OSuc(X1) = X0
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
    inference(rectify,[],[f553]) ).

fof(f553,axiom,
    ! [X18] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X18)
    <=> ? [X63] : c_Nat_OSuc(X63) = X18 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr0__conv__Suc) ).

fof(f21464,plain,
    ( spl24_143
    | ~ spl24_28
    | ~ spl24_141 ),
    inference(avatar_split_clause,[],[f21463,f7942,f6361,f9142]) ).

fof(f6361,plain,
    ( spl24_28
  <=> class_Divides_Osemiring__div(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_28])]) ).

fof(f21463,plain,
    ( ! [X7] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ spl24_28
    | ~ spl24_141 ),
    inference(forward_demodulation,[],[f21433,f13481]) ).

fof(f13481,plain,
    ( ! [X0] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
    | ~ spl24_28 ),
    inference(resolution,[],[f4827,f6363]) ).

fof(f6363,plain,
    ( class_Divides_Osemiring__div(tc_Nat_Onat)
    | ~ spl24_28 ),
    inference(avatar_component_clause,[],[f6361]) ).

fof(f21433,plain,
    ( ! [X7] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X7,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ spl24_141 ),
    inference(resolution,[],[f7944,f5246]) ).

fof(f5246,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,X1),X1) ),
    inference(cnf_transformation,[],[f3437]) ).

fof(f3437,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,X1),X1)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(ennf_transformation,[],[f1513]) ).

fof(f1513,plain,
    ! [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_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,X1),X1) ),
    inference(rectify,[],[f898]) ).

fof(f898,axiom,
    ! [X23,X17] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X17)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X23,X17),X17) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__less__divisor) ).

fof(f21460,plain,
    ( spl24_467
    | ~ spl24_141 ),
    inference(avatar_split_clause,[],[f21455,f7942,f21457]) ).

fof(f21457,plain,
    ( spl24_467
  <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK14(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_467])]) ).

fof(f21455,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK14(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ spl24_141 ),
    inference(forward_demodulation,[],[f21450,f5628]) ).

fof(f21450,plain,
    ( 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_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),sK14(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
    | ~ spl24_141 ),
    inference(resolution,[],[f7944,f5962]) ).

fof(f21454,plain,
    ~ spl24_141,
    inference(avatar_contradiction_clause,[],[f21438]) ).

fof(f21438,plain,
    ( $false
    | ~ spl24_141 ),
    inference(resolution,[],[f7944,f5444]) ).

fof(f5444,plain,
    ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(cnf_transformation,[],[f2060]) ).

fof(f2060,plain,
    ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(rectify,[],[f475]) ).

fof(f475,axiom,
    ! [X17] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less0) ).

fof(f21453,plain,
    ~ spl24_141,
    inference(avatar_contradiction_clause,[],[f21439]) ).

fof(f21439,plain,
    ( $false
    | ~ spl24_141 ),
    inference(resolution,[],[f7944,f5751]) ).

fof(f5751,plain,
    ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X0),
    inference(cnf_transformation,[],[f1405]) ).

fof(f1405,plain,
    ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X0),
    inference(rectify,[],[f440]) ).

fof(f440,axiom,
    ! [X17] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X17),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__irrefl__nat) ).

fof(f21427,plain,
    ( spl24_161
    | ~ spl24_147 ),
    inference(avatar_split_clause,[],[f21404,f9165,f9332]) ).

fof(f9165,plain,
    ( spl24_147
  <=> ! [X2,X3] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_147])]) ).

fof(f21404,plain,
    ( ! [X3] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X3
    | ~ spl24_147 ),
    inference(resolution,[],[f9166,f5082]) ).

fof(f9166,plain,
    ( ! [X2,X3] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
    | ~ spl24_147 ),
    inference(avatar_component_clause,[],[f9165]) ).

fof(f21426,plain,
    ( spl24_146
    | ~ spl24_147 ),
    inference(avatar_split_clause,[],[f21411,f9165,f9162]) ).

fof(f9162,plain,
    ( spl24_146
  <=> ! [X0,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_146])]) ).

fof(f21411,plain,
    ( ! [X6,X5] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5,X6)
    | ~ spl24_147 ),
    inference(resolution,[],[f9166,f5957]) ).

fof(f21425,plain,
    ( ~ spl24_111
    | ~ spl24_147 ),
    inference(avatar_contradiction_clause,[],[f21401]) ).

fof(f21401,plain,
    ( $false
    | ~ spl24_111
    | ~ spl24_147 ),
    inference(resolution,[],[f9166,f6885]) ).

fof(f21424,plain,
    ~ spl24_147,
    inference(avatar_contradiction_clause,[],[f21417]) ).

fof(f21417,plain,
    ( $false
    | ~ spl24_147 ),
    inference(resolution,[],[f9166,f5904]) ).

fof(f5904,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,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)),
    inference(definition_unfolding,[],[f4826,f4877]) ).

fof(f4826,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,[],[f3733]) ).

fof(f3733,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,[],[f2012]) ).

fof(f2012,plain,
    ! [X1,X0] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),c_Nat_OSuc(X0)),
    inference(rectify,[],[f957]) ).

fof(f957,axiom,
    ! [X23,X17] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X23,X17),c_Nat_OSuc(X23)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less__Suc) ).

fof(f21423,plain,
    ( ~ spl24_111
    | ~ spl24_147 ),
    inference(avatar_contradiction_clause,[],[f21412]) ).

fof(f21412,plain,
    ( $false
    | ~ spl24_111
    | ~ spl24_147 ),
    inference(resolution,[],[f9166,f11292]) ).

fof(f21422,plain,
    ~ spl24_147,
    inference(avatar_contradiction_clause,[],[f21405]) ).

fof(f21405,plain,
    ( $false
    | ~ spl24_147 ),
    inference(resolution,[],[f9166,f6048]) ).

fof(f21421,plain,
    ~ spl24_147,
    inference(avatar_contradiction_clause,[],[f21409]) ).

fof(f21409,plain,
    ( $false
    | ~ spl24_147 ),
    inference(resolution,[],[f9166,f5984]) ).

fof(f21420,plain,
    ( ~ spl24_111
    | ~ spl24_147 ),
    inference(avatar_contradiction_clause,[],[f21406]) ).

fof(f21406,plain,
    ( $false
    | ~ spl24_111
    | ~ spl24_147 ),
    inference(resolution,[],[f9166,f11012]) ).

fof(f21419,plain,
    ~ spl24_147,
    inference(avatar_contradiction_clause,[],[f21408]) ).

fof(f21408,plain,
    ( $false
    | ~ spl24_147 ),
    inference(resolution,[],[f9166,f6091]) ).

fof(f21418,plain,
    ~ spl24_147,
    inference(avatar_contradiction_clause,[],[f21410]) ).

fof(f21410,plain,
    ( $false
    | ~ spl24_147 ),
    inference(resolution,[],[f9166,f5993]) ).

fof(f21385,plain,
    ( spl24_144
    | ~ spl24_5
    | ~ spl24_461 ),
    inference(avatar_split_clause,[],[f21384,f21167,f6228,f9145]) ).

fof(f21384,plain,
    ( ! [X145] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X145)
    | ~ spl24_5
    | ~ spl24_461 ),
    inference(forward_demodulation,[],[f21270,f4924]) ).

fof(f4924,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,[],[f1520]) ).

fof(f1520,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,[],[f118]) ).

fof(f118,axiom,
    ! [X17] : 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)),X17),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__0) ).

fof(f21270,plain,
    ( ! [X145,X144] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X144,X145)),X145)
    | ~ spl24_5
    | ~ spl24_461 ),
    inference(backward_demodulation,[],[f21145,f21169]) ).

fof(f21169,plain,
    ( 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_Oone__class_Oone(tc_Nat_Onat))
    | ~ spl24_461 ),
    inference(avatar_component_clause,[],[f21167]) ).

fof(f21145,plain,
    ( ! [X145,X144] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X144,X145)),X145)
    | ~ spl24_5 ),
    inference(superposition,[],[f7403,f7700]) ).

fof(f7403,plain,
    ! [X26,X27,X25] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X25,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X26,X27)),X27),
    inference(superposition,[],[f4777,f4588]) ).

fof(f4588,plain,
    ! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),X1),
    inference(cnf_transformation,[],[f3570]) ).

fof(f3570,plain,
    ! [X0,X1,X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),X1),
    inference(rectify,[],[f1237]) ).

fof(f1237,plain,
    ! [X2,X1,X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0),X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)),
    inference(rectify,[],[f170]) ).

fof(f170,axiom,
    ! [X17,X51,X23] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X23,X17),X51) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X23,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X51)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__assoc) ).

fof(f4777,plain,
    ! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X1),
    inference(cnf_transformation,[],[f3700]) ).

fof(f3700,plain,
    ! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X1),
    inference(rectify,[],[f1619]) ).

fof(f1619,plain,
    ! [X1,X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X0),
    inference(rectify,[],[f500]) ).

fof(f500,axiom,
    ! [X54,X52] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X52,X54),X54),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__add__less2) ).

fof(f21383,plain,
    ( spl24_194
    | spl24_161
    | ~ spl24_5
    | ~ spl24_461 ),
    inference(avatar_split_clause,[],[f21382,f21167,f6228,f9332,f9939]) ).

fof(f9939,plain,
    ( spl24_194
  <=> ! [X48] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X48,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_194])]) ).

fof(f21382,plain,
    ( ! [X94,X95] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X94
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X95,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
    | ~ spl24_5
    | ~ spl24_461 ),
    inference(forward_demodulation,[],[f21255,f4924]) ).

fof(f21255,plain,
    ( ! [X94,X95] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X95,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X94))
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X94 )
    | ~ spl24_5
    | ~ spl24_461 ),
    inference(backward_demodulation,[],[f21120,f21169]) ).

fof(f21120,plain,
    ( ! [X94,X95] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X94
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X95,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X94)) )
    | ~ spl24_5 ),
    inference(superposition,[],[f7410,f7700]) ).

fof(f7410,plain,
    ! [X50,X48,X49] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X48,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X49,X50))
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X50 ),
    inference(superposition,[],[f5475,f4588]) ).

fof(f5475,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 ),
    inference(cnf_transformation,[],[f4126]) ).

fof(f4126,plain,
    ! [X0,X1] :
      ( ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
          & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) )
      & ( 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(flattening,[],[f4125]) ).

fof(f4125,plain,
    ! [X0,X1] :
      ( ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
          & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) )
      & ( 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(nnf_transformation,[],[f1268]) ).

fof(f1268,plain,
    ! [X0,X1] :
      ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
        & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
    <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) ),
    inference(rectify,[],[f116]) ).

fof(f116,axiom,
    ! [X18,X43] :
      ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X43
        & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X18 )
    <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X43,X18) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__is__0) ).

fof(f21367,plain,
    ( spl24_144
    | ~ spl24_5
    | ~ spl24_461 ),
    inference(avatar_split_clause,[],[f21366,f21167,f6228,f9145]) ).

fof(f21366,plain,
    ( ! [X169] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X169)
    | ~ spl24_5
    | ~ spl24_461 ),
    inference(forward_demodulation,[],[f21277,f4924]) ).

fof(f21277,plain,
    ( ! [X170,X169] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X169,X170)),X169)
    | ~ spl24_5
    | ~ spl24_461 ),
    inference(backward_demodulation,[],[f21156,f21169]) ).

fof(f21156,plain,
    ( ! [X170,X169] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X169,X170)),X169)
    | ~ spl24_5 ),
    inference(superposition,[],[f7531,f7700]) ).

fof(f7531,plain,
    ! [X70,X71,X69] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X70,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X69,X71)),X69),
    inference(superposition,[],[f5755,f5318]) ).

fof(f5318,plain,
    ! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)),
    inference(cnf_transformation,[],[f4013]) ).

fof(f4013,plain,
    ! [X0,X1,X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)),
    inference(rectify,[],[f1383]) ).

fof(f1383,plain,
    ! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)),
    inference(rectify,[],[f168]) ).

fof(f168,axiom,
    ! [X42,X19,X35] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X35,X42)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X35,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X42)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__commute) ).

fof(f5755,plain,
    ! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X0),
    inference(cnf_transformation,[],[f1374]) ).

fof(f1374,plain,
    ! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X0),
    inference(rectify,[],[f501]) ).

fof(f501,axiom,
    ! [X54,X52] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X54,X52),X54),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__add__less1) ).

fof(f21361,plain,
    ( spl24_144
    | ~ spl24_5
    | ~ spl24_461 ),
    inference(avatar_split_clause,[],[f21360,f21167,f6228,f9145]) ).

fof(f21360,plain,
    ( ! [X164] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X164)
    | ~ spl24_5
    | ~ spl24_461 ),
    inference(forward_demodulation,[],[f21359,f4924]) ).

fof(f21359,plain,
    ( ! [X164,X165] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X164,X165)),X164)
    | ~ spl24_5
    | ~ spl24_461 ),
    inference(forward_demodulation,[],[f21358,f4540]) ).

fof(f21358,plain,
    ( ! [X164,X165] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X164,X165)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X164,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ spl24_5
    | ~ spl24_461 ),
    inference(forward_demodulation,[],[f21288,f21304]) ).

fof(f21304,plain,
    ( ! [X2] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X2)
    | ~ spl24_5
    | ~ spl24_461 ),
    inference(forward_demodulation,[],[f21212,f6045]) ).

fof(f21212,plain,
    ( ! [X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ spl24_5
    | ~ spl24_461 ),
    inference(backward_demodulation,[],[f21008,f21169]) ).

fof(f21008,plain,
    ( ! [X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | ~ spl24_5 ),
    inference(superposition,[],[f7700,f5329]) ).

fof(f5329,plain,
    ! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1),
    inference(cnf_transformation,[],[f4024]) ).

fof(f4024,plain,
    ! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1),
    inference(rectify,[],[f1945]) ).

fof(f1945,plain,
    ! [X1,X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1),
    inference(rectify,[],[f167]) ).

fof(f167,axiom,
    ! [X23,X17] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23),X17) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X23),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__commute) ).

fof(f21288,plain,
    ( ! [X164,X165] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X164,X165)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X164,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X165,X165)))
    | ~ spl24_5
    | ~ spl24_461 ),
    inference(backward_demodulation,[],[f21195,f21169]) ).

fof(f21195,plain,
    ( ! [X164,X165] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X164,X165)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X164,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X165,X165)))
    | ~ spl24_5 ),
    inference(forward_demodulation,[],[f21154,f4588]) ).

fof(f21154,plain,
    ( ! [X164,X165] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X164,X165)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X164,X165),X165))
    | ~ spl24_5 ),
    inference(superposition,[],[f7519,f7700]) ).

fof(f7519,plain,
    ! [X28,X29,X27] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X28,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X27,X29)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X28,X29)),
    inference(superposition,[],[f4777,f5318]) ).

fof(f21334,plain,
    ( spl24_144
    | ~ spl24_5
    | ~ spl24_461 ),
    inference(avatar_split_clause,[],[f21333,f21167,f6228,f9145]) ).

fof(f21333,plain,
    ( ! [X40] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X40)
    | ~ spl24_5
    | ~ spl24_461 ),
    inference(forward_demodulation,[],[f21238,f4924]) ).

fof(f21238,plain,
    ( ! [X40] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X40),X40)
    | ~ spl24_5
    | ~ spl24_461 ),
    inference(backward_demodulation,[],[f21088,f21169]) ).

fof(f21088,plain,
    ( ! [X40] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X40),X40)
    | ~ spl24_5 ),
    inference(superposition,[],[f5755,f7700]) ).

fof(f21302,plain,
    ( spl24_144
    | ~ spl24_5
    | ~ spl24_461 ),
    inference(avatar_split_clause,[],[f21301,f21167,f6228,f9145]) ).

fof(f21301,plain,
    ( ! [X156] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X156)
    | ~ spl24_5
    | ~ spl24_461 ),
    inference(backward_demodulation,[],[f21296,f21300]) ).

fof(f21300,plain,
    ( ! [X28,X27] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X27,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X28,X27)) = X28
    | ~ spl24_5
    | ~ spl24_461 ),
    inference(forward_demodulation,[],[f21299,f4540]) ).

fof(f21299,plain,
    ( ! [X28,X27] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X27,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X28,X27)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X28,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ spl24_5
    | ~ spl24_461 ),
    inference(forward_demodulation,[],[f21232,f4924]) ).

fof(f21232,plain,
    ( ! [X28,X27] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X27,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X28,X27)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X28,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X27))
    | ~ spl24_5
    | ~ spl24_461 ),
    inference(backward_demodulation,[],[f21080,f21169]) ).

fof(f21080,plain,
    ( ! [X28,X27] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X27,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X28,X27)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X28,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X27))
    | ~ spl24_5 ),
    inference(superposition,[],[f5318,f7700]) ).

fof(f21296,plain,
    ( ! [X155,X156] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X155,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X156,X155)))
    | ~ spl24_5
    | ~ spl24_461 ),
    inference(forward_demodulation,[],[f21287,f4924]) ).

fof(f21287,plain,
    ( ! [X155,X156] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X155,X156)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X155,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X156,X155)))
    | ~ spl24_5
    | ~ spl24_461 ),
    inference(backward_demodulation,[],[f21192,f21169]) ).

fof(f21192,plain,
    ( ! [X155,X156] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X155,X156)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X155,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X156,X155)))
    | ~ spl24_5 ),
    inference(forward_demodulation,[],[f21150,f4588]) ).

fof(f21150,plain,
    ( ! [X155,X156] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X155,X156)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X155,X156),X155))
    | ~ spl24_5 ),
    inference(superposition,[],[f7415,f7700]) ).

fof(f7415,plain,
    ! [X68,X69,X67] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X67,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X68,X69)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X67,X68)),
    inference(superposition,[],[f5755,f4588]) ).

fof(f21291,plain,
    ( spl24_147
    | ~ spl24_5
    | ~ spl24_461 ),
    inference(avatar_split_clause,[],[f21290,f21167,f6228,f9165]) ).

fof(f21290,plain,
    ( ! [X120,X119] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X120,X119)
    | ~ spl24_5
    | ~ spl24_461 ),
    inference(forward_demodulation,[],[f21289,f4540]) ).

fof(f21289,plain,
    ( ! [X120,X119] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X120,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X119)
    | ~ spl24_5
    | ~ spl24_461 ),
    inference(forward_demodulation,[],[f21263,f4924]) ).

fof(f21263,plain,
    ( ! [X120,X119] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X120,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X119)),X119)
    | ~ spl24_5
    | ~ spl24_461 ),
    inference(backward_demodulation,[],[f21131,f21169]) ).

fof(f21131,plain,
    ( ! [X120,X119] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X120,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X119)),X119)
    | ~ spl24_5 ),
    inference(superposition,[],[f7531,f7700]) ).

fof(f21204,plain,
    ( spl24_461
    | spl24_466
    | ~ spl24_5 ),
    inference(avatar_split_clause,[],[f21046,f6228,f21202,f21167]) ).

fof(f21202,plain,
    ( spl24_466
  <=> ! [X46] :
        ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X46,X46) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) = X46 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_466])]) ).

fof(f21046,plain,
    ( ! [X46] :
        ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X46,X46) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) = X46
        | 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_Oone__class_Oone(tc_Nat_Onat)) )
    | ~ spl24_5 ),
    inference(superposition,[],[f5763,f7700]) ).

fof(f5763,plain,
    ! [X0,X1] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) != X1
      | c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 ),
    inference(cnf_transformation,[],[f2853]) ).

fof(f2853,plain,
    ! [X0,X1] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) != X1
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
      | c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0 ),
    inference(flattening,[],[f2852]) ).

fof(f2852,plain,
    ! [X1,X0] :
      ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) != X1 ),
    inference(ennf_transformation,[],[f1967]) ).

fof(f1967,plain,
    ! [X1,X0] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) = X1
     => ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 ) ),
    inference(rectify,[],[f328]) ).

fof(f328,axiom,
    ! [X17,X23] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23),X17) = X23
     => ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X17
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X23 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__self__implies__10) ).

fof(f21199,plain,
    ( spl24_461
    | spl24_465
    | ~ spl24_5 ),
    inference(avatar_split_clause,[],[f21044,f6228,f21197,f21167]) ).

fof(f21197,plain,
    ( spl24_465
  <=> ! [X43,X44] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X44) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X43,X43)
        | X43 = X44 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_465])]) ).

fof(f21044,plain,
    ( ! [X44,X43] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X44) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X43,X43)
        | X43 = X44
        | 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_Oone__class_Oone(tc_Nat_Onat)) )
    | ~ spl24_5 ),
    inference(superposition,[],[f5710,f7700]) ).

fof(f5710,plain,
    ! [X2,X0,X1] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2)
      | X1 = X2
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
    inference(cnf_transformation,[],[f4290]) ).

fof(f4290,plain,
    ! [X0,X1,X2] :
      ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
        | X1 = X2
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2) )
      & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2)
        | ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
          & X1 != X2 ) ) ),
    inference(rectify,[],[f4289]) ).

fof(f4289,plain,
    ! [X2,X1,X0] :
      ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2
        | X0 = X1
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) )
      & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)
        | ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2
          & X0 != X1 ) ) ),
    inference(flattening,[],[f4288]) ).

fof(f4288,plain,
    ! [X2,X1,X0] :
      ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2
        | X0 = X1
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) )
      & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)
        | ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2
          & X0 != X1 ) ) ),
    inference(nnf_transformation,[],[f2028]) ).

fof(f2028,plain,
    ! [X2,X1,X0] :
      ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2
        | X0 = X1 )
    <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) ),
    inference(rectify,[],[f181]) ).

fof(f181,axiom,
    ! [X43,X18,X44] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X44),X43) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X44),X18)
    <=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X44
        | X18 = X43 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel__disj) ).

fof(f21185,plain,
    ( spl24_463
    | spl24_464
    | ~ spl24_5 ),
    inference(avatar_split_clause,[],[f21048,f6228,f21183,f21179]) ).

fof(f21183,plain,
    ( spl24_464
  <=> ! [X48] : c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X48,X48) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_464])]) ).

fof(f21048,plain,
    ( ! [X48] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X48,X48)
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
    | ~ spl24_5 ),
    inference(superposition,[],[f6616,f7700]) ).

fof(f6616,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)
      | c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1 ),
    inference(forward_demodulation,[],[f6599,f5628]) ).

fof(f6599,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(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)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) ),
    inference(backward_demodulation,[],[f6284,f5628]) ).

fof(f6284,plain,
    ! [X0,X1] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) ),
    inference(forward_demodulation,[],[f6283,f4806]) ).

fof(f6283,plain,
    ! [X0,X1] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1 ),
    inference(backward_demodulation,[],[f5979,f4806]) ).

fof(f5979,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
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(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)) ),
    inference(definition_unfolding,[],[f5553,f4877,f4877]) ).

fof(f5553,plain,
    ! [X0,X1] :
      ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
      | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) ),
    inference(cnf_transformation,[],[f4186]) ).

fof(f4186,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 )
        | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) )
      & ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)
        | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0
        | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ) ),
    inference(flattening,[],[f4185]) ).

fof(f4185,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 )
        | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) )
      & ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)
        | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0
        | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ) ),
    inference(nnf_transformation,[],[f1418]) ).

fof(f1418,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 )
    <=> c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) ),
    inference(rectify,[],[f140]) ).

fof(f140,axiom,
    ! [X18,X43] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X43),X18) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    <=> ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X18
        & c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X43 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__1__iff) ).

fof(f21173,plain,
    ( spl24_461
    | spl24_462
    | ~ spl24_5 ),
    inference(avatar_split_clause,[],[f21043,f6228,f21171,f21167]) ).

fof(f21171,plain,
    ( spl24_462
  <=> ! [X41,X42] :
        ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X41,X41) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X42)
        | X41 = X42 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_462])]) ).

fof(f21043,plain,
    ( ! [X41,X42] :
        ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X41,X41) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X42)
        | X41 = X42
        | 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_Oone__class_Oone(tc_Nat_Onat)) )
    | ~ spl24_5 ),
    inference(superposition,[],[f5710,f7700]) ).

fof(f20970,plain,
    ( spl24_269
    | spl24_271 ),
    inference(avatar_split_clause,[],[f12723,f12701,f12649]) ).

fof(f12649,plain,
    ( spl24_269
  <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_269])]) ).

fof(f12723,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | spl24_271 ),
    inference(resolution,[],[f12703,f5360]) ).

fof(f12703,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | spl24_271 ),
    inference(avatar_component_clause,[],[f12701]) ).

fof(f20969,plain,
    ( spl24_460
    | ~ spl24_272 ),
    inference(avatar_split_clause,[],[f20943,f12705,f20966]) ).

fof(f20966,plain,
    ( spl24_460
  <=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_460])]) ).

fof(f12705,plain,
    ( spl24_272
  <=> c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_272])]) ).

fof(f20943,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ spl24_272 ),
    inference(superposition,[],[f20237,f12707]) ).

fof(f12707,plain,
    ( c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ spl24_272 ),
    inference(avatar_component_clause,[],[f12705]) ).

fof(f20237,plain,
    ! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X0),
    inference(trivial_inequality_removal,[],[f20227]) ).

fof(f20227,plain,
    ! [X0] :
      ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X0)
      | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(superposition,[],[f4778,f4793]) ).

fof(f4778,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0)
      | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X0) ),
    inference(cnf_transformation,[],[f2555]) ).

fof(f2555,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X0)
      | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0) ),
    inference(ennf_transformation,[],[f1386]) ).

fof(f1386,plain,
    ! [X1,X0] :
      ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X0)
     => c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0) ),
    inference(rectify,[],[f905]) ).

fof(f905,axiom,
    ! [X56,X51] :
      ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X51),X56)
     => c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Divides_Odiv__class_Omod(tc_Int_Oint,X51,X56) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zminus1__not__zero) ).

fof(f20964,plain,
    ( spl24_459
    | ~ spl24_272 ),
    inference(avatar_split_clause,[],[f20933,f12705,f20961]) ).

fof(f20933,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ spl24_272 ),
    inference(superposition,[],[f4772,f12707]) ).

fof(f20957,plain,
    ( spl24_458
    | ~ spl24_9
    | ~ spl24_272 ),
    inference(avatar_split_clause,[],[f20941,f12705,f6248,f20954]) ).

fof(f20954,plain,
    ( spl24_458
  <=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_458])]) ).

fof(f20941,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ spl24_9
    | ~ spl24_272 ),
    inference(superposition,[],[f13360,f12707]) ).

fof(f20950,plain,
    ( spl24_457
    | ~ spl24_272 ),
    inference(avatar_split_clause,[],[f20934,f12705,f20947]) ).

fof(f20947,plain,
    ( spl24_457
  <=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_457])]) ).

fof(f20934,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ spl24_272 ),
    inference(superposition,[],[f5009,f12707]) ).

fof(f20945,plain,
    ( spl24_314
    | ~ spl24_272 ),
    inference(avatar_split_clause,[],[f20940,f12705,f13763]) ).

fof(f20940,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ spl24_272 ),
    inference(superposition,[],[f12434,f12707]) ).

fof(f20854,plain,
    ( spl24_272
    | spl24_456
    | ~ spl24_258 ),
    inference(avatar_split_clause,[],[f20814,f12472,f20851,f12705]) ).

fof(f20851,plain,
    ( spl24_456
  <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_456])]) ).

fof(f20814,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ spl24_258 ),
    inference(resolution,[],[f12647,f4658]) ).

fof(f4658,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)))
      | X0 = X1
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1) ),
    inference(cnf_transformation,[],[f3618]) ).

fof(f12647,plain,
    ( ! [X2] : c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))
    | ~ spl24_258 ),
    inference(forward_demodulation,[],[f12645,f4706]) ).

fof(f12645,plain,
    ( ! [X2] : c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))
    | ~ spl24_258 ),
    inference(resolution,[],[f12474,f5603]) ).

fof(f12474,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ spl24_258 ),
    inference(avatar_component_clause,[],[f12472]) ).

fof(f20759,plain,
    ( spl24_448
    | ~ spl24_423 ),
    inference(avatar_split_clause,[],[f20645,f18639,f20647]) ).

fof(f20645,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ spl24_423 ),
    inference(forward_demodulation,[],[f20640,f4706]) ).

fof(f20640,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ spl24_423 ),
    inference(resolution,[],[f18641,f7226]) ).

fof(f18641,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_423 ),
    inference(avatar_component_clause,[],[f18639]) ).

fof(f20758,plain,
    ( spl24_450
    | ~ spl24_423 ),
    inference(avatar_split_clause,[],[f20642,f18639,f20662]) ).

fof(f20642,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_423 ),
    inference(resolution,[],[f18641,f5695]) ).

fof(f20757,plain,
    ( spl24_451
    | ~ spl24_423 ),
    inference(avatar_split_clause,[],[f20638,f18639,f20667]) ).

fof(f20638,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ spl24_423 ),
    inference(resolution,[],[f18641,f7228]) ).

fof(f20756,plain,
    ( spl24_455
    | spl24_452
    | spl24_423 ),
    inference(avatar_split_clause,[],[f20736,f18639,f20738,f20752]) ).

fof(f20738,plain,
    ( spl24_452
  <=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_452])]) ).

fof(f20736,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | spl24_423 ),
    inference(resolution,[],[f18640,f5285]) ).

fof(f20755,plain,
    ( spl24_452
    | spl24_455
    | spl24_423 ),
    inference(avatar_split_clause,[],[f20735,f18639,f20752,f20738]) ).

fof(f20735,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | spl24_423 ),
    inference(resolution,[],[f18640,f5285]) ).

fof(f20750,plain,
    ( spl24_452
    | spl24_454
    | spl24_423 ),
    inference(avatar_split_clause,[],[f20733,f18639,f20747,f20738]) ).

fof(f20733,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | spl24_423 ),
    inference(resolution,[],[f18640,f7145]) ).

fof(f20745,plain,
    ( spl24_452
    | spl24_453
    | spl24_423 ),
    inference(avatar_split_clause,[],[f20732,f18639,f20742,f20738]) ).

fof(f20732,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | spl24_423 ),
    inference(resolution,[],[f18640,f7146]) ).

fof(f7146,plain,
    ! [X3] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X3
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3) ),
    inference(resolution,[],[f5285,f5095]) ).

fof(f20670,plain,
    ( spl24_451
    | ~ spl24_423 ),
    inference(avatar_split_clause,[],[f20638,f18639,f20667]) ).

fof(f20665,plain,
    ( spl24_450
    | ~ spl24_423 ),
    inference(avatar_split_clause,[],[f20642,f18639,f20662]) ).

fof(f20660,plain,
    ( spl24_449
    | ~ spl24_423 ),
    inference(avatar_split_clause,[],[f20655,f18639,f20657]) ).

fof(f20655,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_423 ),
    inference(forward_demodulation,[],[f20654,f19715]) ).

fof(f19715,plain,
    ! [X16,X14,X17,X15] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X17,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X16,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X14,X15))) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X14,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X17,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X15,X16))),
    inference(superposition,[],[f5388,f7545]) ).

fof(f20654,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_423 ),
    inference(forward_demodulation,[],[f20653,f7557]) ).

fof(f7557,plain,
    ! [X16,X14,X17,X15] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X14,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X17,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X15,X16))) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X17,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X15,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X14,X16))),
    inference(superposition,[],[f5388,f5388]) ).

fof(f20653,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_423 ),
    inference(forward_demodulation,[],[f20652,f19675]) ).

fof(f19675,plain,
    ! [X38,X39,X36,X37] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X39,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X36,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X37,X38))) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X38,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X39,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X36,X37))),
    inference(superposition,[],[f7545,f5810]) ).

fof(f20652,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_423 ),
    inference(forward_demodulation,[],[f20651,f7557]) ).

fof(f20651,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_423 ),
    inference(forward_demodulation,[],[f20639,f5388]) ).

fof(f20639,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_423 ),
    inference(resolution,[],[f18641,f6872]) ).

fof(f20650,plain,
    ( spl24_448
    | ~ spl24_423 ),
    inference(avatar_split_clause,[],[f20645,f18639,f20647]) ).

fof(f20632,plain,
    ( spl24_447
    | ~ spl24_111 ),
    inference(avatar_split_clause,[],[f20627,f6883,f20629]) ).

fof(f20629,plain,
    ( spl24_447
  <=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK14(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_447])]) ).

fof(f20627,plain,
    ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK14(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | ~ spl24_111 ),
    inference(forward_demodulation,[],[f20603,f5628]) ).

fof(f20603,plain,
    ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),sK14(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | ~ spl24_111 ),
    inference(resolution,[],[f5962,f6885]) ).

fof(f20585,plain,
    ( ~ spl24_446
    | spl24_403 ),
    inference(avatar_split_clause,[],[f20576,f18015,f20581]) ).

fof(f20576,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | spl24_403 ),
    inference(resolution,[],[f18017,f7241]) ).

fof(f7241,plain,
    ! [X2,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X2)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(superposition,[],[f5133,f5830]) ).

fof(f5133,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1) ),
    inference(cnf_transformation,[],[f3928]) ).

fof(f20584,plain,
    ( ~ spl24_446
    | spl24_403 ),
    inference(avatar_split_clause,[],[f20577,f18015,f20581]) ).

fof(f20577,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | spl24_403 ),
    inference(resolution,[],[f18017,f5133]) ).

fof(f20481,plain,
    ( spl24_444
    | spl24_443 ),
    inference(avatar_split_clause,[],[f20460,f20391,f20462]) ).

fof(f20460,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | spl24_443 ),
    inference(resolution,[],[f20392,f5360]) ).

fof(f20392,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | spl24_443 ),
    inference(avatar_component_clause,[],[f20391]) ).

fof(f20480,plain,
    ( spl24_444
    | spl24_443 ),
    inference(avatar_split_clause,[],[f20459,f20391,f20462]) ).

fof(f20459,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | spl24_443 ),
    inference(resolution,[],[f20392,f5360]) ).

fof(f20479,plain,
    ( spl24_445
    | ~ spl24_443 ),
    inference(avatar_split_clause,[],[f20472,f20391,f20476]) ).

fof(f20476,plain,
    ( spl24_445
  <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_445])]) ).

fof(f20472,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ spl24_443 ),
    inference(resolution,[],[f20393,f5678]) ).

fof(f20466,plain,
    ( spl24_444
    | spl24_443 ),
    inference(avatar_split_clause,[],[f20460,f20391,f20462]) ).

fof(f20465,plain,
    ( spl24_444
    | spl24_443 ),
    inference(avatar_split_clause,[],[f20459,f20391,f20462]) ).

fof(f20397,plain,
    ( spl24_443
    | ~ spl24_255
    | ~ spl24_314 ),
    inference(avatar_split_clause,[],[f20386,f13763,f12451,f20391]) ).

fof(f20396,plain,
    ( spl24_443
    | ~ spl24_314 ),
    inference(avatar_split_clause,[],[f20395,f13763,f20391]) ).

fof(f20394,plain,
    ( spl24_443
    | ~ spl24_255
    | ~ spl24_314 ),
    inference(avatar_split_clause,[],[f20389,f13763,f12451,f20391]) ).

fof(f20355,plain,
    ( spl24_442
    | ~ spl24_9 ),
    inference(avatar_split_clause,[],[f20315,f6248,f20351]) ).

fof(f20351,plain,
    ( spl24_442
  <=> ! [X38,X37] : c_Rings_Odvd__class_Odvd(tc_Int_Oint,X37,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X37,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X37),X38))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_442])]) ).

fof(f20315,plain,
    ( ! [X0,X1] : c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X1)))
    | ~ spl24_9 ),
    inference(resolution,[],[f4791,f12913]) ).

fof(f4791,plain,
    ! [X2,X0,X1] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X1)
      | c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0))) ),
    inference(cnf_transformation,[],[f3710]) ).

fof(f3710,plain,
    ! [X0,X1,X2] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0)))
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X1) )
      & ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X1)
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0))) ) ),
    inference(rectify,[],[f3709]) ).

fof(f3709,plain,
    ! [X1,X2,X0] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X1)))
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,X2) )
      & ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,X2)
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X1))) ) ),
    inference(nnf_transformation,[],[f1488]) ).

fof(f1488,plain,
    ! [X1,X2,X0] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X1)))
    <=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,X2) ),
    inference(rectify,[],[f770]) ).

fof(f770,axiom,
    ! [X44,X43,X18] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X44,X18)
    <=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,X44,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X18,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X44),X43))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__reduce) ).

fof(f20353,plain,
    ( ~ spl24_9
    | spl24_442 ),
    inference(avatar_split_clause,[],[f20329,f20351,f6248]) ).

fof(f20329,plain,
    ! [X38,X37] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X37,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X37,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X37),X38)))
      | ~ class_Rings_Ocomm__semiring__1(tc_Int_Oint) ),
    inference(resolution,[],[f4791,f5375]) ).

fof(f5375,plain,
    ! [X0,X1] :
      ( c_Rings_Odvd__class_Odvd(X1,X0,X0)
      | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(cnf_transformation,[],[f3263]) ).

fof(f3263,plain,
    ! [X0,X1] :
      ( ~ class_Rings_Ocomm__semiring__1(X1)
      | c_Rings_Odvd__class_Odvd(X1,X0,X0) ),
    inference(ennf_transformation,[],[f1302]) ).

fof(f1302,plain,
    ! [X0,X1] :
      ( class_Rings_Ocomm__semiring__1(X1)
     => c_Rings_Odvd__class_Odvd(X1,X0,X0) ),
    inference(rectify,[],[f431]) ).

fof(f431,axiom,
    ! [X5,X4] :
      ( class_Rings_Ocomm__semiring__1(X4)
     => c_Rings_Odvd__class_Odvd(X4,X5,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__refl) ).

fof(f20349,plain,
    ( ~ spl24_9
    | spl24_441 ),
    inference(avatar_split_clause,[],[f20334,f20347,f6248]) ).

fof(f20347,plain,
    ( spl24_441
  <=> ! [X55,X54,X53,X52] :
        ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X52),X53),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X52),X54),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X52),X53)),X55)))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53,X54) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_441])]) ).

fof(f20334,plain,
    ! [X54,X55,X52,X53] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X52),X53),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X52),X54),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X52),X53)),X55)))
      | ~ class_Rings_Ocomm__semiring__1(tc_Int_Oint)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53,X54) ),
    inference(resolution,[],[f4791,f5448]) ).

fof(f20344,plain,
    ( ~ spl24_9
    | spl24_440 ),
    inference(avatar_split_clause,[],[f20333,f20342,f6248]) ).

fof(f20342,plain,
    ( spl24_440
  <=> ! [X48,X51,X47,X50,X49] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48,X50)
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X47,X49)
        | c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X47),X48),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X49),X50),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X47),X48)),X51))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_440])]) ).

fof(f20333,plain,
    ! [X50,X51,X48,X49,X47] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48,X50)
      | c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X47),X48),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X49),X50),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X47),X48)),X51)))
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X47,X49)
      | ~ class_Rings_Ocomm__semiring__1(tc_Int_Oint) ),
    inference(resolution,[],[f4791,f5752]) ).

fof(f20339,plain,
    ( spl24_439
    | ~ spl24_9 ),
    inference(avatar_split_clause,[],[f20332,f6248,f20337]) ).

fof(f20337,plain,
    ( spl24_439
  <=> ! [X44,X43,X46,X45] :
        ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X43),X44),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X45),X44),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X43),X44)),X46)))
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X43,X45) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_439])]) ).

fof(f20332,plain,
    ! [X46,X44,X45,X43] :
      ( ~ class_Rings_Ocomm__semiring__1(tc_Int_Oint)
      | c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X43),X44),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X45),X44),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X43),X44)),X46)))
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X43,X45) ),
    inference(resolution,[],[f4791,f4750]) ).

fof(f20196,plain,
    ( ~ spl24_153
    | spl24_438
    | ~ spl24_314 ),
    inference(avatar_split_clause,[],[f20190,f13763,f20194,f9279]) ).

fof(f20190,plain,
    ( ! [X7] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X7,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
    | ~ spl24_314 ),
    inference(resolution,[],[f20120,f5024]) ).

fof(f5024,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X1))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(cnf_transformation,[],[f2610]) ).

fof(f2610,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X1))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(ennf_transformation,[],[f1423]) ).

fof(f1423,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
     => c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X1)) ),
    inference(rectify,[],[f896]) ).

fof(f896,axiom,
    ! [X5,X29] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X29,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
     => c_Orderings_Oord__class_Oless(tc_Int_Oint,X29,c_Divides_Odiv__class_Omod(tc_Int_Oint,X5,X29)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__mod__bound) ).

fof(f20120,plain,
    ( ! [X2] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) )
    | ~ spl24_314 ),
    inference(superposition,[],[f5133,f13765]) ).

fof(f20147,plain,
    ( ~ spl24_1
    | ~ spl24_314
    | spl24_424 ),
    inference(avatar_split_clause,[],[f20146,f18662,f13763,f6208]) ).

fof(f18662,plain,
    ( spl24_424
  <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_424])]) ).

fof(f20146,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ spl24_314
    | spl24_424 ),
    inference(backward_demodulation,[],[f18663,f20143]) ).

fof(f20143,plain,
    ( ! [X8] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X8,c_Groups_Oone__class_Oone(tc_Int_Oint))) = X8
    | ~ spl24_314 ),
    inference(forward_demodulation,[],[f20132,f4958]) ).

fof(f20132,plain,
    ( ! [X8] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X8,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X8,c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ spl24_314 ),
    inference(superposition,[],[f5388,f13765]) ).

fof(f18663,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    | spl24_424 ),
    inference(avatar_component_clause,[],[f18662]) ).

fof(f20115,plain,
    ( ~ spl24_9
    | spl24_437
    | ~ spl24_9 ),
    inference(avatar_split_clause,[],[f20101,f6248,f20113,f6248]) ).

fof(f20113,plain,
    ( spl24_437
  <=> ! [X55,X54,X53,X52] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X52),X53),X54)
        | c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X52),X53),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X52),X55),X54))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53,X55) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_437])]) ).

fof(f20101,plain,
    ( ! [X54,X55,X52,X53] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X52),X53),X54)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53,X55)
        | c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X52),X53),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X52),X55),X54))
        | ~ class_Rings_Ocomm__semiring__1(tc_Int_Oint) )
    | ~ spl24_9 ),
    inference(resolution,[],[f7653,f5448]) ).

fof(f7653,plain,
    ( ! [X3,X4,X5] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X3,X4)
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X3,X5)
        | c_Rings_Odvd__class_Odvd(tc_Int_Oint,X3,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4,X5)) )
    | ~ spl24_9 ),
    inference(resolution,[],[f5758,f6250]) ).

fof(f5758,plain,
    ! [X2,X3,X0,X1] :
      ( ~ class_Rings_Ocomm__semiring__1(X3)
      | ~ c_Rings_Odvd__class_Odvd(X3,X2,X1)
      | c_Rings_Odvd__class_Odvd(X3,X2,c_Groups_Oplus__class_Oplus(X3,X1,X0))
      | ~ c_Rings_Odvd__class_Odvd(X3,X2,X0) ),
    inference(cnf_transformation,[],[f4322]) ).

fof(f4322,plain,
    ! [X0,X1,X2,X3] :
      ( ~ c_Rings_Odvd__class_Odvd(X3,X2,X1)
      | ~ class_Rings_Ocomm__semiring__1(X3)
      | c_Rings_Odvd__class_Odvd(X3,X2,c_Groups_Oplus__class_Oplus(X3,X1,X0))
      | ~ c_Rings_Odvd__class_Odvd(X3,X2,X0) ),
    inference(rectify,[],[f3124]) ).

fof(f3124,plain,
    ! [X2,X3,X0,X1] :
      ( ~ c_Rings_Odvd__class_Odvd(X1,X0,X3)
      | ~ class_Rings_Ocomm__semiring__1(X1)
      | c_Rings_Odvd__class_Odvd(X1,X0,c_Groups_Oplus__class_Oplus(X1,X3,X2))
      | ~ c_Rings_Odvd__class_Odvd(X1,X0,X2) ),
    inference(flattening,[],[f3123]) ).

fof(f3123,plain,
    ! [X0,X3,X2,X1] :
      ( c_Rings_Odvd__class_Odvd(X1,X0,c_Groups_Oplus__class_Oplus(X1,X3,X2))
      | ~ c_Rings_Odvd__class_Odvd(X1,X0,X2)
      | ~ c_Rings_Odvd__class_Odvd(X1,X0,X3)
      | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(ennf_transformation,[],[f1676]) ).

fof(f1676,plain,
    ! [X0,X3,X2,X1] :
      ( class_Rings_Ocomm__semiring__1(X1)
     => ( c_Rings_Odvd__class_Odvd(X1,X0,X3)
       => ( c_Rings_Odvd__class_Odvd(X1,X0,X2)
         => c_Rings_Odvd__class_Odvd(X1,X0,c_Groups_Oplus__class_Oplus(X1,X3,X2)) ) ) ),
    inference(rectify,[],[f419]) ).

fof(f419,axiom,
    ! [X5,X4,X22,X29] :
      ( class_Rings_Ocomm__semiring__1(X4)
     => ( c_Rings_Odvd__class_Odvd(X4,X5,X29)
       => ( c_Rings_Odvd__class_Odvd(X4,X5,X22)
         => c_Rings_Odvd__class_Odvd(X4,X5,c_Groups_Oplus__class_Oplus(X4,X29,X22)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__add) ).

fof(f20110,plain,
    ( ~ spl24_9
    | spl24_436
    | ~ spl24_9 ),
    inference(avatar_split_clause,[],[f20099,f6248,f20108,f6248]) ).

fof(f20108,plain,
    ( spl24_436
  <=> ! [X44,X43,X46,X45] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X43),X44),X45)
        | c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X43),X44),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X46),X44),X45))
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X43,X46) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_436])]) ).

fof(f20099,plain,
    ( ! [X46,X44,X45,X43] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X43),X44),X45)
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X43,X46)
        | ~ class_Rings_Ocomm__semiring__1(tc_Int_Oint)
        | c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X43),X44),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X46),X44),X45)) )
    | ~ spl24_9 ),
    inference(resolution,[],[f7653,f4750]) ).

fof(f20106,plain,
    ( spl24_435
    | ~ spl24_9
    | ~ spl24_9 ),
    inference(avatar_split_clause,[],[f20100,f6248,f6248,f20104]) ).

fof(f20104,plain,
    ( spl24_435
  <=> ! [X48,X51,X50,X49,X47] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X47,X50)
        | c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X47),X48),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X50),X51),X49))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48,X51)
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X47),X48),X49) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_435])]) ).

fof(f20100,plain,
    ( ! [X50,X51,X48,X49,X47] :
        ( ~ class_Rings_Ocomm__semiring__1(tc_Int_Oint)
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X47,X50)
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X47),X48),X49)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48,X51)
        | c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X47),X48),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X50),X51),X49)) )
    | ~ spl24_9 ),
    inference(resolution,[],[f7653,f5752]) ).

fof(f20081,plain,
    ( spl24_434
    | ~ spl24_5
    | ~ spl24_5 ),
    inference(avatar_split_clause,[],[f20067,f6228,f6228,f20079]) ).

fof(f20079,plain,
    ( spl24_434
  <=> ! [X31,X33,X30,X32] :
        ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X30),X31),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X32,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X30),X33)))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31,X33)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X30),X31),X32) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_434])]) ).

fof(f20067,plain,
    ( ! [X31,X32,X30,X33] :
        ( ~ class_Rings_Ocomm__semiring__1(tc_Nat_Onat)
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X30),X31),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X32,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X30),X33)))
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X30),X31),X32)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31,X33) )
    | ~ spl24_5 ),
    inference(resolution,[],[f7652,f5448]) ).

fof(f7652,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,X2)
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,X1) )
    | ~ spl24_5 ),
    inference(resolution,[],[f5758,f6230]) ).

fof(f20076,plain,
    ( ~ spl24_5
    | spl24_433
    | ~ spl24_5 ),
    inference(avatar_split_clause,[],[f20065,f6228,f20074,f6228]) ).

fof(f20074,plain,
    ( spl24_433
  <=> ! [X24,X21,X23,X22] :
        ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X21),X22),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X23,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X24),X22)))
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X21),X22),X23)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X21,X24) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_433])]) ).

fof(f20065,plain,
    ( ! [X21,X24,X22,X23] :
        ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X21),X22),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X23,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X24),X22)))
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X21,X24)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X21),X22),X23)
        | ~ class_Rings_Ocomm__semiring__1(tc_Nat_Onat) )
    | ~ spl24_5 ),
    inference(resolution,[],[f7652,f4750]) ).

fof(f20072,plain,
    ( ~ spl24_5
    | spl24_432
    | ~ spl24_5 ),
    inference(avatar_split_clause,[],[f20066,f6228,f20070,f6228]) ).

fof(f20070,plain,
    ( spl24_432
  <=> ! [X29,X27,X25,X28,X26] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X29)
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X25),X26),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X27,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X28),X29)))
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X25,X28)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X25),X26),X27) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_432])]) ).

fof(f20066,plain,
    ( ! [X28,X29,X26,X27,X25] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X29)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X25),X26),X27)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X25,X28)
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X25),X26),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X27,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X28),X29)))
        | ~ class_Rings_Ocomm__semiring__1(tc_Nat_Onat) )
    | ~ spl24_5 ),
    inference(resolution,[],[f7652,f5752]) ).

fof(f20041,plain,
    ( ~ spl24_315
    | spl24_314
    | ~ spl24_311 ),
    inference(avatar_split_clause,[],[f18848,f13674,f13763,f13767]) ).

fof(f18848,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ spl24_311 ),
    inference(resolution,[],[f13676,f5243]) ).

fof(f20040,plain,
    ( spl24_314
    | ~ spl24_315
    | spl24_234 ),
    inference(avatar_split_clause,[],[f18675,f11152,f13767,f13763]) ).

fof(f18675,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | spl24_234 ),
    inference(resolution,[],[f11153,f5693]) ).

fof(f20036,plain,
    ( spl24_431
    | ~ spl24_402 ),
    inference(avatar_split_clause,[],[f20031,f17755,f20033]) ).

fof(f20031,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_402 ),
    inference(forward_demodulation,[],[f20030,f7557]) ).

fof(f20030,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_402 ),
    inference(forward_demodulation,[],[f20029,f7557]) ).

fof(f20029,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_402 ),
    inference(forward_demodulation,[],[f20028,f7545]) ).

fof(f20028,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_402 ),
    inference(forward_demodulation,[],[f20027,f7557]) ).

fof(f20027,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_402 ),
    inference(forward_demodulation,[],[f20023,f5388]) ).

fof(f20023,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_402 ),
    inference(resolution,[],[f17757,f6872]) ).

fof(f18976,plain,
    ( spl24_430
    | ~ spl24_391
    | ~ spl24_391 ),
    inference(avatar_split_clause,[],[f18971,f16524,f16524,f18974]) ).

fof(f18974,plain,
    ( spl24_430
  <=> ! [X2,X1,X3] : c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Int_Oint)),X1,c_Polynomial_Osmult(tc_Polynomial_Opoly(tc_Int_Oint),X2,c_Polynomial_Osmult(tc_Polynomial_Opoly(tc_Int_Oint),X3,X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_430])]) ).

fof(f18971,plain,
    ( ! [X2,X3,X1] :
        ( ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Int_Oint))
        | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Int_Oint)),X1,c_Polynomial_Osmult(tc_Polynomial_Opoly(tc_Int_Oint),X2,c_Polynomial_Osmult(tc_Polynomial_Opoly(tc_Int_Oint),X3,X1))) )
    | ~ spl24_391 ),
    inference(resolution,[],[f17567,f4770]) ).

fof(f17567,plain,
    ( ! [X10,X9] : c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Int_Oint)),X9,c_Polynomial_Osmult(tc_Polynomial_Opoly(tc_Int_Oint),X10,X9))
    | ~ spl24_391 ),
    inference(resolution,[],[f15743,f16525]) ).

fof(f15743,plain,
    ! [X2,X0,X1] :
      ( ~ class_Rings_Ocomm__semiring__1(X0)
      | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X0),X1,c_Polynomial_Osmult(X0,X2,X1)) ),
    inference(duplicate_literal_removal,[],[f15742]) ).

fof(f15742,plain,
    ! [X2,X0,X1] :
      ( ~ class_Rings_Ocomm__semiring__1(X0)
      | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X0),X1,c_Polynomial_Osmult(X0,X2,X1))
      | ~ class_Rings_Ocomm__semiring__1(X0) ),
    inference(resolution,[],[f7432,f4828]) ).

fof(f7432,plain,
    ! [X2,X0,X1] :
      ( ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__semiring__1(X0)
      | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X0),X1,c_Polynomial_Osmult(X0,X2,X1)) ),
    inference(resolution,[],[f4770,f5375]) ).

fof(f18930,plain,
    ( ~ spl24_384
    | spl24_429
    | ~ spl24_384 ),
    inference(avatar_split_clause,[],[f18925,f16431,f18928,f16431]) ).

fof(f18928,plain,
    ( spl24_429
  <=> ! [X2,X1,X3] : c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Nat_Onat)),X1,c_Polynomial_Osmult(tc_Polynomial_Opoly(tc_Nat_Onat),X2,c_Polynomial_Osmult(tc_Polynomial_Opoly(tc_Nat_Onat),X3,X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_429])]) ).

fof(f18925,plain,
    ( ! [X2,X3,X1] :
        ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Nat_Onat)),X1,c_Polynomial_Osmult(tc_Polynomial_Opoly(tc_Nat_Onat),X2,c_Polynomial_Osmult(tc_Polynomial_Opoly(tc_Nat_Onat),X3,X1)))
        | ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Nat_Onat)) )
    | ~ spl24_384 ),
    inference(resolution,[],[f17566,f4770]) ).

fof(f17566,plain,
    ( ! [X8,X7] : c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Nat_Onat)),X7,c_Polynomial_Osmult(tc_Polynomial_Opoly(tc_Nat_Onat),X8,X7))
    | ~ spl24_384 ),
    inference(resolution,[],[f15743,f16432]) ).

fof(f18923,plain,
    ( spl24_428
    | ~ spl24_336
    | ~ spl24_397 ),
    inference(avatar_split_clause,[],[f18919,f17030,f14289,f18921]) ).

fof(f18921,plain,
    ( spl24_428
  <=> ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Polynomial_Opoly(tc_Int_Oint),c_Polynomial_Osmult(tc_Polynomial_Opoly(tc_Int_Oint),X0,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Int_Oint))))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_428])]) ).

fof(f14289,plain,
    ( spl24_336
  <=> class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_336])]) ).

fof(f17030,plain,
    ( spl24_397
  <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(tc_Polynomial_Opoly(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Int_Oint)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_397])]) ).

fof(f18919,plain,
    ( ! [X0] :
        ( ~ class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(tc_Int_Oint))
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Polynomial_Opoly(tc_Int_Oint),c_Polynomial_Osmult(tc_Polynomial_Opoly(tc_Int_Oint),X0,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Int_Oint))))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
    | ~ spl24_397 ),
    inference(superposition,[],[f5260,f17032]) ).

fof(f17032,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(tc_Polynomial_Opoly(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Int_Oint))))
    | ~ spl24_397 ),
    inference(avatar_component_clause,[],[f17030]) ).

fof(f18918,plain,
    ( ~ spl24_331
    | spl24_427
    | ~ spl24_389 ),
    inference(avatar_split_clause,[],[f18914,f16508,f18916,f14185]) ).

fof(f14185,plain,
    ( spl24_331
  <=> class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_331])]) ).

fof(f18916,plain,
    ( spl24_427
  <=> ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Polynomial_Opoly(tc_Nat_Onat),c_Polynomial_Osmult(tc_Polynomial_Opoly(tc_Nat_Onat),X0,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Nat_Onat))))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_427])]) ).

fof(f16508,plain,
    ( spl24_389
  <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(tc_Polynomial_Opoly(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Nat_Onat)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_389])]) ).

fof(f18914,plain,
    ( ! [X0] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Polynomial_Opoly(tc_Nat_Onat),c_Polynomial_Osmult(tc_Polynomial_Opoly(tc_Nat_Onat),X0,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Nat_Onat))))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(tc_Nat_Onat)) )
    | ~ spl24_389 ),
    inference(superposition,[],[f5260,f16510]) ).

fof(f16510,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(tc_Polynomial_Opoly(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Nat_Onat))))
    | ~ spl24_389 ),
    inference(avatar_component_clause,[],[f16508]) ).

fof(f18823,plain,
    ( spl24_426
    | ~ spl24_235
    | ~ spl24_256 ),
    inference(avatar_split_clause,[],[f18789,f12456,f11215,f18820]) ).

fof(f18820,plain,
    ( spl24_426
  <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_426])]) ).

fof(f18789,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
    | ~ spl24_235
    | ~ spl24_256 ),
    inference(resolution,[],[f12624,f11224]) ).

fof(f11224,plain,
    ( ! [X0] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) )
    | ~ spl24_235 ),
    inference(resolution,[],[f11217,f4403]) ).

fof(f18756,plain,
    ( spl24_425
    | ~ spl24_238 ),
    inference(avatar_split_clause,[],[f18751,f11236,f18753]) ).

fof(f18753,plain,
    ( spl24_425
  <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_425])]) ).

fof(f11236,plain,
    ( spl24_238
  <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_238])]) ).

fof(f18751,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    | ~ spl24_238 ),
    inference(forward_demodulation,[],[f18747,f5830]) ).

fof(f18747,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ spl24_238 ),
    inference(resolution,[],[f11238,f7226]) ).

fof(f11238,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ spl24_238 ),
    inference(avatar_component_clause,[],[f11236]) ).

fof(f18669,plain,
    ( spl24_316
    | ~ spl24_234 ),
    inference(avatar_split_clause,[],[f18648,f11152,f13772]) ).

fof(f18648,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ spl24_234 ),
    inference(resolution,[],[f11154,f5095]) ).

fof(f18668,plain,
    ( spl24_191
    | ~ spl24_234 ),
    inference(avatar_split_clause,[],[f18654,f11152,f9854]) ).

fof(f18654,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ spl24_234 ),
    inference(resolution,[],[f11154,f5679]) ).

fof(f18665,plain,
    ( spl24_424
    | ~ spl24_234 ),
    inference(avatar_split_clause,[],[f18660,f11152,f18662]) ).

fof(f18660,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    | ~ spl24_234 ),
    inference(forward_demodulation,[],[f18659,f5388]) ).

fof(f18659,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    | ~ spl24_234 ),
    inference(forward_demodulation,[],[f18655,f5830]) ).

fof(f18655,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ spl24_234 ),
    inference(resolution,[],[f11154,f7226]) ).

fof(f18658,plain,
    ( spl24_172
    | spl24_317
    | ~ spl24_234 ),
    inference(avatar_split_clause,[],[f18653,f11152,f13777,f9476]) ).

fof(f18653,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ spl24_234 ),
    inference(resolution,[],[f11154,f4658]) ).

fof(f18645,plain,
    ( spl24_423
    | ~ spl24_153
    | ~ spl24_314 ),
    inference(avatar_split_clause,[],[f18629,f13763,f9279,f18639]) ).

fof(f18629,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_153
    | ~ spl24_314 ),
    inference(resolution,[],[f17769,f12083]) ).

fof(f12083,plain,
    ( ! [X0] : c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
    | ~ spl24_153 ),
    inference(superposition,[],[f11317,f5830]) ).

fof(f11317,plain,
    ( ! [X17] : c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X17),X17)
    | ~ spl24_153 ),
    inference(forward_demodulation,[],[f11314,f4706]) ).

fof(f11314,plain,
    ( ! [X17] : c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X17),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X17))
    | ~ spl24_153 ),
    inference(resolution,[],[f5603,f9280]) ).

fof(f9280,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_153 ),
    inference(avatar_component_clause,[],[f9279]) ).

fof(f17769,plain,
    ( ! [X1] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,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)) )
    | ~ spl24_314 ),
    inference(superposition,[],[f4660,f13765]) ).

fof(f18644,plain,
    ( spl24_422
    | ~ spl24_255
    | ~ spl24_314 ),
    inference(avatar_split_clause,[],[f18643,f13763,f12451,f18634]) ).

fof(f18634,plain,
    ( spl24_422
  <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ouminus__class_Ouminus(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,[spl24_422])]) ).

fof(f18643,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_255
    | ~ spl24_314 ),
    inference(forward_demodulation,[],[f18631,f5830]) ).

fof(f18631,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_255
    | ~ spl24_314 ),
    inference(resolution,[],[f17769,f12484]) ).

fof(f18642,plain,
    ( spl24_423
    | ~ spl24_153
    | ~ spl24_314 ),
    inference(avatar_split_clause,[],[f18628,f13763,f9279,f18639]) ).

fof(f18628,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_153
    | ~ spl24_314 ),
    inference(resolution,[],[f17769,f11317]) ).

fof(f18637,plain,
    ( spl24_422
    | ~ spl24_314 ),
    inference(avatar_split_clause,[],[f18630,f13763,f18634]) ).

fof(f18630,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_314 ),
    inference(resolution,[],[f17769,f17632]) ).

fof(f18545,plain,
    ( spl24_421
    | ~ spl24_9 ),
    inference(avatar_split_clause,[],[f18532,f6248,f18543]) ).

fof(f18543,plain,
    ( spl24_421
  <=> ! [X18,X19] :
        ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X19,X18)
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X18)
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X19) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_421])]) ).

fof(f18532,plain,
    ! [X18,X19] :
      ( ~ class_Rings_Ocomm__semiring__1(tc_Int_Oint)
      | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X19,X18)
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X19)
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X18) ),
    inference(resolution,[],[f5446,f4832]) ).

fof(f5446,plain,
    ! [X2,X0,X1] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0))
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X0)
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X1) ),
    inference(cnf_transformation,[],[f4106]) ).

fof(f4106,plain,
    ! [X0,X1,X2] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X1)
      | c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0))
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X0) ),
    inference(rectify,[],[f3259]) ).

fof(f3259,plain,
    ! [X1,X2,X0] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,X2)
      | c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1))
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,X1) ),
    inference(flattening,[],[f3258]) ).

fof(f3258,plain,
    ! [X0,X2,X1] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1))
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,X1)
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,X2) ),
    inference(ennf_transformation,[],[f2198]) ).

fof(f2198,plain,
    ! [X0,X2,X1] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,X2)
     => ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,X1)
       => c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)) ) ),
    inference(rectify,[],[f889]) ).

fof(f889,axiom,
    ! [X84,X17,X23] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X84,X23)
     => ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X84,X17)
       => c_Rings_Odvd__class_Odvd(tc_Int_Oint,X84,c_Divides_Odiv__class_Omod(tc_Int_Oint,X23,X17)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__zmod) ).

fof(f18294,plain,
    ( spl24_137
    | spl24_409 ),
    inference(avatar_split_clause,[],[f18282,f18146,f7320]) ).

fof(f18146,plain,
    ( spl24_409
  <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_409])]) ).

fof(f18282,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | spl24_409 ),
    inference(resolution,[],[f18148,f14537]) ).

fof(f14537,plain,
    ! [X0] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
    inference(forward_demodulation,[],[f14524,f4540]) ).

fof(f14524,plain,
    ! [X0] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
    inference(resolution,[],[f5982,f5082]) ).

fof(f18148,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | spl24_409 ),
    inference(avatar_component_clause,[],[f18146]) ).

fof(f18293,plain,
    ( spl24_137
    | spl24_409 ),
    inference(avatar_split_clause,[],[f18292,f18146,f7320]) ).

fof(f18292,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | spl24_409 ),
    inference(forward_demodulation,[],[f18285,f6813]) ).

fof(f18285,plain,
    ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | spl24_409 ),
    inference(resolution,[],[f18148,f14560]) ).

fof(f14560,plain,
    ! [X14,X15] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X14,X15)
      | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X15,X14) = X15 ),
    inference(resolution,[],[f14508,f5322]) ).

fof(f14508,plain,
    ! [X2,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    inference(resolution,[],[f5976,f5952]) ).

fof(f5952,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1),X0)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
    inference(definition_unfolding,[],[f5282,f4877]) ).

fof(f5282,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X0)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
    inference(cnf_transformation,[],[f3992]) ).

fof(f3992,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X0)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X0) ) ),
    inference(rectify,[],[f3991]) ).

fof(f3991,plain,
    ! [X1,X0] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X0),X1)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X0),X1) ) ),
    inference(nnf_transformation,[],[f1832]) ).

fof(f1832,plain,
    ! [X1,X0] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X0),X1)
    <=> ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
    inference(rectify,[],[f263]) ).

fof(f263,axiom,
    ! [X18,X43] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X18),X43)
    <=> ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X43,X18) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__eq__eq) ).

fof(f5976,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),X1)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
    inference(definition_unfolding,[],[f5531,f4877]) ).

fof(f5531,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X0),X1) ),
    inference(cnf_transformation,[],[f4171]) ).

fof(f4171,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X0),X1)
        | ~ 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__eq(tc_Nat_Onat,c_Nat_OSuc(X0),X1) ) ),
    inference(rectify,[],[f4170]) ).

fof(f4170,plain,
    ! [X1,X0] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X0) ) ),
    inference(nnf_transformation,[],[f2242]) ).

fof(f2242,plain,
    ! [X1,X0] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X0)
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
    inference(rectify,[],[f567]) ).

fof(f567,axiom,
    ! [X43,X18] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X18),X43)
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X43) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__Suc__le) ).

fof(f18291,plain,
    ( spl24_242
    | spl24_409 ),
    inference(avatar_split_clause,[],[f18281,f18146,f11786]) ).

fof(f18281,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | spl24_409 ),
    inference(resolution,[],[f18148,f14438]) ).

fof(f14438,plain,
    ! [X4] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X4) ),
    inference(superposition,[],[f5952,f4540]) ).

fof(f18290,plain,
    spl24_409,
    inference(avatar_contradiction_clause,[],[f18284]) ).

fof(f18284,plain,
    ( $false
    | spl24_409 ),
    inference(resolution,[],[f18148,f6099]) ).

fof(f6099,plain,
    ! [X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
    inference(equality_resolution,[],[f5129]) ).

fof(f5129,plain,
    ! [X0,X1] :
      ( X0 != X1
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
    inference(cnf_transformation,[],[f2573]) ).

fof(f2573,plain,
    ! [X0,X1] :
      ( X0 != X1
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
    inference(ennf_transformation,[],[f2059]) ).

fof(f2059,plain,
    ! [X0,X1] :
      ( X0 = X1
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
    inference(rectify,[],[f198]) ).

fof(f198,axiom,
    ! [X23,X17] :
      ( X17 = X23
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X23,X17) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__imp__le) ).

fof(f18249,plain,
    ( ~ spl24_420
    | ~ spl24_406
    | spl24_410 ),
    inference(avatar_split_clause,[],[f18231,f18150,f18127,f18246]) ).

fof(f18246,plain,
    ( spl24_420
  <=> c_Orderings_Oord__class_Oless__eq(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,[spl24_420])]) ).

fof(f18127,plain,
    ( spl24_406
  <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = sK20(c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_406])]) ).

fof(f18150,plain,
    ( spl24_410
  <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK20(c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_410])]) ).

fof(f18231,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ spl24_406
    | spl24_410 ),
    inference(backward_demodulation,[],[f18151,f18129]) ).

fof(f18129,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = sK20(c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ spl24_406 ),
    inference(avatar_component_clause,[],[f18127]) ).

fof(f18151,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK20(c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | spl24_410 ),
    inference(avatar_component_clause,[],[f18150]) ).

fof(f18204,plain,
    ( spl24_419
    | ~ spl24_361 ),
    inference(avatar_split_clause,[],[f18071,f15487,f18201]) ).

fof(f18201,plain,
    ( spl24_419
  <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK20(c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_419])]) ).

fof(f15487,plain,
    ( spl24_361
  <=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK20(c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_361])]) ).

fof(f18071,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK20(c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ spl24_361 ),
    inference(superposition,[],[f4883,f15489]) ).

fof(f15489,plain,
    ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK20(c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | ~ spl24_361 ),
    inference(avatar_component_clause,[],[f15487]) ).

fof(f4883,plain,
    ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)),
    inference(cnf_transformation,[],[f1786]) ).

fof(f1786,plain,
    ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)),
    inference(rectify,[],[f276]) ).

fof(f276,axiom,
    ! [X23,X17] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X23,X17)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add2) ).

fof(f18199,plain,
    ( spl24_418
    | ~ spl24_361 ),
    inference(avatar_split_clause,[],[f18082,f15487,f18196]) ).

fof(f18196,plain,
    ( spl24_418
  <=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK20(c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_418])]) ).

fof(f18082,plain,
    ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK20(c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | ~ spl24_361 ),
    inference(superposition,[],[f5743,f15489]) ).

fof(f5743,plain,
    ! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X1) = X0,
    inference(cnf_transformation,[],[f4313]) ).

fof(f4313,plain,
    ! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X1) = X0,
    inference(rectify,[],[f2168]) ).

fof(f2168,plain,
    ! [X1,X0] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X0) = X1,
    inference(rectify,[],[f977]) ).

fof(f977,axiom,
    ! [X17,X23] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X23,X17),X17) = X23,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__inverse2) ).

fof(f18194,plain,
    ( spl24_137
    | ~ spl24_416
    | ~ spl24_361 ),
    inference(avatar_split_clause,[],[f18087,f15487,f18183,f7320]) ).

fof(f18183,plain,
    ( spl24_416
  <=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = sK20(c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_416])]) ).

fof(f18087,plain,
    ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != sK20(c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ spl24_361 ),
    inference(superposition,[],[f7101,f15489]) ).

fof(f7101,plain,
    ! [X2,X1] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) != X1
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2 ),
    inference(superposition,[],[f4590,f4806]) ).

fof(f4590,plain,
    ! [X0,X1] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) != X1
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
    inference(cnf_transformation,[],[f3572]) ).

fof(f3572,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,[],[f3185]) ).

fof(f3185,plain,
    ! [X1,X0] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) != X0
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 ),
    inference(ennf_transformation,[],[f1560]) ).

fof(f1560,plain,
    ! [X1,X0] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) = X0
     => c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 ),
    inference(rectify,[],[f117]) ).

fof(f117,axiom,
    ! [X23,X17] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X23,X17) = X23
     => c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X17 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__eq__self__zero) ).

fof(f18193,plain,
    ( spl24_406
    | ~ spl24_361 ),
    inference(avatar_split_clause,[],[f18124,f15487,f18127]) ).

fof(f18124,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = sK20(c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ spl24_361 ),
    inference(trivial_inequality_removal,[],[f18065]) ).

fof(f18065,plain,
    ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = sK20(c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ spl24_361 ),
    inference(superposition,[],[f4590,f15489]) ).

fof(f18191,plain,
    ( spl24_417
    | ~ spl24_361 ),
    inference(avatar_split_clause,[],[f18120,f15487,f18188]) ).

fof(f18188,plain,
    ( spl24_417
  <=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = sK4(sK20(c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_417])]) ).

fof(f18120,plain,
    ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = sK4(sK20(c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ spl24_361 ),
    inference(superposition,[],[f16658,f15489]) ).

fof(f16658,plain,
    ! [X0,X1] : sK4(X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = X1,
    inference(forward_demodulation,[],[f16577,f5743]) ).

fof(f16577,plain,
    ! [X0,X1] : sK4(X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X0),
    inference(superposition,[],[f4420,f7231]) ).

fof(f7231,plain,
    ! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,sK4(X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),
    inference(resolution,[],[f4835,f4883]) ).

fof(f4835,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,sK4(X0,X1)) = X1 ),
    inference(cnf_transformation,[],[f3740]) ).

fof(f3740,plain,
    ! [X0,X1] :
      ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,sK4(X0,X1)) = X1
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
        | ! [X3] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3) != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f3738,f3739]) ).

fof(f3739,plain,
    ! [X0,X1] :
      ( ? [X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2) = X1
     => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,sK4(X0,X1)) = X1 ),
    introduced(choice_axiom,[]) ).

fof(f3738,plain,
    ! [X0,X1] :
      ( ( ? [X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2) = X1
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
        | ! [X3] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3) != X1 ) ),
    inference(rectify,[],[f3737]) ).

fof(f3737,plain,
    ! [X1,X0] :
      ( ( ? [X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = X0
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
        | ! [X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != X0 ) ),
    inference(nnf_transformation,[],[f1414]) ).

fof(f1414,plain,
    ! [X1,X0] :
      ( ? [X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = X0
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
    inference(rectify,[],[f340]) ).

fof(f340,axiom,
    ! [X59,X44] :
      ( ? [X25] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X44,X25) = X59
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X44,X59) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__Suc__ex__iff) ).

fof(f4420,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,[],[f3467]) ).

fof(f3467,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,[],[f1417]) ).

fof(f1417,plain,
    ! [X1,X0] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X0) = X1,
    inference(rectify,[],[f978]) ).

fof(f978,axiom,
    ! [X17,X23] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X23),X17) = X23,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__inverse) ).

fof(f18186,plain,
    ( ~ spl24_416
    | ~ spl24_361 ),
    inference(avatar_split_clause,[],[f18051,f15487,f18183]) ).

fof(f18051,plain,
    ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != sK20(c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ spl24_361 ),
    inference(superposition,[],[f5990,f15489]) ).

fof(f5990,plain,
    ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) != X0,
    inference(definition_unfolding,[],[f5676,f4877]) ).

fof(f5676,plain,
    ! [X0] : c_Nat_OSuc(X0) != X0,
    inference(cnf_transformation,[],[f2206]) ).

fof(f2206,plain,
    ! [X0] : c_Nat_OSuc(X0) != X0,
    inference(rectify,[],[f76]) ).

fof(f76,axiom,
    ! [X17] : c_Nat_OSuc(X17) != X17,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).

fof(f18181,plain,
    ( spl24_415
    | ~ spl24_361 ),
    inference(avatar_split_clause,[],[f18084,f15487,f18178]) ).

fof(f18178,plain,
    ( spl24_415
  <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK20(c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_415])]) ).

fof(f18084,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK20(c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | ~ spl24_361 ),
    inference(superposition,[],[f5984,f15489]) ).

fof(f18176,plain,
    ( spl24_414
    | ~ spl24_361 ),
    inference(avatar_split_clause,[],[f18122,f15487,f18173]) ).

fof(f18173,plain,
    ( spl24_414
  <=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = sK5(sK20(c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_414])]) ).

fof(f18122,plain,
    ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = sK5(sK20(c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ spl24_361 ),
    inference(superposition,[],[f16917,f15489]) ).

fof(f16917,plain,
    ! [X0,X1] : sK5(X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = X1,
    inference(forward_demodulation,[],[f16848,f5743]) ).

fof(f16848,plain,
    ! [X0,X1] : sK5(X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X0),
    inference(superposition,[],[f4420,f7233]) ).

fof(f7233,plain,
    ! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,sK5(X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),
    inference(resolution,[],[f4977,f4883]) ).

fof(f4977,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,sK5(X0,X1)) = X1 ),
    inference(cnf_transformation,[],[f3834]) ).

fof(f3834,plain,
    ! [X0,X1] :
      ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,sK5(X0,X1)) = X1
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
        | ! [X3] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3) != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f3832,f3833]) ).

fof(f3833,plain,
    ! [X0,X1] :
      ( ? [X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2) = X1
     => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,sK5(X0,X1)) = X1 ),
    introduced(choice_axiom,[]) ).

fof(f3832,plain,
    ! [X0,X1] :
      ( ( ? [X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2) = X1
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
        | ! [X3] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3) != X1 ) ),
    inference(rectify,[],[f3831]) ).

fof(f3831,plain,
    ! [X1,X0] :
      ( ( ? [X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = X0
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
        | ! [X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != X0 ) ),
    inference(nnf_transformation,[],[f2215]) ).

fof(f2215,plain,
    ! [X1,X0] :
      ( ? [X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = X0
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
    inference(rectify,[],[f274]) ).

fof(f274,axiom,
    ! [X18,X43] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X43,X18)
    <=> ? [X57] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X43,X57) = X18 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__iff__add) ).

fof(f18171,plain,
    ( ~ spl24_413
    | ~ spl24_361 ),
    inference(avatar_split_clause,[],[f18047,f15487,f18168]) ).

fof(f18168,plain,
    ( spl24_413
  <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK20(c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_413])]) ).

fof(f18047,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK20(c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | ~ spl24_361 ),
    inference(superposition,[],[f5924,f15489]) ).

fof(f5924,plain,
    ! [X0] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),X0),
    inference(definition_unfolding,[],[f5058,f4877]) ).

fof(f5058,plain,
    ! [X0] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X0),X0),
    inference(cnf_transformation,[],[f2029]) ).

fof(f2029,plain,
    ! [X0] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X0),X0),
    inference(rectify,[],[f264]) ).

fof(f264,axiom,
    ! [X17] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X17),X17),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__le__n) ).

fof(f18166,plain,
    ( spl24_412
    | spl24_408
    | ~ spl24_361 ),
    inference(avatar_split_clause,[],[f18055,f15487,f18139,f18163]) ).

fof(f18163,plain,
    ( spl24_412
  <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK20(c_Groups_Oone__class_Oone(tc_Nat_Onat)),sK20(c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_412])]) ).

fof(f18139,plain,
    ( spl24_408
  <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK20(c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_408])]) ).

fof(f18055,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK20(c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK20(c_Groups_Oone__class_Oone(tc_Nat_Onat)),sK20(c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | ~ spl24_361 ),
    inference(superposition,[],[f6121,f15489]) ).

fof(f18161,plain,
    ( spl24_406
    | ~ spl24_361 ),
    inference(avatar_split_clause,[],[f18160,f15487,f18127]) ).

fof(f18160,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = sK20(c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ spl24_361 ),
    inference(forward_demodulation,[],[f18057,f6813]) ).

fof(f18057,plain,
    ( sK20(c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,sK20(c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ spl24_361 ),
    inference(superposition,[],[f13382,f15489]) ).

fof(f13382,plain,
    ! [X3] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X3)) = X3,
    inference(resolution,[],[f5322,f6091]) ).

fof(f18159,plain,
    ( spl24_411
    | ~ spl24_361
    | ~ spl24_362 ),
    inference(avatar_split_clause,[],[f18154,f15507,f15487,f18156]) ).

fof(f18156,plain,
    ( spl24_411
  <=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Onat_Onat__size(sK20(c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_411])]) ).

fof(f15507,plain,
    ( spl24_362
  <=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_Onat_Onat__size(c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_362])]) ).

fof(f18154,plain,
    ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Onat_Onat__size(sK20(c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ spl24_361
    | ~ spl24_362 ),
    inference(forward_demodulation,[],[f18056,f15509]) ).

fof(f15509,plain,
    ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_Onat_Onat__size(c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ spl24_362 ),
    inference(avatar_component_clause,[],[f15507]) ).

fof(f18056,plain,
    ( c_Nat_Onat_Onat__size(c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Onat_Onat__size(sK20(c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ spl24_361 ),
    inference(superposition,[],[f6790,f15489]) ).

fof(f6790,plain,
    ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Onat_Onat__size(X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Nat_Onat_Onat__size(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)),
    inference(forward_demodulation,[],[f6789,f5628]) ).

fof(f6789,plain,
    ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Onat_Onat__size(X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Nat_Onat_Onat__size(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)),
    inference(forward_demodulation,[],[f5951,f4806]) ).

fof(f5951,plain,
    ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Onat_Onat__size(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_Nat_Onat_Onat__size(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)),
    inference(definition_unfolding,[],[f5272,f4877,f4877]) ).

fof(f5272,plain,
    ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Onat_Onat__size(X0),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Nat_Onat_Onat__size(c_Nat_OSuc(X0)),
    inference(cnf_transformation,[],[f1249]) ).

fof(f1249,plain,
    ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Onat_Onat__size(X0),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Nat_Onat_Onat__size(c_Nat_OSuc(X0)),
    inference(rectify,[],[f182]) ).

fof(f182,axiom,
    ! [X55] : c_Nat_Onat_Onat__size(c_Nat_OSuc(X55)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Onat_Onat__size(X55),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osize_I2_J) ).

fof(f18153,plain,
    ( ~ spl24_409
    | spl24_410
    | ~ spl24_361 ),
    inference(avatar_split_clause,[],[f18095,f15487,f18150,f18146]) ).

fof(f18095,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK20(c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ spl24_361 ),
    inference(superposition,[],[f7336,f15489]) ).

fof(f7336,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X0)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(superposition,[],[f5131,f4540]) ).

fof(f5131,plain,
    ! [X2,X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0))
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
    inference(cnf_transformation,[],[f3926]) ).

fof(f3926,plain,
    ! [X0,X1,X2] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)) ) ),
    inference(rectify,[],[f3925]) ).

fof(f3925,plain,
    ! [X0,X2,X1] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) ) ),
    inference(nnf_transformation,[],[f1717]) ).

fof(f1717,plain,
    ! [X0,X2,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0) ),
    inference(rectify,[],[f273]) ).

fof(f273,axiom,
    ! [X18,X44,X43] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X44,X43),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X44,X18))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X43,X18) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel__le) ).

fof(f18144,plain,
    ( spl24_406
    | ~ spl24_361 ),
    inference(avatar_split_clause,[],[f18143,f15487,f18127]) ).

fof(f18143,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = sK20(c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ spl24_361 ),
    inference(forward_demodulation,[],[f18059,f4651]) ).

fof(f4651,plain,
    ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X0),
    inference(cnf_transformation,[],[f1735]) ).

fof(f1735,plain,
    ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X0),
    inference(rectify,[],[f994]) ).

fof(f994,axiom,
    ! [X23] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X23,X23),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__self__eq__0) ).

fof(f18059,plain,
    ( sK20(c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ spl24_361 ),
    inference(superposition,[],[f4420,f15489]) ).

fof(f18142,plain,
    ( spl24_408
    | ~ spl24_361 ),
    inference(avatar_split_clause,[],[f18054,f15487,f18139]) ).

fof(f18054,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK20(c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ spl24_361 ),
    inference(superposition,[],[f6091,f15489]) ).

fof(f18137,plain,
    ( spl24_406
    | ~ spl24_361 ),
    inference(avatar_split_clause,[],[f18136,f15487,f18127]) ).

fof(f18136,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = sK20(c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ spl24_361 ),
    inference(forward_demodulation,[],[f18123,f11920]) ).

fof(f11920,plain,
    ! [X10] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = sK5(X10,X10),
    inference(trivial_inequality_removal,[],[f11897]) ).

fof(f11897,plain,
    ! [X10] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = sK5(X10,X10)
      | X10 != X10 ),
    inference(superposition,[],[f4590,f7451]) ).

fof(f7451,plain,
    ! [X9] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X9,sK5(X9,X9)) = X9,
    inference(resolution,[],[f6099,f4977]) ).

fof(f18123,plain,
    ( sK20(c_Groups_Oone__class_Oone(tc_Nat_Onat)) = sK5(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ spl24_361 ),
    inference(superposition,[],[f17159,f15489]) ).

fof(f17159,plain,
    ! [X0,X1] : sK5(X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) = X1,
    inference(forward_demodulation,[],[f17082,f4420]) ).

fof(f17082,plain,
    ! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X0) = sK5(X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)),
    inference(superposition,[],[f4420,f7234]) ).

fof(f7234,plain,
    ! [X2,X3] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,sK5(X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3),
    inference(resolution,[],[f4977,f6056]) ).

fof(f6056,plain,
    ! [X3,X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3)),
    inference(equality_resolution,[],[f4834]) ).

fof(f4834,plain,
    ! [X3,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3) != X1 ),
    inference(cnf_transformation,[],[f3740]) ).

fof(f18135,plain,
    ( ~ spl24_407
    | ~ spl24_361 ),
    inference(avatar_split_clause,[],[f18069,f15487,f18132]) ).

fof(f18132,plain,
    ( spl24_407
  <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK20(c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_407])]) ).

fof(f18069,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK20(c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | ~ spl24_361 ),
    inference(superposition,[],[f4777,f15489]) ).

fof(f18130,plain,
    ( spl24_406
    | ~ spl24_361 ),
    inference(avatar_split_clause,[],[f18125,f15487,f18127]) ).

fof(f18125,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = sK20(c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ spl24_361 ),
    inference(forward_demodulation,[],[f18121,f11976]) ).

fof(f11976,plain,
    ! [X10] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = sK4(X10,X10),
    inference(trivial_inequality_removal,[],[f11953]) ).

fof(f11953,plain,
    ! [X10] :
      ( X10 != X10
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = sK4(X10,X10) ),
    inference(superposition,[],[f4590,f7452]) ).

fof(f7452,plain,
    ! [X10] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,sK4(X10,X10)) = X10,
    inference(resolution,[],[f6099,f4835]) ).

fof(f18121,plain,
    ( sK20(c_Groups_Oone__class_Oone(tc_Nat_Onat)) = sK4(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ spl24_361 ),
    inference(superposition,[],[f16781,f15489]) ).

fof(f16781,plain,
    ! [X0,X1] : sK4(X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) = X1,
    inference(forward_demodulation,[],[f16712,f4420]) ).

fof(f16712,plain,
    ! [X0,X1] : sK4(X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X0),
    inference(superposition,[],[f4420,f7232]) ).

fof(f7232,plain,
    ! [X2,X3] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,sK4(X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))),
    inference(resolution,[],[f4835,f6056]) ).

fof(f18028,plain,
    ( spl24_405
    | ~ spl24_342 ),
    inference(avatar_split_clause,[],[f18023,f14802,f18025]) ).

fof(f18025,plain,
    ( spl24_405
  <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_405])]) ).

fof(f18023,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    | ~ spl24_342 ),
    inference(forward_demodulation,[],[f18011,f5830]) ).

fof(f18011,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ spl24_342 ),
    inference(resolution,[],[f14804,f5678]) ).

fof(f14804,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ spl24_342 ),
    inference(avatar_component_clause,[],[f14802]) ).

fof(f18022,plain,
    ( ~ spl24_403
    | spl24_404
    | ~ spl24_342 ),
    inference(avatar_split_clause,[],[f18013,f14802,f18019,f18015]) ).

fof(f18019,plain,
    ( spl24_404
  <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_404])]) ).

fof(f18013,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ spl24_342 ),
    inference(resolution,[],[f14804,f5243]) ).

fof(f17759,plain,
    ( spl24_314
    | spl24_402
    | ~ spl24_153 ),
    inference(avatar_split_clause,[],[f17746,f9279,f17755,f13763]) ).

fof(f17746,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ spl24_153 ),
    inference(resolution,[],[f7428,f11317]) ).

fof(f7428,plain,
    ! [X0] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))
      | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(superposition,[],[f4658,f4706]) ).

fof(f17758,plain,
    ( spl24_402
    | spl24_314
    | ~ spl24_153 ),
    inference(avatar_split_clause,[],[f17753,f9279,f13763,f17755]) ).

fof(f17753,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_153 ),
    inference(forward_demodulation,[],[f17752,f5830]) ).

fof(f17752,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_153 ),
    inference(forward_demodulation,[],[f17747,f5830]) ).

fof(f17747,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_153 ),
    inference(resolution,[],[f7428,f12083]) ).

fof(f17662,plain,
    ( spl24_401
    | ~ spl24_9
    | ~ spl24_9 ),
    inference(avatar_split_clause,[],[f17655,f6248,f6248,f17660]) ).

fof(f17660,plain,
    ( spl24_401
  <=> ! [X2,X1,X3] : c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Int_Oint),X1,c_Polynomial_Osmult(tc_Int_Oint,X2,c_Polynomial_Osmult(tc_Int_Oint,X3,X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_401])]) ).

fof(f17655,plain,
    ( ! [X2,X3,X1] :
        ( ~ class_Rings_Ocomm__semiring__1(tc_Int_Oint)
        | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Int_Oint),X1,c_Polynomial_Osmult(tc_Int_Oint,X2,c_Polynomial_Osmult(tc_Int_Oint,X3,X1))) )
    | ~ spl24_9 ),
    inference(resolution,[],[f17564,f4770]) ).

fof(f17564,plain,
    ( ! [X2,X3] : c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Int_Oint),X2,c_Polynomial_Osmult(tc_Int_Oint,X3,X2))
    | ~ spl24_9 ),
    inference(resolution,[],[f15743,f6250]) ).

fof(f17581,plain,
    ( spl24_400
    | ~ spl24_5
    | ~ spl24_5 ),
    inference(avatar_split_clause,[],[f17569,f6228,f6228,f17579]) ).

fof(f17579,plain,
    ( spl24_400
  <=> ! [X2,X1,X3] : c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Nat_Onat),X1,c_Polynomial_Osmult(tc_Nat_Onat,X2,c_Polynomial_Osmult(tc_Nat_Onat,X3,X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_400])]) ).

fof(f17569,plain,
    ( ! [X2,X3,X1] :
        ( ~ class_Rings_Ocomm__semiring__1(tc_Nat_Onat)
        | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Nat_Onat),X1,c_Polynomial_Osmult(tc_Nat_Onat,X2,c_Polynomial_Osmult(tc_Nat_Onat,X3,X1))) )
    | ~ spl24_5 ),
    inference(resolution,[],[f17563,f4770]) ).

fof(f17563,plain,
    ( ! [X0,X1] : c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Nat_Onat),X0,c_Polynomial_Osmult(tc_Nat_Onat,X1,X0))
    | ~ spl24_5 ),
    inference(resolution,[],[f15743,f6230]) ).

fof(f17577,plain,
    ( spl24_399
    | ~ spl24_5
    | ~ spl24_15 ),
    inference(avatar_split_clause,[],[f17572,f6277,f6228,f17574]) ).

fof(f17574,plain,
    ( spl24_399
  <=> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_399])]) ).

fof(f17572,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)))
    | ~ spl24_5
    | ~ spl24_15 ),
    inference(superposition,[],[f17563,f7276]) ).

fof(f7276,plain,
    ( ! [X2] : c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)) = c_Polynomial_Osmult(tc_Nat_Onat,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)))
    | ~ spl24_15 ),
    inference(resolution,[],[f5732,f6279]) ).

fof(f5732,plain,
    ! [X0,X1] :
      ( ~ class_Rings_Ocomm__semiring__0(X0)
      | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Osmult(X0,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) ),
    inference(cnf_transformation,[],[f3411]) ).

fof(f3411,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Osmult(X0,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))
      | ~ class_Rings_Ocomm__semiring__0(X0) ),
    inference(ennf_transformation,[],[f1571]) ).

fof(f1571,plain,
    ! [X0,X1] :
      ( class_Rings_Ocomm__semiring__0(X0)
     => c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Osmult(X0,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) ),
    inference(rectify,[],[f39]) ).

fof(f39,axiom,
    ! [X4,X5] :
      ( class_Rings_Ocomm__semiring__0(X4)
     => c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = c_Polynomial_Osmult(X4,X5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__0__right) ).

fof(f17370,plain,
    ( ~ spl24_398
    | ~ spl24_9 ),
    inference(avatar_split_clause,[],[f17361,f6248,f17366]) ).

fof(f17366,plain,
    ( spl24_398
  <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_398])]) ).

fof(f17361,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ spl24_9 ),
    inference(resolution,[],[f15447,f15969]) ).

fof(f15969,plain,
    ( ! [X3] : c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),X3)
    | ~ spl24_9 ),
    inference(resolution,[],[f15953,f13394]) ).

fof(f15953,plain,
    ( ! [X0,X1] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))
        | c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X0) )
    | ~ spl24_9 ),
    inference(superposition,[],[f7465,f4730]) ).

fof(f7465,plain,
    ( ! [X3,X4,X5] :
        ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X5))
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X3,X4) )
    | ~ spl24_9 ),
    inference(resolution,[],[f5251,f6250]) ).

fof(f5251,plain,
    ! [X2,X3,X0,X1] :
      ( ~ class_Rings_Ocomm__semiring__1(X2)
      | ~ c_Rings_Odvd__class_Odvd(X2,X3,X0)
      | c_Rings_Odvd__class_Odvd(X2,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1)) ),
    inference(cnf_transformation,[],[f3973]) ).

fof(f3973,plain,
    ! [X0,X1,X2,X3] :
      ( c_Rings_Odvd__class_Odvd(X2,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1))
      | ~ class_Rings_Ocomm__semiring__1(X2)
      | ~ c_Rings_Odvd__class_Odvd(X2,X3,X0) ),
    inference(rectify,[],[f2730]) ).

fof(f2730,plain,
    ! [X1,X3,X0,X2] :
      ( c_Rings_Odvd__class_Odvd(X0,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X3))
      | ~ class_Rings_Ocomm__semiring__1(X0)
      | ~ c_Rings_Odvd__class_Odvd(X0,X2,X1) ),
    inference(flattening,[],[f2729]) ).

fof(f2729,plain,
    ! [X2,X0,X3,X1] :
      ( c_Rings_Odvd__class_Odvd(X0,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X3))
      | ~ c_Rings_Odvd__class_Odvd(X0,X2,X1)
      | ~ class_Rings_Ocomm__semiring__1(X0) ),
    inference(ennf_transformation,[],[f1748]) ).

fof(f1748,plain,
    ! [X2,X0,X3,X1] :
      ( class_Rings_Ocomm__semiring__1(X0)
     => ( c_Rings_Odvd__class_Odvd(X0,X2,X1)
       => c_Rings_Odvd__class_Odvd(X0,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X3)) ) ),
    inference(rectify,[],[f416]) ).

fof(f416,axiom,
    ! [X4,X29,X5,X22] :
      ( class_Rings_Ocomm__semiring__1(X4)
     => ( c_Rings_Odvd__class_Odvd(X4,X5,X29)
       => c_Rings_Odvd__class_Odvd(X4,X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X29),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult2) ).

fof(f17369,plain,
    ( ~ spl24_398
    | ~ spl24_9 ),
    inference(avatar_split_clause,[],[f17360,f6248,f17366]) ).

fof(f17360,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ spl24_9 ),
    inference(resolution,[],[f15447,f13394]) ).

fof(f17033,plain,
    ( spl24_397
    | ~ spl24_391 ),
    inference(avatar_split_clause,[],[f16983,f16524,f17030]) ).

fof(f16983,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(tc_Polynomial_Opoly(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Int_Oint))))
    | ~ spl24_391 ),
    inference(resolution,[],[f16525,f4889]) ).

fof(f4889,plain,
    ! [X0] :
      ( ~ class_Rings_Ocomm__semiring__1(X0)
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X0,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X0))) ),
    inference(cnf_transformation,[],[f2354]) ).

fof(f2354,plain,
    ! [X0] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X0,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X0)))
      | ~ class_Rings_Ocomm__semiring__1(X0) ),
    inference(ennf_transformation,[],[f1410]) ).

fof(f1410,plain,
    ! [X0] :
      ( class_Rings_Ocomm__semiring__1(X0)
     => c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X0,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X0))) ),
    inference(rectify,[],[f329]) ).

fof(f329,axiom,
    ! [X4] :
      ( class_Rings_Ocomm__semiring__1(X4)
     => c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X4,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X4))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__1) ).

fof(f17028,plain,
    ( spl24_396
    | ~ spl24_391 ),
    inference(avatar_split_clause,[],[f16975,f16524,f17025]) ).

fof(f17025,plain,
    ( spl24_396
  <=> c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Int_Oint))) = c_Polynomial_OpCons(tc_Polynomial_Opoly(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Int_Oint)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_396])]) ).

fof(f16975,plain,
    ( c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Int_Oint))) = c_Polynomial_OpCons(tc_Polynomial_Opoly(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Int_Oint))))
    | ~ spl24_391 ),
    inference(resolution,[],[f16525,f4567]) ).

fof(f16546,plain,
    ( ~ spl24_9
    | spl24_391 ),
    inference(avatar_split_clause,[],[f16545,f16524,f6248]) ).

fof(f16545,plain,
    ( ~ class_Rings_Ocomm__semiring__1(tc_Int_Oint)
    | spl24_391 ),
    inference(resolution,[],[f16526,f4828]) ).

fof(f16526,plain,
    ( ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Int_Oint))
    | spl24_391 ),
    inference(avatar_component_clause,[],[f16524]) ).

fof(f16543,plain,
    ( spl24_395
    | ~ spl24_391
    | ~ spl24_9 ),
    inference(avatar_split_clause,[],[f16519,f6248,f16524,f16541]) ).

fof(f16541,plain,
    ( spl24_395
  <=> ! [X6,X7] :
        ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Int_Oint)),X6),X7),X6)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_395])]) ).

fof(f16519,plain,
    ( ! [X6,X7] :
        ( ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Int_Oint))
        | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Int_Oint)),X6),X7),X6)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
    | ~ spl24_9 ),
    inference(superposition,[],[f5448,f14728]) ).

fof(f14728,plain,
    ( ! [X1] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Int_Oint)),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1
    | ~ spl24_9 ),
    inference(resolution,[],[f7120,f6250]) ).

fof(f7120,plain,
    ! [X2,X3] :
      ( ~ class_Rings_Ocomm__semiring__1(X2)
      | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X2)),X3),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X3 ),
    inference(resolution,[],[f4671,f4828]) ).

fof(f4671,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(cnf_transformation,[],[f3627]) ).

fof(f3627,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(rectify,[],[f2371]) ).

fof(f2371,plain,
    ! [X1,X0] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1
      | ~ class_Rings_Ocomm__semiring__1(X0) ),
    inference(ennf_transformation,[],[f1730]) ).

fof(f1730,plain,
    ! [X0,X1] :
      ( class_Rings_Ocomm__semiring__1(X0)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1 ),
    inference(rectify,[],[f688]) ).

fof(f688,axiom,
    ! [X4,X19] :
      ( class_Rings_Ocomm__semiring__1(X4)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X4),X19),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X19 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).

fof(f16539,plain,
    ( ~ spl24_391
    | spl24_394
    | ~ spl24_9 ),
    inference(avatar_split_clause,[],[f16518,f6248,f16537,f16524]) ).

fof(f16537,plain,
    ( spl24_394
  <=> ! [X4,X5,X3] :
        ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Int_Oint),X3,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Int_Oint)),X4),X5))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X5)
        | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Int_Oint),X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_394])]) ).

fof(f16518,plain,
    ( ! [X3,X4,X5] :
        ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Int_Oint),X3,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Int_Oint)),X4),X5))
        | ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Int_Oint))
        | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Int_Oint),X3,X4)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X5) )
    | ~ spl24_9 ),
    inference(superposition,[],[f5752,f14728]) ).

fof(f16535,plain,
    ( ~ spl24_391
    | spl24_393
    | ~ spl24_9 ),
    inference(avatar_split_clause,[],[f16517,f6248,f16533,f16524]) ).

fof(f16533,plain,
    ( spl24_393
  <=> ! [X2,X0,X1] :
        ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Int_Oint)),X1),X2),X0)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Int_Oint),X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_393])]) ).

fof(f16517,plain,
    ( ! [X2,X0,X1] :
        ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Int_Oint)),X1),X2),X0)
        | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Int_Oint),X1,X0)
        | ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
    | ~ spl24_9 ),
    inference(superposition,[],[f5752,f14728]) ).

fof(f16530,plain,
    ( ~ spl24_391
    | spl24_392
    | ~ spl24_9 ),
    inference(avatar_split_clause,[],[f16520,f6248,f16528,f16524]) ).

fof(f16528,plain,
    ( spl24_392
  <=> ! [X9,X8] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X9)
        | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Int_Oint),X8,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Int_Oint)),X8),X9)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_392])]) ).

fof(f16520,plain,
    ( ! [X8,X9] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X9)
        | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Int_Oint),X8,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Int_Oint)),X8),X9))
        | ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Int_Oint)) )
    | ~ spl24_9 ),
    inference(superposition,[],[f5448,f14728]) ).

fof(f16516,plain,
    ( spl24_390
    | ~ spl24_384 ),
    inference(avatar_split_clause,[],[f16458,f16431,f16513]) ).

fof(f16513,plain,
    ( spl24_390
  <=> c_Polynomial_OpCons(tc_Polynomial_Opoly(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Nat_Onat)))) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Nat_Onat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_390])]) ).

fof(f16458,plain,
    ( c_Polynomial_OpCons(tc_Polynomial_Opoly(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Nat_Onat)))) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Nat_Onat)))
    | ~ spl24_384 ),
    inference(resolution,[],[f16432,f4567]) ).

fof(f16511,plain,
    ( spl24_389
    | ~ spl24_384 ),
    inference(avatar_split_clause,[],[f16466,f16431,f16508]) ).

fof(f16466,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(tc_Polynomial_Opoly(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Nat_Onat))))
    | ~ spl24_384 ),
    inference(resolution,[],[f16432,f4889]) ).

fof(f16453,plain,
    ( ~ spl24_5
    | spl24_384 ),
    inference(avatar_split_clause,[],[f16452,f16431,f6228]) ).

fof(f16452,plain,
    ( ~ class_Rings_Ocomm__semiring__1(tc_Nat_Onat)
    | spl24_384 ),
    inference(resolution,[],[f16433,f4828]) ).

fof(f16433,plain,
    ( ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Nat_Onat))
    | spl24_384 ),
    inference(avatar_component_clause,[],[f16431]) ).

fof(f16451,plain,
    ( ~ spl24_384
    | spl24_388
    | ~ spl24_5 ),
    inference(avatar_split_clause,[],[f16424,f6228,f16449,f16431]) ).

fof(f16449,plain,
    ( spl24_388
  <=> ! [X2,X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Nat_Onat)),X1),X2),X0)
        | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Nat_Onat),X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_388])]) ).

fof(f16424,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Nat_Onat),X1,X0)
        | ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Nat_Onat))
        | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Nat_Onat)),X1),X2),X0) )
    | ~ spl24_5 ),
    inference(superposition,[],[f5752,f14727]) ).

fof(f14727,plain,
    ( ! [X0] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Nat_Onat)),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0
    | ~ spl24_5 ),
    inference(resolution,[],[f7120,f6230]) ).

fof(f16446,plain,
    ( spl24_387
    | ~ spl24_384
    | ~ spl24_5 ),
    inference(avatar_split_clause,[],[f16425,f6228,f16431,f16444]) ).

fof(f16444,plain,
    ( spl24_387
  <=> ! [X4,X5,X3] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X5)
        | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Nat_Onat),X3,X4)
        | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Nat_Onat),X3,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Nat_Onat)),X4),X5)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_387])]) ).

fof(f16425,plain,
    ( ! [X3,X4,X5] :
        ( ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Nat_Onat))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X5)
        | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Nat_Onat),X3,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Nat_Onat)),X4),X5))
        | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Nat_Onat),X3,X4) )
    | ~ spl24_5 ),
    inference(superposition,[],[f5752,f14727]) ).

fof(f16441,plain,
    ( spl24_386
    | ~ spl24_384
    | ~ spl24_5 ),
    inference(avatar_split_clause,[],[f16427,f6228,f16431,f16439]) ).

fof(f16439,plain,
    ( spl24_386
  <=> ! [X9,X8] :
        ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Nat_Onat),X8,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Nat_Onat)),X8),X9))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X9) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_386])]) ).

fof(f16427,plain,
    ( ! [X8,X9] :
        ( ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Nat_Onat))
        | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Nat_Onat),X8,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Nat_Onat)),X8),X9))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X9) )
    | ~ spl24_5 ),
    inference(superposition,[],[f5448,f14727]) ).

fof(f16437,plain,
    ( ~ spl24_384
    | spl24_385
    | ~ spl24_5 ),
    inference(avatar_split_clause,[],[f16426,f6228,f16435,f16431]) ).

fof(f16435,plain,
    ( spl24_385
  <=> ! [X6,X7] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Nat_Onat)),X6),X7),X6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_385])]) ).

fof(f16426,plain,
    ( ! [X6,X7] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Nat_Onat))
        | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Nat_Onat)),X6),X7),X6) )
    | ~ spl24_5 ),
    inference(superposition,[],[f5448,f14727]) ).

fof(f16239,plain,
    ( ~ spl24_5
    | spl24_383 ),
    inference(avatar_split_clause,[],[f16226,f16237,f6228]) ).

fof(f16237,plain,
    ( spl24_383
  <=> ! [X18,X17,X16,X15] :
        ( 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),X17),X18))
        | ~ 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),X15),X16))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X16)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X17,X15) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_383])]) ).

fof(f16226,plain,
    ! [X18,X16,X17,X15] :
      ( 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),X17),X18))
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X17,X15)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X16)
      | ~ class_Rings_Ocomm__semiring__1(tc_Nat_Onat)
      | ~ 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),X15),X16)) ),
    inference(resolution,[],[f5099,f5752]) ).

fof(f5099,plain,
    ! [X0,X1] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,X1)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
    inference(cnf_transformation,[],[f3301]) ).

fof(f3301,plain,
    ! [X0,X1] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,X1)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(flattening,[],[f3300]) ).

fof(f3300,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,X1)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(ennf_transformation,[],[f2024]) ).

fof(f2024,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,X1)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ) ),
    inference(rectify,[],[f683]) ).

fof(f683,axiom,
    ! [X23,X17] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X17)
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X17)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X23) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__pos__nat) ).

fof(f16235,plain,
    ( ~ spl24_5
    | spl24_382 ),
    inference(avatar_split_clause,[],[f16227,f16233,f6228]) ).

fof(f16233,plain,
    ( spl24_382
  <=> ! [X20,X21,X19] :
        ( ~ 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),X19),X20))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X20)
        | 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),X19),X21)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_382])]) ).

fof(f16227,plain,
    ! [X21,X19,X20] :
      ( ~ 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),X19),X20))
      | 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),X19),X21))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X20)
      | ~ class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ),
    inference(resolution,[],[f5099,f5448]) ).

fof(f16231,plain,
    ( ~ spl24_5
    | spl24_381 ),
    inference(avatar_split_clause,[],[f16225,f16229,f6228]) ).

fof(f16229,plain,
    ( spl24_381
  <=> ! [X13,X12,X14] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X14,X12)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X12),X13))
        | 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),X14),X13)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_381])]) ).

fof(f16225,plain,
    ! [X14,X12,X13] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X14,X12)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X14),X13))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X12),X13))
      | ~ class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ),
    inference(resolution,[],[f5099,f4750]) ).

fof(f16215,plain,
    ( spl24_380
    | ~ spl24_92
    | ~ spl24_128 ),
    inference(avatar_split_clause,[],[f16210,f6992,f6764,f16212]) ).

fof(f16212,plain,
    ( spl24_380
  <=> hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_a,v_p)),v_h) = c_Groups_Ozero__class_Ozero(t_a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_380])]) ).

fof(f16210,plain,
    ( hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_a,v_p)),v_h) = c_Groups_Ozero__class_Ozero(t_a)
    | ~ spl24_92
    | ~ spl24_128 ),
    inference(superposition,[],[f7639,f14970]) ).

fof(f14970,plain,
    ( ! [X6] : c_Groups_Oplus__class_Oplus(t_a,X6,c_Groups_Ozero__class_Ozero(t_a)) = X6
    | ~ spl24_92 ),
    inference(resolution,[],[f13132,f6766]) ).

fof(f13132,plain,
    ! [X0,X1] :
      ( ~ class_Rings_Ocomm__semiring__0(X0)
      | c_Groups_Oplus__class_Oplus(X0,X1,c_Groups_Ozero__class_Ozero(X0)) = X1 ),
    inference(resolution,[],[f4402,f4442]) ).

fof(f4442,plain,
    ! [X0] :
      ( class_Groups_Ocomm__monoid__add(X0)
      | ~ class_Rings_Ocomm__semiring__0(X0) ),
    inference(cnf_transformation,[],[f2862]) ).

fof(f2862,plain,
    ! [X0] :
      ( ~ class_Rings_Ocomm__semiring__0(X0)
      | class_Groups_Ocomm__monoid__add(X0) ),
    inference(ennf_transformation,[],[f2232]) ).

fof(f2232,plain,
    ! [X0] :
      ( class_Rings_Ocomm__semiring__0(X0)
     => class_Groups_Ocomm__monoid__add(X0) ),
    inference(rectify,[],[f998]) ).

fof(f998,axiom,
    ! [X93] :
      ( class_Rings_Ocomm__semiring__0(X93)
     => class_Groups_Ocomm__monoid__add(X93) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Ocomm__semiring__0__Groups_Ocomm__monoid__add) ).

fof(f4402,plain,
    ! [X0,X1] :
      ( ~ class_Groups_Ocomm__monoid__add(X1)
      | c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0 ),
    inference(cnf_transformation,[],[f3455]) ).

fof(f3455,plain,
    ! [X0,X1] :
      ( c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0
      | ~ class_Groups_Ocomm__monoid__add(X1) ),
    inference(rectify,[],[f2710]) ).

fof(f2710,plain,
    ! [X1,X0] :
      ( c_Groups_Oplus__class_Oplus(X0,X1,c_Groups_Ozero__class_Ozero(X0)) = X1
      | ~ class_Groups_Ocomm__monoid__add(X0) ),
    inference(ennf_transformation,[],[f2226]) ).

fof(f2226,plain,
    ! [X0,X1] :
      ( class_Groups_Ocomm__monoid__add(X0)
     => c_Groups_Oplus__class_Oplus(X0,X1,c_Groups_Ozero__class_Ozero(X0)) = X1 ),
    inference(rectify,[],[f66]) ).

fof(f66,axiom,
    ! [X4,X5] :
      ( class_Groups_Ocomm__monoid__add(X4)
     => c_Groups_Oplus__class_Oplus(X4,X5,c_Groups_Ozero__class_Ozero(X4)) = X5 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add_Ocomm__neutral) ).

fof(f7639,plain,
    ( ! [X0] : c_Groups_Ozero__class_Ozero(t_a) = hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_a,v_p)),c_Groups_Oplus__class_Oplus(t_a,v_h,X0))
    | ~ spl24_92
    | ~ spl24_128 ),
    inference(forward_demodulation,[],[f7633,f7206]) ).

fof(f7206,plain,
    ( ! [X4] : c_Groups_Ozero__class_Ozero(t_a) = hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),X4)
    | ~ spl24_92 ),
    inference(resolution,[],[f4404,f6766]) ).

fof(f4404,plain,
    ! [X0,X1] :
      ( ~ class_Rings_Ocomm__semiring__0(X1)
      | hAPP(c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X0) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(cnf_transformation,[],[f3456]) ).

fof(f3456,plain,
    ! [X0,X1] :
      ( ~ class_Rings_Ocomm__semiring__0(X1)
      | hAPP(c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X0) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(rectify,[],[f3393]) ).

fof(f3393,plain,
    ! [X1,X0] :
      ( ~ class_Rings_Ocomm__semiring__0(X0)
      | hAPP(c_Polynomial_Opoly(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))),X1) = c_Groups_Ozero__class_Ozero(X0) ),
    inference(ennf_transformation,[],[f1734]) ).

fof(f1734,plain,
    ! [X1,X0] :
      ( class_Rings_Ocomm__semiring__0(X0)
     => hAPP(c_Polynomial_Opoly(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))),X1) = c_Groups_Ozero__class_Ozero(X0) ),
    inference(rectify,[],[f27]) ).

fof(f27,axiom,
    ! [X4,X19] :
      ( class_Rings_Ocomm__semiring__0(X4)
     => c_Groups_Ozero__class_Ozero(X4) = hAPP(c_Polynomial_Opoly(X4,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))),X19) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__0) ).

fof(f7633,plain,
    ( ! [X0] : hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),X0) = hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_a,v_p)),c_Groups_Oplus__class_Oplus(t_a,v_h,X0))
    | ~ spl24_92
    | ~ spl24_128 ),
    inference(superposition,[],[f7041,f6994]) ).

fof(f7041,plain,
    ( ! [X10,X11,X12] : hAPP(c_Polynomial_Opoly(t_a,X10),c_Groups_Oplus__class_Oplus(t_a,X11,X12)) = hAPP(c_Polynomial_Opoly(t_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,X10,X11)),X12)
    | ~ spl24_92 ),
    inference(resolution,[],[f4669,f6766]) ).

fof(f4669,plain,
    ! [X2,X3,X0,X1] :
      ( ~ class_Rings_Ocomm__semiring__0(X2)
      | hAPP(c_Polynomial_Opoly(X2,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,X0,X1)),X3) = hAPP(c_Polynomial_Opoly(X2,X0),c_Groups_Oplus__class_Oplus(X2,X1,X3)) ),
    inference(cnf_transformation,[],[f3625]) ).

fof(f3625,plain,
    ! [X0,X1,X2,X3] :
      ( hAPP(c_Polynomial_Opoly(X2,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,X0,X1)),X3) = hAPP(c_Polynomial_Opoly(X2,X0),c_Groups_Oplus__class_Oplus(X2,X1,X3))
      | ~ class_Rings_Ocomm__semiring__0(X2) ),
    inference(rectify,[],[f2817]) ).

fof(f2817,plain,
    ! [X1,X3,X2,X0] :
      ( hAPP(c_Polynomial_Opoly(X2,X1),c_Groups_Oplus__class_Oplus(X2,X3,X0)) = hAPP(c_Polynomial_Opoly(X2,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,X1,X3)),X0)
      | ~ class_Rings_Ocomm__semiring__0(X2) ),
    inference(ennf_transformation,[],[f1981]) ).

fof(f1981,plain,
    ! [X1,X0,X3,X2] :
      ( class_Rings_Ocomm__semiring__0(X2)
     => hAPP(c_Polynomial_Opoly(X2,X1),c_Groups_Oplus__class_Oplus(X2,X3,X0)) = hAPP(c_Polynomial_Opoly(X2,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,X1,X3)),X0) ),
    inference(rectify,[],[f74]) ).

fof(f74,axiom,
    ! [X19,X24,X4,X3] :
      ( class_Rings_Ocomm__semiring__0(X4)
     => hAPP(c_Polynomial_Opoly(X4,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X4,X24,X3)),X19) = hAPP(c_Polynomial_Opoly(X4,X24),c_Groups_Oplus__class_Oplus(X4,X3,X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__offset__poly) ).

fof(f16154,plain,
    ( ~ spl24_378
    | spl24_379
    | ~ spl24_308 ),
    inference(avatar_split_clause,[],[f16129,f13463,f16151,f16147]) ).

fof(f16147,plain,
    ( spl24_378
  <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(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,[spl24_378])]) ).

fof(f16151,plain,
    ( spl24_379
  <=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_379])]) ).

fof(f13463,plain,
    ( spl24_308
  <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_308])]) ).

fof(f16129,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_308 ),
    inference(resolution,[],[f13465,f5243]) ).

fof(f13465,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ spl24_308 ),
    inference(avatar_component_clause,[],[f13463]) ).

fof(f16141,plain,
    ( spl24_377
    | ~ spl24_308 ),
    inference(avatar_split_clause,[],[f16115,f13463,f16135]) ).

fof(f16135,plain,
    ( spl24_377
  <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_377])]) ).

fof(f16115,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    | ~ spl24_308 ),
    inference(resolution,[],[f13465,f4618]) ).

fof(f16138,plain,
    ( spl24_377
    | ~ spl24_308 ),
    inference(avatar_split_clause,[],[f16133,f13463,f16135]) ).

fof(f16133,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    | ~ spl24_308 ),
    inference(forward_demodulation,[],[f16127,f5830]) ).

fof(f16127,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,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),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ spl24_308 ),
    inference(resolution,[],[f13465,f5678]) ).

fof(f16062,plain,
    ( ~ spl24_9
    | spl24_376
    | ~ spl24_9 ),
    inference(avatar_split_clause,[],[f16050,f6248,f16060,f6248]) ).

fof(f16060,plain,
    ( spl24_376
  <=> ! [X16,X15] :
        ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X16),X15)
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X15) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_376])]) ).

fof(f16050,plain,
    ( ! [X16,X15] :
        ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X16),X15)
        | ~ class_Rings_Ocomm__semiring__1(tc_Int_Oint)
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X15) )
    | ~ spl24_9 ),
    inference(resolution,[],[f7579,f4832]) ).

fof(f16045,plain,
    ( ~ spl24_5
    | spl24_375
    | ~ spl24_5 ),
    inference(avatar_split_clause,[],[f16041,f6228,f16043,f6228]) ).

fof(f16043,plain,
    ( spl24_375
  <=> ! [X31,X33,X30,X32] :
        ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X30),X31),hAPP(c_Polynomial_Opoly(tc_Nat_Onat,c_Polynomial_Omonom(tc_Nat_Onat,X32,X33)),X30))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31,X33) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_375])]) ).

fof(f16041,plain,
    ( ! [X31,X32,X30,X33] :
        ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X30),X31),hAPP(c_Polynomial_Opoly(tc_Nat_Onat,c_Polynomial_Omonom(tc_Nat_Onat,X32,X33)),X30))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31,X33)
        | ~ class_Rings_Ocomm__semiring__1(tc_Nat_Onat) )
    | ~ spl24_5 ),
    inference(forward_subsumption_demodulation,[],[f16028,f5620]) ).

fof(f16028,plain,
    ( ! [X31,X32,X30,X33] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31,X33)
        | ~ class_Rings_Ocomm__semiring__1(tc_Nat_Onat)
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X30),X31),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X32),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X30),X33))) )
    | ~ spl24_5 ),
    inference(resolution,[],[f7578,f5448]) ).

fof(f7578,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,X2)
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)) )
    | ~ spl24_5 ),
    inference(resolution,[],[f5779,f6230]) ).

fof(f16039,plain,
    ( spl24_374
    | ~ spl24_5
    | ~ spl24_5 ),
    inference(avatar_split_clause,[],[f16035,f6228,f6228,f16037]) ).

fof(f16037,plain,
    ( spl24_374
  <=> ! [X28,X29,X27,X25,X26] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X25,X28)
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X25),X26),hAPP(c_Polynomial_Opoly(tc_Nat_Onat,c_Polynomial_Omonom(tc_Nat_Onat,X27,X29)),X28))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X29) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_374])]) ).

fof(f16035,plain,
    ( ! [X28,X29,X26,X27,X25] :
        ( ~ class_Rings_Ocomm__semiring__1(tc_Nat_Onat)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X25,X28)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X29)
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X25),X26),hAPP(c_Polynomial_Opoly(tc_Nat_Onat,c_Polynomial_Omonom(tc_Nat_Onat,X27,X29)),X28)) )
    | ~ spl24_5 ),
    inference(forward_subsumption_demodulation,[],[f16027,f5620]) ).

fof(f16027,plain,
    ( ! [X28,X29,X26,X27,X25] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X25,X28)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X29)
        | ~ class_Rings_Ocomm__semiring__1(tc_Nat_Onat)
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X25),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X27),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X28),X29))) )
    | ~ spl24_5 ),
    inference(resolution,[],[f7578,f5752]) ).

fof(f16034,plain,
    ( spl24_373
    | ~ spl24_5
    | ~ spl24_5 ),
    inference(avatar_split_clause,[],[f16030,f6228,f6228,f16032]) ).

fof(f16032,plain,
    ( spl24_373
  <=> ! [X24,X21,X23,X22] :
        ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X21),X22),hAPP(c_Polynomial_Opoly(tc_Nat_Onat,c_Polynomial_Omonom(tc_Nat_Onat,X23,X22)),X24))
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X21,X24) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_373])]) ).

fof(f16030,plain,
    ( ! [X21,X24,X22,X23] :
        ( ~ class_Rings_Ocomm__semiring__1(tc_Nat_Onat)
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X21),X22),hAPP(c_Polynomial_Opoly(tc_Nat_Onat,c_Polynomial_Omonom(tc_Nat_Onat,X23,X22)),X24))
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X21,X24) )
    | ~ spl24_5 ),
    inference(forward_subsumption_demodulation,[],[f16026,f5620]) ).

fof(f16026,plain,
    ( ! [X21,X24,X22,X23] :
        ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X21),X22),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X24),X22)))
        | ~ class_Rings_Ocomm__semiring__1(tc_Nat_Onat)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X21,X24) )
    | ~ spl24_5 ),
    inference(resolution,[],[f7578,f4750]) ).

fof(f15963,plain,
    ( ~ spl24_9
    | spl24_372
    | ~ spl24_9 ),
    inference(avatar_split_clause,[],[f15951,f6248,f15961,f6248]) ).

fof(f15961,plain,
    ( spl24_372
  <=> ! [X16,X15] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X15)
        | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X15),X16) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_372])]) ).

fof(f15951,plain,
    ( ! [X16,X15] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X15)
        | ~ class_Rings_Ocomm__semiring__1(tc_Int_Oint)
        | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X15),X16) )
    | ~ spl24_9 ),
    inference(resolution,[],[f7465,f4832]) ).

fof(f15926,plain,
    ( spl24_371
    | ~ spl24_92 ),
    inference(avatar_split_clause,[],[f15911,f6764,f15923]) ).

fof(f15911,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))
    | ~ spl24_92 ),
    inference(resolution,[],[f13339,f6766]) ).

fof(f13339,plain,
    ! [X0] :
      ( ~ class_Rings_Ocomm__semiring__0(X0)
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) ),
    inference(resolution,[],[f4522,f4574]) ).

fof(f4574,plain,
    ! [X0] :
      ( class_Groups_Ozero(X0)
      | ~ class_Rings_Ocomm__semiring__0(X0) ),
    inference(cnf_transformation,[],[f3340]) ).

fof(f3340,plain,
    ! [X0] :
      ( ~ class_Rings_Ocomm__semiring__0(X0)
      | class_Groups_Ozero(X0) ),
    inference(ennf_transformation,[],[f1720]) ).

fof(f1720,plain,
    ! [X0] :
      ( class_Rings_Ocomm__semiring__0(X0)
     => class_Groups_Ozero(X0) ),
    inference(rectify,[],[f1004]) ).

fof(f1004,axiom,
    ! [X93] :
      ( class_Rings_Ocomm__semiring__0(X93)
     => class_Groups_Ozero(X93) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Ocomm__semiring__0__Groups_Ozero) ).

fof(f4522,plain,
    ! [X0] :
      ( ~ class_Groups_Ozero(X0)
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) ),
    inference(cnf_transformation,[],[f3244]) ).

fof(f3244,plain,
    ! [X0] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))
      | ~ class_Groups_Ozero(X0) ),
    inference(ennf_transformation,[],[f1636]) ).

fof(f1636,plain,
    ! [X0] :
      ( class_Groups_Ozero(X0)
     => c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) ),
    inference(rectify,[],[f135]) ).

fof(f135,axiom,
    ! [X4] :
      ( class_Groups_Ozero(X4)
     => c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X4,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__0) ).

fof(f15921,plain,
    ( spl24_370
    | ~ spl24_336 ),
    inference(avatar_split_clause,[],[f15908,f14289,f15918]) ).

fof(f15918,plain,
    ( spl24_370
  <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(tc_Polynomial_Opoly(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Int_Oint)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_370])]) ).

fof(f15908,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(tc_Polynomial_Opoly(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Int_Oint))))
    | ~ spl24_336 ),
    inference(resolution,[],[f13339,f14290]) ).

fof(f14290,plain,
    ( class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(tc_Int_Oint))
    | ~ spl24_336 ),
    inference(avatar_component_clause,[],[f14289]) ).

fof(f15916,plain,
    ( spl24_369
    | ~ spl24_331 ),
    inference(avatar_split_clause,[],[f15907,f14185,f15913]) ).

fof(f15913,plain,
    ( spl24_369
  <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(tc_Polynomial_Opoly(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Nat_Onat)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_369])]) ).

fof(f15907,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(tc_Polynomial_Opoly(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Nat_Onat))))
    | ~ spl24_331 ),
    inference(resolution,[],[f13339,f14186]) ).

fof(f14186,plain,
    ( class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(tc_Nat_Onat))
    | ~ spl24_331 ),
    inference(avatar_component_clause,[],[f14185]) ).

fof(f15905,plain,
    ( ~ spl24_5
    | spl24_368
    | ~ spl24_5 ),
    inference(avatar_split_clause,[],[f15887,f6228,f15903,f6228]) ).

fof(f15903,plain,
    ( spl24_368
  <=> ! [X24,X21,X23,X22] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X21,X23)
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X21),X22),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X23),X22)),X24)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_368])]) ).

fof(f15887,plain,
    ( ! [X21,X24,X22,X23] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X21,X23)
        | ~ class_Rings_Ocomm__semiring__1(tc_Nat_Onat)
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X21),X22),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X23),X22)),X24)) )
    | ~ spl24_5 ),
    inference(resolution,[],[f7464,f4750]) ).

fof(f7464,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,X1)
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)) )
    | ~ spl24_5 ),
    inference(resolution,[],[f5251,f6230]) ).

fof(f15899,plain,
    ( ~ spl24_5
    | spl24_367
    | ~ spl24_5 ),
    inference(avatar_split_clause,[],[f15889,f6228,f15897,f6228]) ).

fof(f15897,plain,
    ( spl24_367
  <=> ! [X31,X33,X32,X30] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31,X32)
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X30),X31),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X30),X32)),X33)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_367])]) ).

fof(f15889,plain,
    ( ! [X31,X32,X30,X33] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31,X32)
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X30),X31),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X30),X32)),X33))
        | ~ class_Rings_Ocomm__semiring__1(tc_Nat_Onat) )
    | ~ spl24_5 ),
    inference(resolution,[],[f7464,f5448]) ).

fof(f15893,plain,
    ( ~ spl24_5
    | spl24_366
    | ~ spl24_5 ),
    inference(avatar_split_clause,[],[f15888,f6228,f15891,f6228]) ).

fof(f15891,plain,
    ( spl24_366
  <=> ! [X29,X27,X25,X28,X26] :
        ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X25),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X27),X28)),X29))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X28)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X25,X27) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_366])]) ).

fof(f15888,plain,
    ( ! [X28,X29,X26,X27,X25] :
        ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X25),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X27),X28)),X29))
        | ~ class_Rings_Ocomm__semiring__1(tc_Nat_Onat)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X25,X27)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X28) )
    | ~ spl24_5 ),
    inference(resolution,[],[f7464,f5752]) ).

fof(f15533,plain,
    ( spl24_365
    | ~ spl24_331 ),
    inference(avatar_split_clause,[],[f15514,f14185,f15530]) ).

fof(f15530,plain,
    ( spl24_365
  <=> c_Polynomial_OpCons(tc_Polynomial_Opoly(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Nat_Onat)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Nat_Onat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_365])]) ).

fof(f15514,plain,
    ( c_Polynomial_OpCons(tc_Polynomial_Opoly(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Nat_Onat)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Nat_Onat)))
    | ~ spl24_331 ),
    inference(resolution,[],[f7050,f14186]) ).

fof(f7050,plain,
    ! [X0] :
      ( ~ class_Rings_Ocomm__semiring__0(X0)
      | c_Polynomial_OpCons(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) ),
    inference(resolution,[],[f4574,f5674]) ).

fof(f5674,plain,
    ! [X0] :
      ( ~ class_Groups_Ozero(X0)
      | c_Polynomial_OpCons(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) ),
    inference(cnf_transformation,[],[f3351]) ).

fof(f3351,plain,
    ! [X0] :
      ( ~ class_Groups_Ozero(X0)
      | c_Polynomial_OpCons(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) ),
    inference(ennf_transformation,[],[f2238]) ).

fof(f2238,plain,
    ! [X0] :
      ( class_Groups_Ozero(X0)
     => c_Polynomial_OpCons(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f4]) ).

fof(f4,axiom,
    ! [X4] :
      ( class_Groups_Ozero(X4)
     => c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = c_Polynomial_OpCons(X4,c_Groups_Ozero__class_Ozero(X4),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pCons__0__0) ).

fof(f15528,plain,
    ( spl24_364
    | ~ spl24_336 ),
    inference(avatar_split_clause,[],[f15515,f14289,f15525]) ).

fof(f15525,plain,
    ( spl24_364
  <=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Int_Oint))) = c_Polynomial_OpCons(tc_Polynomial_Opoly(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Int_Oint)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_364])]) ).

fof(f15515,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Int_Oint))) = c_Polynomial_OpCons(tc_Polynomial_Opoly(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Int_Oint))))
    | ~ spl24_336 ),
    inference(resolution,[],[f7050,f14290]) ).

fof(f15523,plain,
    ( spl24_363
    | ~ spl24_92 ),
    inference(avatar_split_clause,[],[f15518,f6764,f15520]) ).

fof(f15518,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = c_Polynomial_OpCons(t_a,c_Groups_Ozero__class_Ozero(t_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))
    | ~ spl24_92 ),
    inference(resolution,[],[f7050,f6766]) ).

fof(f15510,plain,
    ( spl24_362
    | ~ spl24_101 ),
    inference(avatar_split_clause,[],[f15505,f6815,f15507]) ).

fof(f6815,plain,
    ( spl24_101
  <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_101])]) ).

fof(f15505,plain,
    ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_Onat_Onat__size(c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ spl24_101 ),
    inference(forward_demodulation,[],[f15504,f5628]) ).

fof(f15504,plain,
    ( 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_Nat_Onat_Onat__size(c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ spl24_101 ),
    inference(forward_demodulation,[],[f15501,f6817]) ).

fof(f6817,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ spl24_101 ),
    inference(avatar_component_clause,[],[f6815]) ).

fof(f15501,plain,
    c_Nat_Onat_Onat__size(c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(superposition,[],[f6790,f4540]) ).

fof(f15491,plain,
    ( spl24_361
    | ~ spl24_111 ),
    inference(avatar_split_clause,[],[f15471,f6883,f15487]) ).

fof(f15471,plain,
    ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK20(c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | ~ spl24_111 ),
    inference(resolution,[],[f5987,f6885]) ).

fof(f15490,plain,
    ( spl24_361
    | ~ spl24_111 ),
    inference(avatar_split_clause,[],[f15485,f6883,f15487]) ).

fof(f15485,plain,
    ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK20(c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | ~ spl24_111 ),
    inference(forward_demodulation,[],[f15481,f5628]) ).

fof(f15481,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK20(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_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ spl24_111 ),
    inference(resolution,[],[f5987,f11292]) ).

fof(f15470,plain,
    ( spl24_360
    | ~ spl24_357 ),
    inference(avatar_split_clause,[],[f15465,f15397,f15467]) ).

fof(f15467,plain,
    ( spl24_360
  <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_360])]) ).

fof(f15465,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
    | ~ spl24_357 ),
    inference(forward_demodulation,[],[f15453,f5830]) ).

fof(f15453,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ spl24_357 ),
    inference(resolution,[],[f15399,f5678]) ).

fof(f15464,plain,
    ( ~ spl24_358
    | spl24_359
    | ~ spl24_357 ),
    inference(avatar_split_clause,[],[f15455,f15397,f15461,f15457]) ).

fof(f15455,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ spl24_357 ),
    inference(resolution,[],[f15399,f5243]) ).

fof(f15400,plain,
    ( spl24_357
    | ~ spl24_163
    | ~ spl24_256 ),
    inference(avatar_split_clause,[],[f15387,f12456,f9358,f15397]) ).

fof(f15387,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ spl24_163
    | ~ spl24_256 ),
    inference(resolution,[],[f11210,f12458]) ).

fof(f11210,plain,
    ( ! [X0] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) )
    | ~ spl24_163 ),
    inference(resolution,[],[f9360,f4403]) ).

fof(f15360,plain,
    ( ~ spl24_5
    | spl24_356 ),
    inference(avatar_split_clause,[],[f15346,f15358,f6228]) ).

fof(f15358,plain,
    ( spl24_356
  <=> ! [X13,X12,X14] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X14,X12)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X12),X13))
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X14),X13),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X12),X13)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_356])]) ).

fof(f15346,plain,
    ! [X14,X12,X13] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X14,X12)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X14),X13),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X12),X13))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X12),X13))
      | ~ class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ),
    inference(resolution,[],[f4640,f4750]) ).

fof(f15356,plain,
    ( ~ spl24_5
    | spl24_355 ),
    inference(avatar_split_clause,[],[f15348,f15354,f6228]) ).

fof(f15354,plain,
    ( spl24_355
  <=> ! [X20,X21,X19] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X19),X21),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X19),X20))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X20)
        | ~ 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),X19),X20)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_355])]) ).

fof(f15348,plain,
    ! [X21,X19,X20] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X19),X21),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X19),X20))
      | ~ 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),X19),X20))
      | ~ class_Rings_Ocomm__semiring__1(tc_Nat_Onat)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X20) ),
    inference(resolution,[],[f4640,f5448]) ).

fof(f15352,plain,
    ( ~ spl24_5
    | spl24_354 ),
    inference(avatar_split_clause,[],[f15347,f15350,f6228]) ).

fof(f15350,plain,
    ( spl24_354
  <=> ! [X18,X17,X16,X15] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X17,X15)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X17),X18),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X15),X16))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X16)
        | ~ 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),X15),X16)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_354])]) ).

fof(f15347,plain,
    ! [X18,X16,X17,X15] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X17,X15)
      | ~ 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),X15),X16))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X16)
      | ~ class_Rings_Ocomm__semiring__1(tc_Nat_Onat)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X17),X18),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X15),X16)) ),
    inference(resolution,[],[f4640,f5752]) ).

fof(f15336,plain,
    ( ~ spl24_5
    | spl24_353 ),
    inference(avatar_split_clause,[],[f15319,f15334,f6228]) ).

fof(f15334,plain,
    ( spl24_353
  <=> ! [X20,X21,X19] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X19),X20),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X19),X21))
        | ~ 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),X19),X20))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X20) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_353])]) ).

fof(f15319,plain,
    ! [X21,X19,X20] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X19),X20),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X19),X21))
      | ~ class_Rings_Ocomm__semiring__1(tc_Nat_Onat)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X20)
      | ~ 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),X19),X20)) ),
    inference(resolution,[],[f4538,f5448]) ).

fof(f4538,plain,
    ! [X0,X1] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
    inference(cnf_transformation,[],[f2632]) ).

fof(f2632,plain,
    ! [X0,X1] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0)
      | ~ 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),X0) ),
    inference(flattening,[],[f2631]) ).

fof(f2631,plain,
    ! [X1,X0] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0)
      | ~ 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),X0) ),
    inference(ennf_transformation,[],[f1603]) ).

fof(f1603,plain,
    ! [X1,X0] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
       => ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0) ) ),
    inference(rectify,[],[f624]) ).

fof(f624,axiom,
    ! [X23,X17] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X23)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X23,X17)
       => ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X17,X23) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__dvd__not__less) ).

fof(f15332,plain,
    spl24_351,
    inference(avatar_split_clause,[],[f15309,f15325]) ).

fof(f15309,plain,
    ! [X1] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(resolution,[],[f4538,f4894]) ).

fof(f15331,plain,
    ( ~ spl24_5
    | spl24_352 ),
    inference(avatar_split_clause,[],[f15317,f15329,f6228]) ).

fof(f15329,plain,
    ( spl24_352
  <=> ! [X13,X12,X14] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X12),X13))
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X14,X12)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X12),X13),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X14),X13)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_352])]) ).

fof(f15317,plain,
    ! [X14,X12,X13] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X12),X13))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X12),X13),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X14),X13))
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X14,X12)
      | ~ class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ),
    inference(resolution,[],[f4538,f4750]) ).

fof(f15327,plain,
    ( spl24_351
    | ~ spl24_5 ),
    inference(avatar_split_clause,[],[f15316,f6228,f15325]) ).

fof(f15316,plain,
    ! [X11] :
      ( ~ class_Rings_Ocomm__semiring__1(tc_Nat_Onat)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X11)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X11,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(resolution,[],[f4538,f5811]) ).

fof(f5811,plain,
    ! [X0,X1] :
      ( c_Rings_Odvd__class_Odvd(X1,c_Groups_Oone__class_Oone(X1),X0)
      | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(cnf_transformation,[],[f2473]) ).

fof(f2473,plain,
    ! [X0,X1] :
      ( c_Rings_Odvd__class_Odvd(X1,c_Groups_Oone__class_Oone(X1),X0)
      | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(ennf_transformation,[],[f1262]) ).

fof(f1262,plain,
    ! [X0,X1] :
      ( class_Rings_Ocomm__semiring__1(X1)
     => c_Rings_Odvd__class_Odvd(X1,c_Groups_Oone__class_Oone(X1),X0) ),
    inference(rectify,[],[f426]) ).

fof(f426,axiom,
    ! [X5,X4] :
      ( class_Rings_Ocomm__semiring__1(X4)
     => c_Rings_Odvd__class_Odvd(X4,c_Groups_Oone__class_Oone(X4),X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__dvd) ).

fof(f15323,plain,
    ( ~ spl24_5
    | spl24_350 ),
    inference(avatar_split_clause,[],[f15318,f15321,f6228]) ).

fof(f15321,plain,
    ( spl24_350
  <=> ! [X18,X17,X16,X15] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X17,X15)
        | ~ 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),X15),X16))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X15),X16),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X17),X18))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X16) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_350])]) ).

fof(f15318,plain,
    ! [X18,X16,X17,X15] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X17,X15)
      | ~ class_Rings_Ocomm__semiring__1(tc_Nat_Onat)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X16)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X15),X16),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X17),X18))
      | ~ 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),X15),X16)) ),
    inference(resolution,[],[f4538,f5752]) ).

fof(f15147,plain,
    ( ~ spl24_348
    | spl24_349
    | ~ spl24_94 ),
    inference(avatar_split_clause,[],[f15138,f6774,f15144,f15140]) ).

fof(f15140,plain,
    ( spl24_348
  <=> class_Rings_Ocomm__semiring__0(tc_HOL_Obool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_348])]) ).

fof(f15144,plain,
    ( spl24_349
  <=> c_fequal = c_HOL_Oequal__class_Oequal(tc_Polynomial_Opoly(tc_HOL_Obool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_349])]) ).

fof(f6774,plain,
    ( spl24_94
  <=> class_HOL_Oequal(tc_HOL_Obool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_94])]) ).

fof(f15138,plain,
    ( c_fequal = c_HOL_Oequal__class_Oequal(tc_Polynomial_Opoly(tc_HOL_Obool))
    | ~ class_Rings_Ocomm__semiring__0(tc_HOL_Obool)
    | ~ spl24_94 ),
    inference(resolution,[],[f14067,f6776]) ).

fof(f6776,plain,
    ( class_HOL_Oequal(tc_HOL_Obool)
    | ~ spl24_94 ),
    inference(avatar_component_clause,[],[f6774]) ).

fof(f14067,plain,
    ! [X0] :
      ( ~ class_HOL_Oequal(X0)
      | ~ class_Rings_Ocomm__semiring__0(X0)
      | c_fequal = c_HOL_Oequal__class_Oequal(tc_Polynomial_Opoly(X0)) ),
    inference(resolution,[],[f11668,f4574]) ).

fof(f11668,plain,
    ! [X0] :
      ( ~ class_Groups_Ozero(X0)
      | ~ class_HOL_Oequal(X0)
      | c_fequal = c_HOL_Oequal__class_Oequal(tc_Polynomial_Opoly(X0)) ),
    inference(resolution,[],[f4714,f4657]) ).

fof(f4657,plain,
    ! [X0] :
      ( ~ class_HOL_Oequal(X0)
      | c_fequal = c_HOL_Oequal__class_Oequal(X0) ),
    inference(cnf_transformation,[],[f3205]) ).

fof(f3205,plain,
    ! [X0] :
      ( c_fequal = c_HOL_Oequal__class_Oequal(X0)
      | ~ class_HOL_Oequal(X0) ),
    inference(ennf_transformation,[],[f1568]) ).

fof(f1568,plain,
    ! [X0] :
      ( class_HOL_Oequal(X0)
     => c_fequal = c_HOL_Oequal__class_Oequal(X0) ),
    inference(rectify,[],[f24]) ).

fof(f24,axiom,
    ! [X8] :
      ( class_HOL_Oequal(X8)
     => c_fequal = c_HOL_Oequal__class_Oequal(X8) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__equal) ).

fof(f4714,plain,
    ! [X0] :
      ( class_HOL_Oequal(tc_Polynomial_Opoly(X0))
      | ~ class_HOL_Oequal(X0)
      | ~ class_Groups_Ozero(X0) ),
    inference(cnf_transformation,[],[f2935]) ).

fof(f2935,plain,
    ! [X0] :
      ( class_HOL_Oequal(tc_Polynomial_Opoly(X0))
      | ~ class_Groups_Ozero(X0)
      | ~ class_HOL_Oequal(X0) ),
    inference(flattening,[],[f2934]) ).

fof(f2934,plain,
    ! [X0] :
      ( class_HOL_Oequal(tc_Polynomial_Opoly(X0))
      | ~ class_HOL_Oequal(X0)
      | ~ class_Groups_Ozero(X0) ),
    inference(ennf_transformation,[],[f1951]) ).

fof(f1951,plain,
    ! [X0] :
      ( ( class_HOL_Oequal(X0)
        & class_Groups_Ozero(X0) )
     => class_HOL_Oequal(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1175]) ).

fof(f1175,axiom,
    ! [X94] :
      ( ( class_HOL_Oequal(X94)
        & class_Groups_Ozero(X94) )
     => class_HOL_Oequal(tc_Polynomial_Opoly(X94)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__HOL_Oequal) ).

fof(f15064,plain,
    ( ~ spl24_9
    | spl24_347
    | ~ spl24_9 ),
    inference(avatar_split_clause,[],[f15055,f6248,f15062,f6248]) ).

fof(f15062,plain,
    ( spl24_347
  <=> ! [X37,X34,X36,X33,X35] :
        ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X33),X34),X35)
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X36),X37),X35)
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X33,X36)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X37) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_347])]) ).

fof(f15055,plain,
    ( ! [X36,X37,X34,X35,X33] :
        ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X33),X34),X35)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X37)
        | ~ class_Rings_Ocomm__semiring__1(tc_Int_Oint)
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X33,X36)
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X36),X37),X35) )
    | ~ spl24_9 ),
    inference(resolution,[],[f7329,f5752]) ).

fof(f7329,plain,
    ( ! [X3,X4,X5] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X3,X4)
        | c_Rings_Odvd__class_Odvd(tc_Int_Oint,X3,X5)
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X4,X5) )
    | ~ spl24_9 ),
    inference(resolution,[],[f4718,f6250]) ).

fof(f4718,plain,
    ! [X2,X3,X0,X1] :
      ( ~ class_Rings_Ocomm__semiring__1(X0)
      | ~ c_Rings_Odvd__class_Odvd(X0,X1,X3)
      | c_Rings_Odvd__class_Odvd(X0,X1,X2)
      | ~ c_Rings_Odvd__class_Odvd(X0,X3,X2) ),
    inference(cnf_transformation,[],[f3659]) ).

fof(f3659,plain,
    ! [X0,X1,X2,X3] :
      ( ~ c_Rings_Odvd__class_Odvd(X0,X1,X3)
      | ~ c_Rings_Odvd__class_Odvd(X0,X3,X2)
      | c_Rings_Odvd__class_Odvd(X0,X1,X2)
      | ~ class_Rings_Ocomm__semiring__1(X0) ),
    inference(rectify,[],[f3262]) ).

fof(f3262,plain,
    ! [X3,X1,X2,X0] :
      ( ~ c_Rings_Odvd__class_Odvd(X3,X1,X0)
      | ~ c_Rings_Odvd__class_Odvd(X3,X0,X2)
      | c_Rings_Odvd__class_Odvd(X3,X1,X2)
      | ~ class_Rings_Ocomm__semiring__1(X3) ),
    inference(flattening,[],[f3261]) ).

fof(f3261,plain,
    ! [X3,X2,X0,X1] :
      ( c_Rings_Odvd__class_Odvd(X3,X1,X2)
      | ~ c_Rings_Odvd__class_Odvd(X3,X0,X2)
      | ~ c_Rings_Odvd__class_Odvd(X3,X1,X0)
      | ~ class_Rings_Ocomm__semiring__1(X3) ),
    inference(ennf_transformation,[],[f2005]) ).

fof(f2005,plain,
    ! [X3,X2,X0,X1] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => ( c_Rings_Odvd__class_Odvd(X3,X1,X0)
       => ( c_Rings_Odvd__class_Odvd(X3,X0,X2)
         => c_Rings_Odvd__class_Odvd(X3,X1,X2) ) ) ),
    inference(rectify,[],[f435]) ).

fof(f435,axiom,
    ! [X29,X5,X22,X4] :
      ( class_Rings_Ocomm__semiring__1(X4)
     => ( c_Rings_Odvd__class_Odvd(X4,X5,X29)
       => ( c_Rings_Odvd__class_Odvd(X4,X29,X22)
         => c_Rings_Odvd__class_Odvd(X4,X5,X22) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__trans) ).

fof(f15060,plain,
    ( ~ spl24_9
    | spl24_346
    | ~ spl24_9 ),
    inference(avatar_split_clause,[],[f15054,f6248,f15058,f6248]) ).

fof(f15058,plain,
    ( spl24_346
  <=> ! [X31,X29,X32,X30] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X32),X30),X31)
        | c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X29),X30),X31)
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X29,X32) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_346])]) ).

fof(f15054,plain,
    ( ! [X31,X29,X32,X30] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X32),X30),X31)
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X29,X32)
        | ~ class_Rings_Ocomm__semiring__1(tc_Int_Oint)
        | c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X29),X30),X31) )
    | ~ spl24_9 ),
    inference(resolution,[],[f7329,f4750]) ).

fof(f14826,plain,
    ( spl24_345
    | ~ spl24_258 ),
    inference(avatar_split_clause,[],[f14821,f12472,f14823]) ).

fof(f14823,plain,
    ( spl24_345
  <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_345])]) ).

fof(f14821,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
    | ~ spl24_258 ),
    inference(forward_demodulation,[],[f14792,f5830]) ).

fof(f14792,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ spl24_258 ),
    inference(resolution,[],[f7226,f12474]) ).

fof(f14819,plain,
    ( spl24_344
    | ~ spl24_264 ),
    inference(avatar_split_clause,[],[f14799,f12593,f14816]) ).

fof(f14816,plain,
    ( spl24_344
  <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_344])]) ).

fof(f12593,plain,
    ( spl24_264
  <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_264])]) ).

fof(f14799,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ spl24_264 ),
    inference(resolution,[],[f7226,f12595]) ).

fof(f12595,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ spl24_264 ),
    inference(avatar_component_clause,[],[f12593]) ).

fof(f14814,plain,
    ( spl24_343
    | ~ spl24_135 ),
    inference(avatar_split_clause,[],[f14809,f7262,f14811]) ).

fof(f14811,plain,
    ( spl24_343
  <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_343])]) ).

fof(f14809,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    | ~ spl24_135 ),
    inference(forward_demodulation,[],[f14791,f5830]) ).

fof(f14791,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ spl24_135 ),
    inference(resolution,[],[f7226,f7264]) ).

fof(f7264,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ spl24_135 ),
    inference(avatar_component_clause,[],[f7262]) ).

fof(f14805,plain,
    ( spl24_342
    | ~ spl24_233 ),
    inference(avatar_split_clause,[],[f14795,f11143,f14802]) ).

fof(f14795,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ spl24_233 ),
    inference(resolution,[],[f7226,f11145]) ).

fof(f11145,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ spl24_233 ),
    inference(avatar_component_clause,[],[f11143]) ).

fof(f14378,plain,
    ( spl24_341
    | ~ spl24_5 ),
    inference(avatar_split_clause,[],[f14364,f6228,f14376]) ).

fof(f14376,plain,
    ( spl24_341
  <=> ! [X24,X21,X23,X22] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X22,X24)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X21,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X22),X23))
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X21,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X24),X23)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_341])]) ).

fof(f14364,plain,
    ! [X21,X24,X22,X23] :
      ( ~ class_Rings_Ocomm__semiring__1(tc_Nat_Onat)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X22,X24)
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X21,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X24),X23))
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X21,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X22),X23)) ),
    inference(resolution,[],[f4878,f4750]) ).

fof(f4878,plain,
    ! [X2,X0,X1] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X0) ),
    inference(cnf_transformation,[],[f3767]) ).

fof(f3767,plain,
    ! [X0,X1,X2] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X0) ),
    inference(rectify,[],[f3365]) ).

fof(f3365,plain,
    ! [X0,X2,X1] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X0)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0) ),
    inference(flattening,[],[f3364]) ).

fof(f3364,plain,
    ! [X0,X1,X2] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X0)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(ennf_transformation,[],[f2062]) ).

fof(f2062,plain,
    ! [X0,X1,X2] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X0)
       => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0) ) ),
    inference(rectify,[],[f669]) ).

fof(f669,axiom,
    ! [X42,X19,X35] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X19,X35)
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X35,X42)
       => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X19,X42) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oorder__trans) ).

fof(f14374,plain,
    ( ~ spl24_5
    | spl24_340 ),
    inference(avatar_split_clause,[],[f14365,f14372,f6228]) ).

fof(f14372,plain,
    ( spl24_340
  <=> ! [X28,X29,X27,X25,X26] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X25,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X26),X27))
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X26,X28)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X27,X29)
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X25,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X28),X29)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_340])]) ).

fof(f14365,plain,
    ! [X28,X29,X26,X27,X25] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X25,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X26),X27))
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X25,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X28),X29))
      | ~ class_Rings_Ocomm__semiring__1(tc_Nat_Onat)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X27,X29)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X26,X28) ),
    inference(resolution,[],[f4878,f5752]) ).

fof(f14370,plain,
    ( ~ spl24_5
    | spl24_339 ),
    inference(avatar_split_clause,[],[f14366,f14368,f6228]) ).

fof(f14368,plain,
    ( spl24_339
  <=> ! [X31,X33,X32,X30] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X30,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X31),X32))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X32,X33)
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X30,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X31),X33)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_339])]) ).

fof(f14366,plain,
    ! [X31,X32,X30,X33] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X30,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X31),X32))
      | ~ class_Rings_Ocomm__semiring__1(tc_Nat_Onat)
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X30,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X31),X33))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X32,X33) ),
    inference(resolution,[],[f4878,f5448]) ).

fof(f14325,plain,
    ( ~ spl24_121
    | spl24_336 ),
    inference(avatar_split_clause,[],[f14324,f14289,f6941]) ).

fof(f14324,plain,
    ( ~ class_Rings_Ocomm__semiring__0(tc_Int_Oint)
    | spl24_336 ),
    inference(resolution,[],[f14291,f4604]) ).

fof(f4604,plain,
    ! [X0] :
      ( class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__semiring__0(X0) ),
    inference(cnf_transformation,[],[f3235]) ).

fof(f3235,plain,
    ! [X0] :
      ( class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X0))
      | ~ class_Rings_Ocomm__semiring__0(X0) ),
    inference(ennf_transformation,[],[f1929]) ).

fof(f1929,plain,
    ! [X0] :
      ( class_Rings_Ocomm__semiring__0(X0)
     => class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f1147]) ).

fof(f1147,axiom,
    ! [X94] :
      ( class_Rings_Ocomm__semiring__0(X94)
     => class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X94)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__0) ).

fof(f14291,plain,
    ( ~ class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(tc_Int_Oint))
    | spl24_336 ),
    inference(avatar_component_clause,[],[f14289]) ).

fof(f14323,plain,
    ( ~ spl24_58
    | spl24_338 ),
    inference(avatar_split_clause,[],[f14316,f14321,f6521]) ).

fof(f14321,plain,
    ( spl24_338
  <=> ! [X11] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X11,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_338])]) ).

fof(f14316,plain,
    ! [X11] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X11,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | ~ 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(resolution,[],[f4860,f7272]) ).

fof(f7272,plain,
    ! [X0] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(superposition,[],[f5679,f4706]) ).

fof(f4860,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0),X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
    inference(cnf_transformation,[],[f2393]) ).

fof(f14296,plain,
    ( ~ spl24_336
    | spl24_337
    | ~ spl24_9 ),
    inference(avatar_split_clause,[],[f14281,f6248,f14294,f14289]) ).

fof(f14294,plain,
    ( spl24_337
  <=> ! [X2,X3] :
        ( c_Polynomial_OpCons(tc_Polynomial_Opoly(tc_Int_Oint),X3,X2) != X2
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Int_Oint))) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_337])]) ).

fof(f14281,plain,
    ( ! [X2,X3] :
        ( c_Polynomial_OpCons(tc_Polynomial_Opoly(tc_Int_Oint),X3,X2) != X2
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Int_Oint))) = X2
        | ~ class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(tc_Int_Oint)) )
    | ~ spl24_9 ),
    inference(superposition,[],[f4596,f14134]) ).

fof(f14134,plain,
    ( ! [X1] : c_Polynomial_Osmult(tc_Polynomial_Opoly(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Int_Oint)),X1) = X1
    | ~ spl24_9 ),
    inference(resolution,[],[f7086,f6250]) ).

fof(f7086,plain,
    ! [X2,X3] :
      ( ~ class_Rings_Ocomm__semiring__1(X2)
      | c_Polynomial_Osmult(tc_Polynomial_Opoly(X2),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X2)),X3) = X3 ),
    inference(resolution,[],[f4998,f4828]) ).

fof(f4998,plain,
    ! [X0,X1] :
      ( ~ class_Rings_Ocomm__semiring__1(X0)
      | c_Polynomial_Osmult(X0,c_Groups_Oone__class_Oone(X0),X1) = X1 ),
    inference(cnf_transformation,[],[f2931]) ).

fof(f2931,plain,
    ! [X0,X1] :
      ( c_Polynomial_Osmult(X0,c_Groups_Oone__class_Oone(X0),X1) = X1
      | ~ class_Rings_Ocomm__semiring__1(X0) ),
    inference(ennf_transformation,[],[f1803]) ).

fof(f1803,plain,
    ! [X1,X0] :
      ( class_Rings_Ocomm__semiring__1(X0)
     => c_Polynomial_Osmult(X0,c_Groups_Oone__class_Oone(X0),X1) = X1 ),
    inference(rectify,[],[f288]) ).

fof(f288,axiom,
    ! [X4,X24] :
      ( class_Rings_Ocomm__semiring__1(X4)
     => c_Polynomial_Osmult(X4,c_Groups_Oone__class_Oone(X4),X24) = X24 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__1__left) ).

fof(f14292,plain,
    ( spl24_335
    | ~ spl24_336
    | ~ spl24_9 ),
    inference(avatar_split_clause,[],[f14280,f6248,f14289,f14286]) ).

fof(f14286,plain,
    ( spl24_335
  <=> ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Int_Oint))) != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Int_Oint)),X0,c_Polynomial_OpCons(tc_Polynomial_Opoly(tc_Int_Oint),X1,X0))
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Int_Oint))) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_335])]) ).

fof(f14280,plain,
    ( ! [X0,X1] :
        ( ~ class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(tc_Int_Oint))
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Int_Oint))) != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Int_Oint)),X0,c_Polynomial_OpCons(tc_Polynomial_Opoly(tc_Int_Oint),X1,X0))
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Int_Oint))) = X0 )
    | ~ spl24_9 ),
    inference(superposition,[],[f4606,f14134]) ).

fof(f14238,plain,
    ( ~ spl24_15
    | spl24_331 ),
    inference(avatar_split_clause,[],[f14237,f14185,f6277]) ).

fof(f14237,plain,
    ( ~ class_Rings_Ocomm__semiring__0(tc_Nat_Onat)
    | spl24_331 ),
    inference(resolution,[],[f14187,f4604]) ).

fof(f14187,plain,
    ( ~ class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(tc_Nat_Onat))
    | spl24_331 ),
    inference(avatar_component_clause,[],[f14185]) ).

fof(f14225,plain,
    ~ spl24_334,
    inference(avatar_split_clause,[],[f14216,f14222]) ).

fof(f14222,plain,
    ( spl24_334
  <=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(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,[spl24_334])]) ).

fof(f14216,plain,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(superposition,[],[f7174,f12434]) ).

fof(f7174,plain,
    ! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)),
    inference(superposition,[],[f5615,f5830]) ).

fof(f5615,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,[],[f2123]) ).

fof(f2123,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,[],[f802]) ).

fof(f802,axiom,
    ! [X42] : 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),X42),X42),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_odd__nonzero) ).

fof(f14195,plain,
    ( ~ spl24_331
    | spl24_333
    | ~ spl24_5 ),
    inference(avatar_split_clause,[],[f14179,f6228,f14193,f14185]) ).

fof(f14193,plain,
    ( spl24_333
  <=> ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Nat_Onat))) = X0
        | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Nat_Onat)),X0,c_Polynomial_OpCons(tc_Polynomial_Opoly(tc_Nat_Onat),X1,X0)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Nat_Onat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_333])]) ).

fof(f14179,plain,
    ( ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Nat_Onat))) = X0
        | ~ class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(tc_Nat_Onat))
        | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Nat_Onat)),X0,c_Polynomial_OpCons(tc_Polynomial_Opoly(tc_Nat_Onat),X1,X0)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Nat_Onat))) )
    | ~ spl24_5 ),
    inference(superposition,[],[f4606,f14133]) ).

fof(f14133,plain,
    ( ! [X0] : c_Polynomial_Osmult(tc_Polynomial_Opoly(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Nat_Onat)),X0) = X0
    | ~ spl24_5 ),
    inference(resolution,[],[f7086,f6230]) ).

fof(f14191,plain,
    ( ~ spl24_331
    | spl24_332
    | ~ spl24_5 ),
    inference(avatar_split_clause,[],[f14180,f6228,f14189,f14185]) ).

fof(f14189,plain,
    ( spl24_332
  <=> ! [X2,X3] :
        ( c_Polynomial_OpCons(tc_Polynomial_Opoly(tc_Nat_Onat),X3,X2) != X2
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Nat_Onat))) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_332])]) ).

fof(f14180,plain,
    ( ! [X2,X3] :
        ( c_Polynomial_OpCons(tc_Polynomial_Opoly(tc_Nat_Onat),X3,X2) != X2
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Nat_Onat))) = X2
        | ~ class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(tc_Nat_Onat)) )
    | ~ spl24_5 ),
    inference(superposition,[],[f4596,f14133]) ).

fof(f14109,plain,
    ( ~ spl24_103
    | spl24_330
    | ~ spl24_130 ),
    inference(avatar_split_clause,[],[f14082,f7008,f14107,f6828]) ).

fof(f6828,plain,
    ( spl24_103
  <=> class_Rings_Oidom(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_103])]) ).

fof(f14107,plain,
    ( spl24_330
  <=> ! [X2,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(c_Polynomial_Opoly(tc_Int_Oint,X2),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1))
        | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Int_Oint),c_Polynomial_OpCons(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Int_Oint))),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_330])]) ).

fof(f7008,plain,
    ( spl24_130
  <=> c_Polynomial_OpCons(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint))) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_130])]) ).

fof(f14082,plain,
    ( ! [X2,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(c_Polynomial_Opoly(tc_Int_Oint,X2),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1))
        | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Int_Oint),c_Polynomial_OpCons(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Int_Oint))),X2)
        | ~ class_Rings_Oidom(tc_Int_Oint) )
    | ~ spl24_130 ),
    inference(superposition,[],[f4941,f7010]) ).

fof(f7010,plain,
    ( c_Polynomial_OpCons(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint))) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Int_Oint))
    | ~ spl24_130 ),
    inference(avatar_component_clause,[],[f7008]) ).

fof(f14105,plain,
    ( spl24_329
    | ~ spl24_23
    | ~ spl24_130 ),
    inference(avatar_split_clause,[],[f14088,f7008,f6330,f14101]) ).

fof(f14101,plain,
    ( spl24_329
  <=> ! [X9,X10] :
        ( c_Groups_Oone__class_Oone(tc_Int_Oint) = X9
        | c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Int_Oint)) != c_Polynomial_OpCons(tc_Int_Oint,X9,X10) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_329])]) ).

fof(f6330,plain,
    ( spl24_23
  <=> class_Groups_Ozero(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_23])]) ).

fof(f14088,plain,
    ( ! [X11,X12] :
        ( ~ class_Groups_Ozero(tc_Int_Oint)
        | c_Groups_Oone__class_Oone(tc_Int_Oint) = X11
        | c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Int_Oint)) != c_Polynomial_OpCons(tc_Int_Oint,X11,X12) )
    | ~ spl24_130 ),
    inference(superposition,[],[f4842,f7010]) ).

fof(f4842,plain,
    ! [X2,X3,X0,X1,X4] :
      ( c_Polynomial_OpCons(X2,X3,X0) != c_Polynomial_OpCons(X2,X4,X1)
      | X3 = X4
      | ~ class_Groups_Ozero(X2) ),
    inference(cnf_transformation,[],[f3746]) ).

fof(f3746,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ( ( ( X3 = X4
            & X0 = X1 )
          | c_Polynomial_OpCons(X2,X3,X0) != c_Polynomial_OpCons(X2,X4,X1) )
        & ( c_Polynomial_OpCons(X2,X3,X0) = c_Polynomial_OpCons(X2,X4,X1)
          | X3 != X4
          | X0 != X1 ) )
      | ~ class_Groups_Ozero(X2) ),
    inference(rectify,[],[f3745]) ).

fof(f3745,plain,
    ! [X1,X0,X3,X4,X2] :
      ( ( ( ( X2 = X4
            & X0 = X1 )
          | c_Polynomial_OpCons(X3,X4,X1) != c_Polynomial_OpCons(X3,X2,X0) )
        & ( c_Polynomial_OpCons(X3,X4,X1) = c_Polynomial_OpCons(X3,X2,X0)
          | X2 != X4
          | X0 != X1 ) )
      | ~ class_Groups_Ozero(X3) ),
    inference(flattening,[],[f3744]) ).

fof(f3744,plain,
    ! [X1,X0,X3,X4,X2] :
      ( ( ( ( X2 = X4
            & X0 = X1 )
          | c_Polynomial_OpCons(X3,X4,X1) != c_Polynomial_OpCons(X3,X2,X0) )
        & ( c_Polynomial_OpCons(X3,X4,X1) = c_Polynomial_OpCons(X3,X2,X0)
          | X2 != X4
          | X0 != X1 ) )
      | ~ class_Groups_Ozero(X3) ),
    inference(nnf_transformation,[],[f2966]) ).

fof(f2966,plain,
    ! [X1,X0,X3,X4,X2] :
      ( ( ( X2 = X4
          & X0 = X1 )
      <=> c_Polynomial_OpCons(X3,X4,X1) = c_Polynomial_OpCons(X3,X2,X0) )
      | ~ class_Groups_Ozero(X3) ),
    inference(ennf_transformation,[],[f1798]) ).

fof(f1798,plain,
    ! [X0,X2,X3,X1,X4] :
      ( class_Groups_Ozero(X3)
     => ( ( X2 = X4
          & X0 = X1 )
      <=> c_Polynomial_OpCons(X3,X4,X1) = c_Polynomial_OpCons(X3,X2,X0) ) ),
    inference(rectify,[],[f6]) ).

fof(f6,axiom,
    ! [X6,X9,X7,X8,X10] :
      ( class_Groups_Ozero(X8)
     => ( c_Polynomial_OpCons(X8,X7,X6) = c_Polynomial_OpCons(X8,X10,X9)
      <=> ( X7 = X10
          & X6 = X9 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pCons__eq__iff) ).

fof(f14104,plain,
    ( ~ spl24_23
    | spl24_328
    | ~ spl24_130 ),
    inference(avatar_split_clause,[],[f14085,f7008,f14097,f6330]) ).

fof(f14097,plain,
    ( spl24_328
  <=> ! [X8,X7] :
        ( c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Int_Oint)) != c_Polynomial_OpCons(tc_Int_Oint,X7,X8)
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)) = X8 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_328])]) ).

fof(f14085,plain,
    ( ! [X6,X5] :
        ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)) = X6
        | c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Int_Oint)) != c_Polynomial_OpCons(tc_Int_Oint,X5,X6)
        | ~ class_Groups_Ozero(tc_Int_Oint) )
    | ~ spl24_130 ),
    inference(superposition,[],[f4841,f7010]) ).

fof(f4841,plain,
    ! [X2,X3,X0,X1,X4] :
      ( c_Polynomial_OpCons(X2,X3,X0) != c_Polynomial_OpCons(X2,X4,X1)
      | X0 = X1
      | ~ class_Groups_Ozero(X2) ),
    inference(cnf_transformation,[],[f3746]) ).

fof(f14103,plain,
    ( spl24_329
    | ~ spl24_23
    | ~ spl24_130 ),
    inference(avatar_split_clause,[],[f14087,f7008,f6330,f14101]) ).

fof(f14087,plain,
    ( ! [X10,X9] :
        ( ~ class_Groups_Ozero(tc_Int_Oint)
        | c_Groups_Oone__class_Oone(tc_Int_Oint) = X9
        | c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Int_Oint)) != c_Polynomial_OpCons(tc_Int_Oint,X9,X10) )
    | ~ spl24_130 ),
    inference(superposition,[],[f4842,f7010]) ).

fof(f14099,plain,
    ( spl24_328
    | ~ spl24_23
    | ~ spl24_130 ),
    inference(avatar_split_clause,[],[f14086,f7008,f6330,f14097]) ).

fof(f14086,plain,
    ( ! [X8,X7] :
        ( ~ class_Groups_Ozero(tc_Int_Oint)
        | c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Int_Oint)) != c_Polynomial_OpCons(tc_Int_Oint,X7,X8)
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)) = X8 )
    | ~ spl24_130 ),
    inference(superposition,[],[f4841,f7010]) ).

fof(f14095,plain,
    ( spl24_74
    | ~ spl24_23
    | ~ spl24_327
    | ~ spl24_130 ),
    inference(avatar_split_clause,[],[f14089,f7008,f14092,f6330,f6659]) ).

fof(f6659,plain,
    ( spl24_74
  <=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_74])]) ).

fof(f14092,plain,
    ( spl24_327
  <=> c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_327])]) ).

fof(f14089,plain,
    ( c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Int_Oint)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint))
    | ~ class_Groups_Ozero(tc_Int_Oint)
    | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | ~ spl24_130 ),
    inference(superposition,[],[f4901,f7010]) ).

fof(f4901,plain,
    ! [X2,X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) != c_Polynomial_OpCons(X1,X2,X0)
      | ~ class_Groups_Ozero(X1)
      | c_Groups_Ozero__class_Ozero(X1) = X2 ),
    inference(cnf_transformation,[],[f3783]) ).

fof(f3783,plain,
    ! [X0,X1,X2] :
      ( ~ class_Groups_Ozero(X1)
      | ( ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X0
            & c_Groups_Ozero__class_Ozero(X1) = X2 )
          | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) != c_Polynomial_OpCons(X1,X2,X0) )
        & ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_OpCons(X1,X2,X0)
          | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) != X0
          | c_Groups_Ozero__class_Ozero(X1) != X2 ) ) ),
    inference(rectify,[],[f3782]) ).

fof(f3782,plain,
    ! [X1,X0,X2] :
      ( ~ class_Groups_Ozero(X0)
      | ( ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X1
            & c_Groups_Ozero__class_Ozero(X0) = X2 )
          | c_Polynomial_OpCons(X0,X2,X1) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) )
        & ( c_Polynomial_OpCons(X0,X2,X1) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))
          | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) != X1
          | c_Groups_Ozero__class_Ozero(X0) != X2 ) ) ),
    inference(flattening,[],[f3781]) ).

fof(f3781,plain,
    ! [X1,X0,X2] :
      ( ~ class_Groups_Ozero(X0)
      | ( ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X1
            & c_Groups_Ozero__class_Ozero(X0) = X2 )
          | c_Polynomial_OpCons(X0,X2,X1) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) )
        & ( c_Polynomial_OpCons(X0,X2,X1) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))
          | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) != X1
          | c_Groups_Ozero__class_Ozero(X0) != X2 ) ) ),
    inference(nnf_transformation,[],[f2516]) ).

fof(f2516,plain,
    ! [X1,X0,X2] :
      ( ~ class_Groups_Ozero(X0)
      | ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X1
          & c_Groups_Ozero__class_Ozero(X0) = X2 )
      <=> c_Polynomial_OpCons(X0,X2,X1) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) ) ),
    inference(ennf_transformation,[],[f2180]) ).

fof(f2180,plain,
    ! [X2,X0,X1] :
      ( class_Groups_Ozero(X0)
     => ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X1
          & c_Groups_Ozero__class_Ozero(X0) = X2 )
      <=> c_Polynomial_OpCons(X0,X2,X1) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) ) ),
    inference(rectify,[],[f5]) ).

fof(f5,axiom,
    ! [X8,X6,X7] :
      ( class_Groups_Ozero(X8)
     => ( c_Polynomial_OpCons(X8,X7,X6) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))
      <=> ( c_Groups_Ozero__class_Ozero(X8) = X7
          & c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)) = X6 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pCons__eq__0__iff) ).

fof(f14080,plain,
    ( spl24_326
    | ~ spl24_50
    | ~ spl24_24 ),
    inference(avatar_split_clause,[],[f14069,f6335,f6475,f14077]) ).

fof(f14077,plain,
    ( spl24_326
  <=> c_fequal = c_HOL_Oequal__class_Oequal(tc_Polynomial_Opoly(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_326])]) ).

fof(f6475,plain,
    ( spl24_50
  <=> class_HOL_Oequal(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_50])]) ).

fof(f6335,plain,
    ( spl24_24
  <=> class_Groups_Ozero(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_24])]) ).

fof(f14069,plain,
    ( ~ class_HOL_Oequal(tc_Nat_Onat)
    | c_fequal = c_HOL_Oequal__class_Oequal(tc_Polynomial_Opoly(tc_Nat_Onat))
    | ~ spl24_24 ),
    inference(resolution,[],[f11668,f6337]) ).

fof(f6337,plain,
    ( class_Groups_Ozero(tc_Nat_Onat)
    | ~ spl24_24 ),
    inference(avatar_component_clause,[],[f6335]) ).

fof(f14075,plain,
    ( ~ spl24_6
    | spl24_325
    | ~ spl24_23 ),
    inference(avatar_split_clause,[],[f14070,f6330,f14072,f6233]) ).

fof(f6233,plain,
    ( spl24_6
  <=> class_HOL_Oequal(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_6])]) ).

fof(f14072,plain,
    ( spl24_325
  <=> c_fequal = c_HOL_Oequal__class_Oequal(tc_Polynomial_Opoly(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_325])]) ).

fof(f14070,plain,
    ( c_fequal = c_HOL_Oequal__class_Oequal(tc_Polynomial_Opoly(tc_Int_Oint))
    | ~ class_HOL_Oequal(tc_Int_Oint)
    | ~ spl24_23 ),
    inference(resolution,[],[f11668,f6332]) ).

fof(f6332,plain,
    ( class_Groups_Ozero(tc_Int_Oint)
    | ~ spl24_23 ),
    inference(avatar_component_clause,[],[f6330]) ).

fof(f14066,plain,
    ( spl24_321
    | ~ spl24_24
    | ~ spl24_129 ),
    inference(avatar_split_clause,[],[f14043,f7003,f6335,f14050]) ).

fof(f14050,plain,
    ( spl24_321
  <=> ! [X8,X7] :
        ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)) = X8
        | c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Nat_Onat)) != c_Polynomial_OpCons(tc_Nat_Onat,X7,X8) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_321])]) ).

fof(f7003,plain,
    ( spl24_129
  <=> c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Nat_Onat)) = c_Polynomial_OpCons(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_129])]) ).

fof(f14043,plain,
    ( ! [X6,X5] :
        ( ~ class_Groups_Ozero(tc_Nat_Onat)
        | c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Nat_Onat)) != c_Polynomial_OpCons(tc_Nat_Onat,X5,X6)
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)) = X6 )
    | ~ spl24_129 ),
    inference(superposition,[],[f4841,f7005]) ).

fof(f7005,plain,
    ( c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Nat_Onat)) = c_Polynomial_OpCons(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)))
    | ~ spl24_129 ),
    inference(avatar_component_clause,[],[f7003]) ).

fof(f14065,plain,
    ( ~ spl24_323
    | spl24_324
    | ~ spl24_129 ),
    inference(avatar_split_clause,[],[f14040,f7003,f14063,f14059]) ).

fof(f14059,plain,
    ( spl24_323
  <=> class_Rings_Oidom(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_323])]) ).

fof(f14063,plain,
    ( spl24_324
  <=> ! [X2,X1] :
        ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Nat_Onat),c_Polynomial_OpCons(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Nat_Onat))),X2)
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Polynomial_Opoly(tc_Nat_Onat,X2),c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_324])]) ).

fof(f14040,plain,
    ( ! [X2,X1] :
        ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Nat_Onat),c_Polynomial_OpCons(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Nat_Onat))),X2)
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Polynomial_Opoly(tc_Nat_Onat,X2),c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X1))
        | ~ class_Rings_Oidom(tc_Nat_Onat) )
    | ~ spl24_129 ),
    inference(superposition,[],[f4941,f7005]) ).

fof(f14057,plain,
    ( ~ spl24_24
    | spl24_322
    | ~ spl24_129 ),
    inference(avatar_split_clause,[],[f14045,f7003,f14054,f6335]) ).

fof(f14054,plain,
    ( spl24_322
  <=> ! [X12,X11] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X11
        | c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Nat_Onat)) != c_Polynomial_OpCons(tc_Nat_Onat,X11,X12) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_322])]) ).

fof(f14045,plain,
    ( ! [X10,X9] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X9
        | c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Nat_Onat)) != c_Polynomial_OpCons(tc_Nat_Onat,X9,X10)
        | ~ class_Groups_Ozero(tc_Nat_Onat) )
    | ~ spl24_129 ),
    inference(superposition,[],[f4842,f7005]) ).

fof(f14056,plain,
    ( ~ spl24_24
    | spl24_322
    | ~ spl24_129 ),
    inference(avatar_split_clause,[],[f14046,f7003,f14054,f6335]) ).

fof(f14046,plain,
    ( ! [X11,X12] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X11
        | c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Nat_Onat)) != c_Polynomial_OpCons(tc_Nat_Onat,X11,X12)
        | ~ class_Groups_Ozero(tc_Nat_Onat) )
    | ~ spl24_129 ),
    inference(superposition,[],[f4842,f7005]) ).

fof(f14052,plain,
    ( ~ spl24_24
    | spl24_321
    | ~ spl24_129 ),
    inference(avatar_split_clause,[],[f14044,f7003,f14050,f6335]) ).

fof(f14044,plain,
    ( ! [X8,X7] :
        ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)) = X8
        | ~ class_Groups_Ozero(tc_Nat_Onat)
        | c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Nat_Onat)) != c_Polynomial_OpCons(tc_Nat_Onat,X7,X8) )
    | ~ spl24_129 ),
    inference(superposition,[],[f4841,f7005]) ).

fof(f13936,plain,
    ( ~ spl24_5
    | spl24_320 ),
    inference(avatar_split_clause,[],[f13924,f13934,f6228]) ).

fof(f13934,plain,
    ( spl24_320
  <=> ! [X20,X21,X19] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X20)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X19),X20),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X19),X21))
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X19),X21) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X19),X20) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_320])]) ).

fof(f13924,plain,
    ! [X21,X19,X20] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X20)
      | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X19),X21) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X19),X20)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X19),X20),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X19),X21))
      | ~ class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ),
    inference(resolution,[],[f5837,f5448]) ).

fof(f5837,plain,
    ! [X0,X1] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,X1)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0)
      | X0 = X1 ),
    inference(cnf_transformation,[],[f4375]) ).

fof(f4375,plain,
    ! [X0,X1] :
      ( ( ( X0 != X1
          & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0) )
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,X1)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0) )
      & ( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,X1)
          & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0) )
        | X0 = X1
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0) ) ),
    inference(rectify,[],[f4374]) ).

fof(f4374,plain,
    ! [X1,X0] :
      ( ( ( X0 != X1
          & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,X1) )
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,X1) )
      & ( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0)
          & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,X1) )
        | X0 = X1
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,X1) ) ),
    inference(flattening,[],[f4373]) ).

fof(f4373,plain,
    ! [X1,X0] :
      ( ( ( X0 != X1
          & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,X1) )
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,X1) )
      & ( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0)
          & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,X1) )
        | X0 = X1
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,X1) ) ),
    inference(nnf_transformation,[],[f1825]) ).

fof(f1825,plain,
    ! [X1,X0] :
      ( ( X0 != X1
        & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,X1) )
    <=> ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0)
        & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,X1) ) ),
    inference(rectify,[],[f659]) ).

fof(f659,axiom,
    ! [X13,X20] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X13,X20)
        & X13 != X20 )
    <=> ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X20,X13)
        & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X13,X20) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__le) ).

fof(f13932,plain,
    ( ~ spl24_5
    | spl24_319 ),
    inference(avatar_split_clause,[],[f13923,f13930,f6228]) ).

fof(f13930,plain,
    ( spl24_319
  <=> ! [X18,X17,X16,X15] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X15),X16),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X17),X18))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X16)
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X15),X16) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X17),X18)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X17,X15) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_319])]) ).

fof(f13923,plain,
    ! [X18,X16,X17,X15] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X15),X16),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X17),X18))
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X17,X15)
      | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X15),X16) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X17),X18)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X16)
      | ~ class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ),
    inference(resolution,[],[f5837,f5752]) ).

fof(f13928,plain,
    ( ~ spl24_5
    | spl24_318 ),
    inference(avatar_split_clause,[],[f13922,f13926,f6228]) ).

fof(f13926,plain,
    ( spl24_318
  <=> ! [X13,X12,X14] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X12),X13),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X14),X13))
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X14,X12)
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X14),X13) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X12),X13) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_318])]) ).

fof(f13922,plain,
    ! [X14,X12,X13] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X12),X13),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X14),X13))
      | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X14),X13) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X12),X13)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X14,X12)
      | ~ class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ),
    inference(resolution,[],[f5837,f4750]) ).

fof(f13780,plain,
    ( ~ spl24_317
    | spl24_234 ),
    inference(avatar_split_clause,[],[f13758,f11152,f13777]) ).

fof(f13758,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | spl24_234 ),
    inference(resolution,[],[f11153,f4660]) ).

fof(f13775,plain,
    ( ~ spl24_316
    | spl24_234 ),
    inference(avatar_split_clause,[],[f13757,f11152,f13772]) ).

fof(f13757,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | spl24_234 ),
    inference(resolution,[],[f11153,f5094]) ).

fof(f5094,plain,
    ! [X0] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0) ),
    inference(cnf_transformation,[],[f3903]) ).

fof(f13770,plain,
    ( spl24_314
    | ~ spl24_315
    | spl24_234 ),
    inference(avatar_split_clause,[],[f13759,f11152,f13767,f13763]) ).

fof(f13759,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | spl24_234 ),
    inference(resolution,[],[f11153,f5693]) ).

fof(f13718,plain,
    ( spl24_313
    | ~ spl24_9
    | ~ spl24_9 ),
    inference(avatar_split_clause,[],[f13704,f6248,f6248,f13716]) ).

fof(f13716,plain,
    ( spl24_313
  <=> ! [X2,X0,X1] :
        ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X0)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_313])]) ).

fof(f13704,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Rings_Ocomm__semiring__1(tc_Int_Oint)
        | c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X0) )
    | ~ spl24_9 ),
    inference(superposition,[],[f5752,f7280]) ).

fof(f7280,plain,
    ( ! [X1] : c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ spl24_9 ),
    inference(resolution,[],[f5741,f6250]) ).

fof(f5741,plain,
    ! [X0,X1] :
      ( ~ class_Rings_Ocomm__semiring__1(X1)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X1) ),
    inference(cnf_transformation,[],[f4312]) ).

fof(f4312,plain,
    ! [X0,X1] :
      ( ~ class_Rings_Ocomm__semiring__1(X1)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X1) ),
    inference(rectify,[],[f2613]) ).

fof(f2613,plain,
    ! [X1,X0] :
      ( ~ class_Rings_Ocomm__semiring__1(X0)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X0) ),
    inference(ennf_transformation,[],[f1812]) ).

fof(f1812,plain,
    ! [X1,X0] :
      ( class_Rings_Ocomm__semiring__1(X0)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X0) ),
    inference(rectify,[],[f693]) ).

fof(f693,axiom,
    ! [X4,X19] :
      ( class_Rings_Ocomm__semiring__1(X4)
     => c_Groups_Oone__class_Oone(X4) = hAPP(hAPP(c_Power_Opower__class_Opower(X4),X19),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(f13714,plain,
    ( spl24_312
    | ~ spl24_9
    | ~ spl24_9 ),
    inference(avatar_split_clause,[],[f13706,f6248,f6248,f13712]) ).

fof(f13712,plain,
    ( spl24_312
  <=> ! [X6,X7] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X6),X7),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_312])]) ).

fof(f13706,plain,
    ( ! [X6,X7] :
        ( ~ class_Rings_Ocomm__semiring__1(tc_Int_Oint)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X6),X7),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
    | ~ spl24_9 ),
    inference(superposition,[],[f5448,f7280]) ).

fof(f13678,plain,
    ( spl24_311
    | ~ spl24_153 ),
    inference(avatar_split_clause,[],[f13669,f9279,f13674]) ).

fof(f13669,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_153 ),
    inference(resolution,[],[f7272,f11317]) ).

fof(f13677,plain,
    ( spl24_311
    | ~ spl24_153 ),
    inference(avatar_split_clause,[],[f13672,f9279,f13674]) ).

fof(f13672,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_153 ),
    inference(forward_demodulation,[],[f13670,f5830]) ).

fof(f13670,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_153 ),
    inference(resolution,[],[f7272,f12083]) ).

fof(f13480,plain,
    ( ~ spl24_15
    | spl24_310
    | ~ spl24_302 ),
    inference(avatar_split_clause,[],[f13476,f13374,f13478,f6277]) ).

fof(f13478,plain,
    ( spl24_310
  <=> ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Nat_Onat,c_Polynomial_Osmult(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Nat_Onat)))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_310])]) ).

fof(f13374,plain,
    ( spl24_302
  <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Nat_Onat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_302])]) ).

fof(f13476,plain,
    ( ! [X0] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Nat_Onat,c_Polynomial_Osmult(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Nat_Onat)))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ class_Rings_Ocomm__semiring__0(tc_Nat_Onat) )
    | ~ spl24_302 ),
    inference(superposition,[],[f5260,f13376]) ).

fof(f13376,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Nat_Onat)))
    | ~ spl24_302 ),
    inference(avatar_component_clause,[],[f13374]) ).

fof(f13475,plain,
    ( spl24_309
    | ~ spl24_121
    | ~ spl24_301 ),
    inference(avatar_split_clause,[],[f13471,f13369,f6941,f13473]) ).

fof(f13473,plain,
    ( spl24_309
  <=> ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Int_Oint,c_Polynomial_Osmult(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Int_Oint)))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_309])]) ).

fof(f13369,plain,
    ( spl24_301
  <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Int_Oint))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_301])]) ).

fof(f13471,plain,
    ( ! [X0] :
        ( ~ class_Rings_Ocomm__semiring__0(tc_Int_Oint)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Int_Oint,c_Polynomial_Osmult(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Int_Oint)))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
    | ~ spl24_301 ),
    inference(superposition,[],[f5260,f13371]) ).

fof(f13371,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Int_Oint)))
    | ~ spl24_301 ),
    inference(avatar_component_clause,[],[f13369]) ).

fof(f13467,plain,
    spl24_308,
    inference(avatar_split_clause,[],[f13461,f13463]) ).

fof(f13461,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(resolution,[],[f7105,f11861]) ).

fof(f11861,plain,
    ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)),
    inference(superposition,[],[f7063,f5830]) ).

fof(f7063,plain,
    ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(resolution,[],[f6042,f5695]) ).

fof(f7105,plain,
    ! [X0] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
    inference(resolution,[],[f5094,f5695]) ).

fof(f13466,plain,
    spl24_308,
    inference(avatar_split_clause,[],[f13460,f13463]) ).

fof(f13460,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(resolution,[],[f7105,f7063]) ).

fof(f13436,plain,
    ( spl24_307
    | ~ spl24_5 ),
    inference(avatar_split_clause,[],[f13425,f6228,f13434]) ).

fof(f13434,plain,
    ( spl24_307
  <=> ! [X6,X7] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X6),X7),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_307])]) ).

fof(f13425,plain,
    ! [X6,X7] :
      ( ~ class_Rings_Ocomm__semiring__1(tc_Nat_Onat)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X6),X7),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(superposition,[],[f5448,f6880]) ).

fof(f6880,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(forward_demodulation,[],[f6879,f5628]) ).

fof(f6879,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),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(forward_demodulation,[],[f6190,f4806]) ).

fof(f6190,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),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(equality_resolution,[],[f6003]) ).

fof(f6003,plain,
    ! [X0,X1] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),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))
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
    inference(definition_unfolding,[],[f5819,f4877]) ).

fof(f5819,plain,
    ! [X0,X1] :
      ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(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,[],[f4361]) ).

fof(f4361,plain,
    ! [X0,X1] :
      ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1)
        | ( 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_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
        | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1) ) ),
    inference(flattening,[],[f4360]) ).

fof(f4360,plain,
    ! [X0,X1] :
      ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1)
        | ( 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_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
        | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1) ) ),
    inference(nnf_transformation,[],[f1916]) ).

fof(f1916,plain,
    ! [X0,X1] :
      ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1)
    <=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
        | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0 ) ),
    inference(rectify,[],[f716]) ).

fof(f716,axiom,
    ! [X13,X43] :
      ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X13),X43)
    <=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X43
        | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X13 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__power__eq__Suc__0__iff) ).

fof(f13432,plain,
    ( ~ spl24_5
    | spl24_306 ),
    inference(avatar_split_clause,[],[f13423,f13430,f6228]) ).

fof(f13430,plain,
    ( spl24_306
  <=> ! [X2,X0,X1] :
        ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_306])]) ).

fof(f13423,plain,
    ! [X2,X0,X1] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      | ~ class_Rings_Ocomm__semiring__1(tc_Nat_Onat)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0) ),
    inference(superposition,[],[f5752,f6880]) ).

fof(f13422,plain,
    ( ~ spl24_5
    | spl24_305 ),
    inference(avatar_split_clause,[],[f13410,f13420,f6228]) ).

fof(f13420,plain,
    ( spl24_305
  <=> ! [X11,X10] :
        ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X11),X10),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X11,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_305])]) ).

fof(f13410,plain,
    ! [X10,X11] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X11),X10),c_Groups_Oone__class_Oone(tc_Nat_Onat))
      | ~ class_Rings_Ocomm__semiring__1(tc_Nat_Onat)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X11,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(superposition,[],[f4750,f6598]) ).

fof(f6598,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(backward_demodulation,[],[f6282,f5628]) ).

fof(f6282,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(backward_demodulation,[],[f5877,f4806]) ).

fof(f5877,plain,
    ! [X0] : 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) = 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(definition_unfolding,[],[f4523,f4877,f4877]) ).

fof(f4523,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,[],[f2148]) ).

fof(f2148,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,[],[f715]) ).

fof(f715,axiom,
    ! [X17] : 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))),X17),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc__0) ).

fof(f13417,plain,
    ( ~ spl24_5
    | spl24_304 ),
    inference(avatar_split_clause,[],[f13406,f13415,f6228]) ).

fof(f13415,plain,
    ( spl24_304
  <=> ! [X2,X0,X1] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_304])]) ).

fof(f13406,plain,
    ! [X2,X0,X1] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))
      | ~ class_Rings_Ocomm__semiring__1(tc_Nat_Onat)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0) ),
    inference(superposition,[],[f5752,f6598]) ).

fof(f13391,plain,
    ( spl24_303
    | ~ spl24_9 ),
    inference(avatar_split_clause,[],[f13384,f6248,f13389]) ).

fof(f13389,plain,
    ( spl24_303
  <=> ! [X0] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
        | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_303])]) ).

fof(f13384,plain,
    ! [X0] :
      ( ~ class_Rings_Ocomm__semiring__1(tc_Int_Oint)
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
      | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0) ),
    inference(resolution,[],[f5493,f4832]) ).

fof(f5493,plain,
    ! [X0,X1] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1))
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,X1) ),
    inference(cnf_transformation,[],[f4144]) ).

fof(f13377,plain,
    ( spl24_302
    | ~ spl24_5 ),
    inference(avatar_split_clause,[],[f13365,f6228,f13374]) ).

fof(f13365,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Nat_Onat)))
    | ~ spl24_5 ),
    inference(resolution,[],[f4889,f6230]) ).

fof(f13372,plain,
    ( spl24_301
    | ~ spl24_9 ),
    inference(avatar_split_clause,[],[f13366,f6248,f13369]) ).

fof(f13366,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Int_Oint)))
    | ~ spl24_9 ),
    inference(resolution,[],[f4889,f6250]) ).

fof(f13352,plain,
    ( spl24_300
    | ~ spl24_23 ),
    inference(avatar_split_clause,[],[f13342,f6330,f13349]) ).

fof(f13349,plain,
    ( spl24_300
  <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_300])]) ).

fof(f13342,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)))
    | ~ spl24_23 ),
    inference(resolution,[],[f4522,f6332]) ).

fof(f13347,plain,
    ( spl24_299
    | ~ spl24_24 ),
    inference(avatar_split_clause,[],[f13341,f6335,f13344]) ).

fof(f13344,plain,
    ( spl24_299
  <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_299])]) ).

fof(f13341,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)))
    | ~ spl24_24 ),
    inference(resolution,[],[f4522,f6337]) ).

fof(f13129,plain,
    ~ spl24_298,
    inference(avatar_split_clause,[],[f13122,f13126]) ).

fof(f13126,plain,
    ( spl24_298
  <=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_298])]) ).

fof(f13122,plain,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(superposition,[],[f5615,f12434]) ).

fof(f13082,plain,
    ( spl24_297
    | ~ spl24_121 ),
    inference(avatar_split_clause,[],[f13081,f6941,f13076]) ).

fof(f13076,plain,
    ( spl24_297
  <=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_297])]) ).

fof(f13081,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint))
    | ~ spl24_121 ),
    inference(forward_demodulation,[],[f13080,f7032]) ).

fof(f7032,plain,
    ( ! [X3] : c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Int_Oint)),X3),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)))
    | ~ spl24_121 ),
    inference(resolution,[],[f5356,f6943]) ).

fof(f5356,plain,
    ! [X0,X1] :
      ( ~ class_Rings_Ocomm__semiring__0(X1)
      | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) ),
    inference(cnf_transformation,[],[f4038]) ).

fof(f4038,plain,
    ! [X0,X1] :
      ( ~ class_Rings_Ocomm__semiring__0(X1)
      | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) ),
    inference(rectify,[],[f3024]) ).

fof(f3024,plain,
    ! [X1,X0] :
      ( ~ class_Rings_Ocomm__semiring__0(X0)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X0)),X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) ),
    inference(ennf_transformation,[],[f1911]) ).

fof(f1911,plain,
    ! [X1,X0] :
      ( class_Rings_Ocomm__semiring__0(X0)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X0)),X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) ),
    inference(rectify,[],[f128]) ).

fof(f128,axiom,
    ! [X4,X24] :
      ( class_Rings_Ocomm__semiring__0(X4)
     => c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4)),X24),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__poly__0__right) ).

fof(f13080,plain,
    ( ! [X3] : c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Int_Oint)),X3),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint))
    | ~ spl24_121 ),
    inference(forward_demodulation,[],[f13070,f7032]) ).

fof(f13070,plain,
    ( ! [X2,X3] : c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Int_Oint)),X3),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Int_Oint),X2,X3)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)))
    | ~ spl24_121 ),
    inference(superposition,[],[f7048,f7032]) ).

fof(f7048,plain,
    ( ! [X8,X9,X7] : c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Int_Oint)),X7),X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Int_Oint)),X8),X9)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Int_Oint),X7,X8)),X9)
    | ~ spl24_121 ),
    inference(resolution,[],[f4487,f6943]) ).

fof(f4487,plain,
    ! [X2,X3,X0,X1] :
      ( ~ class_Rings_Ocomm__semiring__0(X3)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),X2,X0)),X1) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X0),X1)) ),
    inference(cnf_transformation,[],[f3507]) ).

fof(f3507,plain,
    ! [X0,X1,X2,X3] :
      ( ~ class_Rings_Ocomm__semiring__0(X3)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),X2,X0)),X1) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X0),X1)) ),
    inference(rectify,[],[f3026]) ).

fof(f3026,plain,
    ! [X0,X3,X1,X2] :
      ( ~ class_Rings_Ocomm__semiring__0(X2)
      | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X2)),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X2)),X0),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X2)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),X1,X0)),X3) ),
    inference(ennf_transformation,[],[f1628]) ).

fof(f1628,plain,
    ! [X2,X1,X3,X0] :
      ( class_Rings_Ocomm__semiring__0(X2)
     => c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X2)),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X2)),X0),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X2)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),X1,X0)),X3) ),
    inference(rectify,[],[f133]) ).

fof(f133,axiom,
    ! [X21,X24,X4,X28] :
      ( class_Rings_Ocomm__semiring__0(X4)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),X24,X21)),X28) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4)),X24),X28),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4)),X21),X28)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__poly__add__left) ).

fof(f13079,plain,
    ( spl24_297
    | ~ spl24_121 ),
    inference(avatar_split_clause,[],[f13074,f6941,f13076]) ).

fof(f13074,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint))
    | ~ spl24_121 ),
    inference(forward_demodulation,[],[f13073,f7032]) ).

fof(f13073,plain,
    ( ! [X3] : c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Int_Oint)),X3),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint))
    | ~ spl24_121 ),
    inference(forward_demodulation,[],[f13072,f7032]) ).

fof(f13072,plain,
    ( ! [X2,X3] : c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Int_Oint)),X3),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Int_Oint),X3,X2)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)))
    | ~ spl24_121 ),
    inference(superposition,[],[f7048,f7032]) ).

fof(f13068,plain,
    ( spl24_296
    | ~ spl24_9
    | ~ spl24_121 ),
    inference(avatar_split_clause,[],[f13047,f6941,f6248,f13066]) ).

fof(f13066,plain,
    ( spl24_296
  <=> ! [X9,X8] :
        ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Int_Oint),X8,X9)
        | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)),X9) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_296])]) ).

fof(f13047,plain,
    ( ! [X8,X9] :
        ( ~ class_Rings_Ocomm__semiring__1(tc_Int_Oint)
        | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Int_Oint),X8,X9)
        | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)),X9) )
    | ~ spl24_121 ),
    inference(superposition,[],[f4770,f7191]) ).

fof(f7191,plain,
    ( ! [X3] : c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)) = c_Polynomial_Osmult(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
    | ~ spl24_121 ),
    inference(resolution,[],[f5666,f6943]) ).

fof(f5666,plain,
    ! [X0,X1] :
      ( ~ class_Rings_Ocomm__semiring__0(X1)
      | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Osmult(X1,c_Groups_Ozero__class_Ozero(X1),X0) ),
    inference(cnf_transformation,[],[f2492]) ).

fof(f2492,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Osmult(X1,c_Groups_Ozero__class_Ozero(X1),X0)
      | ~ class_Rings_Ocomm__semiring__0(X1) ),
    inference(ennf_transformation,[],[f1563]) ).

fof(f1563,plain,
    ! [X0,X1] :
      ( class_Rings_Ocomm__semiring__0(X1)
     => c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Osmult(X1,c_Groups_Ozero__class_Ozero(X1),X0) ),
    inference(rectify,[],[f32]) ).

fof(f32,axiom,
    ! [X24,X4] :
      ( class_Rings_Ocomm__semiring__0(X4)
     => c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = c_Polynomial_Osmult(X4,c_Groups_Ozero__class_Ozero(X4),X24) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__0__left) ).

fof(f13064,plain,
    ( ~ spl24_9
    | spl24_295
    | ~ spl24_121 ),
    inference(avatar_split_clause,[],[f13046,f6941,f13062,f6248]) ).

fof(f13062,plain,
    ( spl24_295
  <=> ! [X6,X7] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Int_Oint),X7,X6)
        | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Int_Oint),X7,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_295])]) ).

fof(f13046,plain,
    ( ! [X6,X7] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Int_Oint),X7,X6)
        | ~ class_Rings_Ocomm__semiring__1(tc_Int_Oint)
        | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Int_Oint),X7,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint))) )
    | ~ spl24_121 ),
    inference(superposition,[],[f5403,f7191]) ).

fof(f13060,plain,
    ( spl24_294
    | ~ spl24_121
    | ~ spl24_121 ),
    inference(avatar_split_clause,[],[f13048,f6941,f6941,f13058]) ).

fof(f13058,plain,
    ( spl24_294
  <=> ! [X10] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint))),c_Polynomial_Odegree(tc_Int_Oint,X10)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_294])]) ).

fof(f13048,plain,
    ( ! [X10] :
        ( ~ class_Rings_Ocomm__semiring__0(tc_Int_Oint)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint))),c_Polynomial_Odegree(tc_Int_Oint,X10)) )
    | ~ spl24_121 ),
    inference(superposition,[],[f5260,f7191]) ).

fof(f13056,plain,
    ( spl24_293
    | ~ spl24_121
    | ~ spl24_121 ),
    inference(avatar_split_clause,[],[f13044,f6941,f6941,f13054]) ).

fof(f13054,plain,
    ( spl24_293
  <=> ! [X2,X3] :
        ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)) != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)),c_Polynomial_OpCons(tc_Int_Oint,X3,X2))
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_293])]) ).

fof(f13044,plain,
    ( ! [X2,X3] :
        ( ~ class_Rings_Ocomm__semiring__0(tc_Int_Oint)
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)) != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)),c_Polynomial_OpCons(tc_Int_Oint,X3,X2))
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)) = X2 )
    | ~ spl24_121 ),
    inference(superposition,[],[f4606,f7191]) ).

fof(f13052,plain,
    ( spl24_292
    | ~ spl24_121
    | ~ spl24_121 ),
    inference(avatar_split_clause,[],[f13045,f6941,f6941,f13050]) ).

fof(f13050,plain,
    ( spl24_292
  <=> ! [X4,X5] :
        ( c_Polynomial_OpCons(tc_Int_Oint,X5,X4) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint))
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_292])]) ).

fof(f13045,plain,
    ( ! [X4,X5] :
        ( ~ class_Rings_Ocomm__semiring__0(tc_Int_Oint)
        | c_Polynomial_OpCons(tc_Int_Oint,X5,X4) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint))
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)) = X4 )
    | ~ spl24_121 ),
    inference(superposition,[],[f4596,f7191]) ).

fof(f13042,plain,
    ( ~ spl24_5
    | spl24_291
    | ~ spl24_15 ),
    inference(avatar_split_clause,[],[f13021,f6277,f13040,f6228]) ).

fof(f13040,plain,
    ( spl24_291
  <=> ! [X9,X8] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)),X9)
        | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Nat_Onat),X8,X9) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_291])]) ).

fof(f13021,plain,
    ( ! [X8,X9] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)),X9)
        | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Nat_Onat),X8,X9)
        | ~ class_Rings_Ocomm__semiring__1(tc_Nat_Onat) )
    | ~ spl24_15 ),
    inference(superposition,[],[f4770,f7190]) ).

fof(f7190,plain,
    ( ! [X2] : c_Polynomial_Osmult(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat))
    | ~ spl24_15 ),
    inference(resolution,[],[f5666,f6279]) ).

fof(f13038,plain,
    ( spl24_290
    | ~ spl24_5
    | ~ spl24_15 ),
    inference(avatar_split_clause,[],[f13020,f6277,f6228,f13036]) ).

fof(f13036,plain,
    ( spl24_290
  <=> ! [X6,X7] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Nat_Onat),X7,X6)
        | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Nat_Onat),X7,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_290])]) ).

fof(f13020,plain,
    ( ! [X6,X7] :
        ( ~ class_Rings_Ocomm__semiring__1(tc_Nat_Onat)
        | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Nat_Onat),X7,X6)
        | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Nat_Onat),X7,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat))) )
    | ~ spl24_15 ),
    inference(superposition,[],[f5403,f7190]) ).

fof(f13034,plain,
    ( spl24_289
    | ~ spl24_15
    | ~ spl24_15 ),
    inference(avatar_split_clause,[],[f13018,f6277,f6277,f13032]) ).

fof(f13032,plain,
    ( spl24_289
  <=> ! [X2,X3] :
        ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)),c_Polynomial_OpCons(tc_Nat_Onat,X3,X2)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat))
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_289])]) ).

fof(f13018,plain,
    ( ! [X2,X3] :
        ( ~ class_Rings_Ocomm__semiring__0(tc_Nat_Onat)
        | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)),c_Polynomial_OpCons(tc_Nat_Onat,X3,X2)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat))
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)) = X2 )
    | ~ spl24_15 ),
    inference(superposition,[],[f4606,f7190]) ).

fof(f13030,plain,
    ( spl24_288
    | ~ spl24_15
    | ~ spl24_15 ),
    inference(avatar_split_clause,[],[f13022,f6277,f6277,f13028]) ).

fof(f13028,plain,
    ( spl24_288
  <=> ! [X10] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat))),c_Polynomial_Odegree(tc_Nat_Onat,X10)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_288])]) ).

fof(f13022,plain,
    ( ! [X10] :
        ( ~ class_Rings_Ocomm__semiring__0(tc_Nat_Onat)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat))),c_Polynomial_Odegree(tc_Nat_Onat,X10)) )
    | ~ spl24_15 ),
    inference(superposition,[],[f5260,f7190]) ).

fof(f13026,plain,
    ( ~ spl24_15
    | spl24_287
    | ~ spl24_15 ),
    inference(avatar_split_clause,[],[f13019,f6277,f13024,f6277]) ).

fof(f13024,plain,
    ( spl24_287
  <=> ! [X4,X5] :
        ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)) != c_Polynomial_OpCons(tc_Nat_Onat,X5,X4)
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_287])]) ).

fof(f13019,plain,
    ( ! [X4,X5] :
        ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)) != c_Polynomial_OpCons(tc_Nat_Onat,X5,X4)
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)) = X4
        | ~ class_Rings_Ocomm__semiring__0(tc_Nat_Onat) )
    | ~ spl24_15 ),
    inference(superposition,[],[f4596,f7190]) ).

fof(f13016,plain,
    ( ~ spl24_286
    | spl24_134 ),
    inference(avatar_split_clause,[],[f13009,f7177,f13012]) ).

fof(f13012,plain,
    ( spl24_286
  <=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(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,[spl24_286])]) ).

fof(f7177,plain,
    ( spl24_134
  <=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(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,[spl24_134])]) ).

fof(f13009,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | spl24_134 ),
    inference(superposition,[],[f7179,f5830]) ).

fof(f7179,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | spl24_134 ),
    inference(avatar_component_clause,[],[f7177]) ).

fof(f13015,plain,
    ( ~ spl24_286
    | spl24_134 ),
    inference(avatar_split_clause,[],[f13010,f7177,f13012]) ).

fof(f13010,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | spl24_134 ),
    inference(superposition,[],[f7179,f5830]) ).

fof(f13002,plain,
    ( spl24_285
    | ~ spl24_15 ),
    inference(avatar_split_clause,[],[f13001,f6277,f12996]) ).

fof(f12996,plain,
    ( spl24_285
  <=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_285])]) ).

fof(f13001,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat))
    | ~ spl24_15 ),
    inference(forward_demodulation,[],[f13000,f7031]) ).

fof(f7031,plain,
    ( ! [X2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Nat_Onat)),X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat))
    | ~ spl24_15 ),
    inference(resolution,[],[f5356,f6279]) ).

fof(f13000,plain,
    ( ! [X2,X3] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Nat_Onat),X2,X3)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat))) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)))
    | ~ spl24_15 ),
    inference(forward_demodulation,[],[f12990,f7031]) ).

fof(f12990,plain,
    ( ! [X2,X3] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Nat_Onat),X2,X3)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat))) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Nat_Onat)),X3),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat))))
    | ~ spl24_15 ),
    inference(superposition,[],[f7047,f7031]) ).

fof(f7047,plain,
    ( ! [X6,X4,X5] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Nat_Onat),X4,X5)),X6) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Nat_Onat)),X4),X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Nat_Onat)),X5),X6))
    | ~ spl24_15 ),
    inference(resolution,[],[f4487,f6279]) ).

fof(f12999,plain,
    ( spl24_285
    | ~ spl24_15 ),
    inference(avatar_split_clause,[],[f12994,f6277,f12996]) ).

fof(f12994,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat))
    | ~ spl24_15 ),
    inference(forward_demodulation,[],[f12993,f7031]) ).

fof(f12993,plain,
    ( ! [X2,X3] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Nat_Onat),X3,X2)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat))) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)))
    | ~ spl24_15 ),
    inference(forward_demodulation,[],[f12992,f7031]) ).

fof(f12992,plain,
    ( ! [X2,X3] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Nat_Onat),X3,X2)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat))) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Nat_Onat)),X3),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)))
    | ~ spl24_15 ),
    inference(superposition,[],[f7047,f7031]) ).

fof(f12988,plain,
    ( spl24_284
    | ~ spl24_92 ),
    inference(avatar_split_clause,[],[f12987,f6764,f12982]) ).

fof(f12987,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))
    | ~ spl24_92 ),
    inference(forward_demodulation,[],[f12986,f7033]) ).

fof(f7033,plain,
    ( ! [X4] : c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(t_a)),X4),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))
    | ~ spl24_92 ),
    inference(resolution,[],[f5356,f6766]) ).

fof(f12986,plain,
    ( ! [X2,X3] : c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(t_a)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),X2,X3)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))
    | ~ spl24_92 ),
    inference(forward_demodulation,[],[f12976,f7033]) ).

fof(f12976,plain,
    ( ! [X2,X3] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(t_a)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),X2,X3)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(t_a)),X3),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))
    | ~ spl24_92 ),
    inference(superposition,[],[f7049,f7033]) ).

fof(f7049,plain,
    ( ! [X10,X11,X12] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(t_a)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),X10,X11)),X12) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(t_a)),X10),X12),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(t_a)),X11),X12))
    | ~ spl24_92 ),
    inference(resolution,[],[f4487,f6766]) ).

fof(f12985,plain,
    ( spl24_284
    | ~ spl24_92 ),
    inference(avatar_split_clause,[],[f12980,f6764,f12982]) ).

fof(f12980,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))
    | ~ spl24_92 ),
    inference(forward_demodulation,[],[f12979,f7033]) ).

fof(f12979,plain,
    ( ! [X3] : c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(t_a)),X3),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))
    | ~ spl24_92 ),
    inference(forward_demodulation,[],[f12978,f7033]) ).

fof(f12978,plain,
    ( ! [X2,X3] : c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(t_a)),X3),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(t_a)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),X3,X2)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))
    | ~ spl24_92 ),
    inference(superposition,[],[f7049,f7033]) ).

fof(f12878,plain,
    ( ~ spl24_9
    | spl24_283
    | ~ spl24_9 ),
    inference(avatar_split_clause,[],[f12856,f6248,f12876,f6248]) ).

fof(f12876,plain,
    ( spl24_283
  <=> ! [X4,X5,X3] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X3,X4)
        | c_Rings_Odvd__class_Odvd(tc_Int_Oint,X3,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X4),X5))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X5) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_283])]) ).

fof(f12856,plain,
    ( ! [X3,X4,X5] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X3,X4)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X5)
        | c_Rings_Odvd__class_Odvd(tc_Int_Oint,X3,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X4),X5))
        | ~ class_Rings_Ocomm__semiring__1(tc_Int_Oint) )
    | ~ spl24_9 ),
    inference(superposition,[],[f5752,f7119]) ).

fof(f7119,plain,
    ( ! [X1] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1
    | ~ spl24_9 ),
    inference(resolution,[],[f4671,f6250]) ).

fof(f12874,plain,
    ( spl24_282
    | ~ spl24_9
    | ~ spl24_9 ),
    inference(avatar_split_clause,[],[f12858,f6248,f6248,f12872]) ).

fof(f12872,plain,
    ( spl24_282
  <=> ! [X9,X8] :
        ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X8,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X8),X9))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X9) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_282])]) ).

fof(f12858,plain,
    ( ! [X8,X9] :
        ( ~ class_Rings_Ocomm__semiring__1(tc_Int_Oint)
        | c_Rings_Odvd__class_Odvd(tc_Int_Oint,X8,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X8),X9))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X9) )
    | ~ spl24_9 ),
    inference(superposition,[],[f5448,f7119]) ).

fof(f12869,plain,
    ( spl24_281
    | ~ spl24_9
    | ~ spl24_9 ),
    inference(avatar_split_clause,[],[f12855,f6248,f6248,f12867]) ).

fof(f12867,plain,
    ( spl24_281
  <=> ! [X2,X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2),X0)
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_281])]) ).

fof(f12855,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Rings_Ocomm__semiring__1(tc_Int_Oint)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X0)
        | c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2),X0) )
    | ~ spl24_9 ),
    inference(superposition,[],[f5752,f7119]) ).

fof(f12865,plain,
    ( spl24_280
    | ~ spl24_9
    | ~ spl24_9 ),
    inference(avatar_split_clause,[],[f12857,f6248,f6248,f12863]) ).

fof(f12863,plain,
    ( spl24_280
  <=> ! [X6,X7] :
        ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X6),X7),X6)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_280])]) ).

fof(f12857,plain,
    ( ! [X6,X7] :
        ( ~ class_Rings_Ocomm__semiring__1(tc_Int_Oint)
        | c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X6),X7),X6)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
    | ~ spl24_9 ),
    inference(superposition,[],[f5448,f7119]) ).

fof(f12854,plain,
    ( ~ spl24_121
    | spl24_279
    | ~ spl24_121 ),
    inference(avatar_split_clause,[],[f12848,f6941,f12852,f6941]) ).

fof(f12852,plain,
    ( spl24_279
  <=> ! [X2,X0,X1] :
        ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Int_Oint,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint))
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)) != c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Int_Oint,c_Polynomial_OpCons(tc_Int_Oint,X2,X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_279])]) ).

fof(f12848,plain,
    ( ! [X2,X0,X1] :
        ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Int_Oint,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint))
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)) != c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Int_Oint,c_Polynomial_OpCons(tc_Int_Oint,X2,X1),X0)
        | ~ class_Rings_Ocomm__semiring__0(tc_Int_Oint) )
    | ~ spl24_121 ),
    inference(superposition,[],[f4606,f7044]) ).

fof(f7044,plain,
    ( ! [X8,X9,X7] : c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Int_Oint),c_Polynomial_Osmult(tc_Int_Oint,X9,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Int_Oint,X8,X9)),c_Polynomial_OpCons(tc_Int_Oint,X7,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Int_Oint,X8,X9))) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Int_Oint,c_Polynomial_OpCons(tc_Int_Oint,X7,X8),X9)
    | ~ spl24_121 ),
    inference(resolution,[],[f5228,f6943]) ).

fof(f5228,plain,
    ! [X2,X3,X0,X1] :
      ( ~ class_Rings_Ocomm__semiring__0(X1)
      | c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,c_Polynomial_OpCons(X1,X2,X0),X3) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X3,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X0,X3)),c_Polynomial_OpCons(X1,X2,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X0,X3))) ),
    inference(cnf_transformation,[],[f3954]) ).

fof(f3954,plain,
    ! [X0,X1,X2,X3] :
      ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,c_Polynomial_OpCons(X1,X2,X0),X3) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X3,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X0,X3)),c_Polynomial_OpCons(X1,X2,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X0,X3)))
      | ~ class_Rings_Ocomm__semiring__0(X1) ),
    inference(rectify,[],[f2545]) ).

fof(f2545,plain,
    ! [X1,X0,X3,X2] :
      ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X0,c_Polynomial_OpCons(X0,X3,X1),X2) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),c_Polynomial_Osmult(X0,X2,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X0,X1,X2)),c_Polynomial_OpCons(X0,X3,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X0,X1,X2)))
      | ~ class_Rings_Ocomm__semiring__0(X0) ),
    inference(ennf_transformation,[],[f1933]) ).

fof(f1933,plain,
    ! [X2,X1,X0,X3] :
      ( class_Rings_Ocomm__semiring__0(X0)
     => c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X0,c_Polynomial_OpCons(X0,X3,X1),X2) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),c_Polynomial_Osmult(X0,X2,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X0,X1,X2)),c_Polynomial_OpCons(X0,X3,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X0,X1,X2))) ),
    inference(rectify,[],[f80]) ).

fof(f80,axiom,
    ! [X4,X24,X3,X5] :
      ( class_Rings_Ocomm__semiring__0(X4)
     => c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X4,c_Polynomial_OpCons(X4,X5,X24),X3) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),c_Polynomial_Osmult(X4,X3,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X4,X24,X3)),c_Polynomial_OpCons(X4,X5,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X4,X24,X3))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_offset__poly__pCons) ).

fof(f12842,plain,
    ( ~ spl24_15
    | spl24_278
    | ~ spl24_15 ),
    inference(avatar_split_clause,[],[f12838,f6277,f12840,f6277]) ).

fof(f12840,plain,
    ( spl24_278
  <=> ! [X2,X0,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)) != c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Nat_Onat,c_Polynomial_OpCons(tc_Nat_Onat,X2,X1),X0)
        | c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Nat_Onat,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_278])]) ).

fof(f12838,plain,
    ( ! [X2,X0,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)) != c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Nat_Onat,c_Polynomial_OpCons(tc_Nat_Onat,X2,X1),X0)
        | ~ class_Rings_Ocomm__semiring__0(tc_Nat_Onat)
        | c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Nat_Onat,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)) )
    | ~ spl24_15 ),
    inference(superposition,[],[f4606,f7043]) ).

fof(f7043,plain,
    ( ! [X6,X4,X5] : c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Nat_Onat,c_Polynomial_OpCons(tc_Nat_Onat,X4,X5),X6) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Nat_Onat),c_Polynomial_Osmult(tc_Nat_Onat,X6,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Nat_Onat,X5,X6)),c_Polynomial_OpCons(tc_Nat_Onat,X4,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Nat_Onat,X5,X6)))
    | ~ spl24_15 ),
    inference(resolution,[],[f5228,f6279]) ).

fof(f12834,plain,
    ( ~ spl24_5
    | spl24_277
    | ~ spl24_5 ),
    inference(avatar_split_clause,[],[f12811,f6228,f12832,f6228]) ).

fof(f12832,plain,
    ( spl24_277
  <=> ! [X2,X0,X1] :
        ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2),X0)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_277])]) ).

fof(f12811,plain,
    ( ! [X2,X0,X1] :
        ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2),X0)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0)
        | ~ class_Rings_Ocomm__semiring__1(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
    | ~ spl24_5 ),
    inference(superposition,[],[f5752,f7118]) ).

fof(f7118,plain,
    ( ! [X0] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0
    | ~ spl24_5 ),
    inference(resolution,[],[f4671,f6230]) ).

fof(f12830,plain,
    ( spl24_276
    | ~ spl24_5
    | ~ spl24_5 ),
    inference(avatar_split_clause,[],[f12812,f6228,f6228,f12828]) ).

fof(f12828,plain,
    ( spl24_276
  <=> ! [X4,X5,X3] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X5)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X4)
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X4),X5)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_276])]) ).

fof(f12812,plain,
    ( ! [X3,X4,X5] :
        ( ~ class_Rings_Ocomm__semiring__1(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X5)
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X4),X5))
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X4) )
    | ~ spl24_5 ),
    inference(superposition,[],[f5752,f7118]) ).

fof(f12825,plain,
    ( ~ spl24_5
    | spl24_275
    | ~ spl24_5 ),
    inference(avatar_split_clause,[],[f12814,f6228,f12823,f6228]) ).

fof(f12823,plain,
    ( spl24_275
  <=> ! [X9,X8] :
        ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X8,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X8),X9))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X9) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_275])]) ).

fof(f12814,plain,
    ( ! [X8,X9] :
        ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X8,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X8),X9))
        | ~ class_Rings_Ocomm__semiring__1(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X9) )
    | ~ spl24_5 ),
    inference(superposition,[],[f5448,f7118]) ).

fof(f12821,plain,
    ( ~ spl24_5
    | spl24_274
    | ~ spl24_5 ),
    inference(avatar_split_clause,[],[f12813,f6228,f12819,f6228]) ).

fof(f12819,plain,
    ( spl24_274
  <=> ! [X6,X7] :
        ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X6),X7),X6)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_274])]) ).

fof(f12813,plain,
    ( ! [X6,X7] :
        ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X6),X7),X6)
        | ~ class_Rings_Ocomm__semiring__1(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
    | ~ spl24_5 ),
    inference(superposition,[],[f5448,f7118]) ).

fof(f12718,plain,
    ( ~ spl24_92
    | spl24_273
    | ~ spl24_92 ),
    inference(avatar_split_clause,[],[f12713,f6764,f12716,f6764]) ).

fof(f12713,plain,
    ( ! [X2,X0,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) != c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X2,X1),X0)
        | ~ class_Rings_Ocomm__semiring__0(t_a)
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,X1,X0) )
    | ~ spl24_92 ),
    inference(superposition,[],[f4606,f7045]) ).

fof(f7045,plain,
    ( ! [X10,X11,X12] : c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,X12,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,X11,X12)),c_Polynomial_OpCons(t_a,X10,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,X11,X12))) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X10,X11),X12)
    | ~ spl24_92 ),
    inference(resolution,[],[f5228,f6766]) ).

fof(f12708,plain,
    ( ~ spl24_271
    | spl24_272
    | ~ spl24_269 ),
    inference(avatar_split_clause,[],[f12699,f12649,f12705,f12701]) ).

fof(f12699,plain,
    ( c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ spl24_269 ),
    inference(resolution,[],[f12651,f5243]) ).

fof(f12651,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ spl24_269 ),
    inference(avatar_component_clause,[],[f12649]) ).

fof(f12688,plain,
    ( spl24_270
    | ~ spl24_268 ),
    inference(avatar_split_clause,[],[f12681,f12636,f12685]) ).

fof(f12685,plain,
    ( spl24_270
  <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_270])]) ).

fof(f12636,plain,
    ( spl24_268
  <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_268])]) ).

fof(f12681,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ spl24_268 ),
    inference(resolution,[],[f12638,f5678]) ).

fof(f12638,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ spl24_268 ),
    inference(avatar_component_clause,[],[f12636]) ).

fof(f12652,plain,
    ( spl24_269
    | ~ spl24_258 ),
    inference(avatar_split_clause,[],[f12644,f12472,f12649]) ).

fof(f12644,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ spl24_258 ),
    inference(resolution,[],[f12474,f5095]) ).

fof(f12639,plain,
    ( spl24_268
    | ~ spl24_264 ),
    inference(avatar_split_clause,[],[f12634,f12593,f12636]) ).

fof(f12634,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ spl24_264 ),
    inference(resolution,[],[f12595,f5695]) ).

fof(f12623,plain,
    ( ~ spl24_266
    | spl24_267
    | ~ spl24_256 ),
    inference(avatar_split_clause,[],[f12606,f12456,f12620,f12616]) ).

fof(f12606,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_256 ),
    inference(resolution,[],[f12458,f5243]) ).

fof(f12614,plain,
    ( spl24_265
    | ~ spl24_256 ),
    inference(avatar_split_clause,[],[f12613,f12456,f12609]) ).

fof(f12609,plain,
    ( spl24_265
  <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_265])]) ).

fof(f12613,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
    | ~ spl24_256 ),
    inference(forward_demodulation,[],[f12604,f5830]) ).

fof(f12604,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ spl24_256 ),
    inference(resolution,[],[f12458,f5678]) ).

fof(f12612,plain,
    ( spl24_265
    | ~ spl24_256 ),
    inference(avatar_split_clause,[],[f12601,f12456,f12609]) ).

fof(f12601,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
    | ~ spl24_256 ),
    inference(resolution,[],[f12458,f4618]) ).

fof(f12596,plain,
    ( spl24_264
    | ~ spl24_259 ),
    inference(avatar_split_clause,[],[f12591,f12477,f12593]) ).

fof(f12477,plain,
    ( spl24_259
  <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(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,[spl24_259])]) ).

fof(f12591,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ spl24_259 ),
    inference(forward_demodulation,[],[f12588,f4706]) ).

fof(f12588,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ spl24_259 ),
    inference(resolution,[],[f12479,f5678]) ).

fof(f12479,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_259 ),
    inference(avatar_component_clause,[],[f12477]) ).

fof(f12582,plain,
    ( ~ spl24_263
    | spl24_257 ),
    inference(avatar_split_clause,[],[f12565,f12466,f12579]) ).

fof(f12466,plain,
    ( spl24_257
  <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_257])]) ).

fof(f12565,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | spl24_257 ),
    inference(resolution,[],[f12468,f5094]) ).

fof(f12468,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | spl24_257 ),
    inference(avatar_component_clause,[],[f12466]) ).

fof(f12577,plain,
    ( spl24_261
    | ~ spl24_262
    | spl24_257 ),
    inference(avatar_split_clause,[],[f12566,f12466,f12574,f12570]) ).

fof(f12570,plain,
    ( spl24_261
  <=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_261])]) ).

fof(f12574,plain,
    ( spl24_262
  <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_262])]) ).

fof(f12566,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))
    | spl24_257 ),
    inference(resolution,[],[f12468,f5693]) ).

fof(f12491,plain,
    ( spl24_260
    | ~ spl24_255 ),
    inference(avatar_split_clause,[],[f12486,f12451,f12488]) ).

fof(f12486,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_255 ),
    inference(forward_demodulation,[],[f12485,f5148]) ).

fof(f12485,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_255 ),
    inference(forward_demodulation,[],[f12481,f5388]) ).

fof(f12481,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_255 ),
    inference(resolution,[],[f12453,f6872]) ).

fof(f12480,plain,
    spl24_259,
    inference(avatar_split_clause,[],[f12447,f12477]) ).

fof(f12447,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(superposition,[],[f7063,f5009]) ).

fof(f12475,plain,
    ( spl24_258
    | ~ spl24_153 ),
    inference(avatar_split_clause,[],[f12437,f9279,f12472]) ).

fof(f12437,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ spl24_153 ),
    inference(superposition,[],[f12083,f5009]) ).

fof(f12469,plain,
    ~ spl24_257,
    inference(avatar_split_clause,[],[f12448,f12466]) ).

fof(f12448,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(superposition,[],[f7225,f5009]) ).

fof(f7225,plain,
    ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)),X0),
    inference(resolution,[],[f4660,f6166]) ).

fof(f12459,plain,
    ( spl24_256
    | ~ spl24_163 ),
    inference(avatar_split_clause,[],[f12438,f9358,f12456]) ).

fof(f12438,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ spl24_163 ),
    inference(superposition,[],[f11274,f5009]) ).

fof(f12454,plain,
    spl24_255,
    inference(avatar_split_clause,[],[f12446,f12451]) ).

fof(f12446,plain,
    c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(superposition,[],[f6042,f5009]) ).

fof(f12357,plain,
    ( ~ spl24_251
    | spl24_254
    | ~ spl24_92 ),
    inference(avatar_split_clause,[],[f12332,f6764,f12355,f12343]) ).

fof(f12343,plain,
    ( spl24_251
  <=> class_Rings_Ocomm__semiring__1(t_a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_251])]) ).

fof(f12355,plain,
    ( spl24_254
  <=> ! [X6,X7] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(t_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),X7)
        | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(t_a),X6,X7) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_254])]) ).

fof(f12332,plain,
    ( ! [X6,X7] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(t_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),X7)
        | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(t_a),X6,X7)
        | ~ class_Rings_Ocomm__semiring__1(t_a) )
    | ~ spl24_92 ),
    inference(superposition,[],[f4770,f7192]) ).

fof(f7192,plain,
    ( ! [X4] : c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = c_Polynomial_Osmult(t_a,c_Groups_Ozero__class_Ozero(t_a),X4)
    | ~ spl24_92 ),
    inference(resolution,[],[f5666,f6766]) ).

fof(f12353,plain,
    ( ~ spl24_92
    | spl24_253
    | ~ spl24_92 ),
    inference(avatar_split_clause,[],[f12329,f6764,f12351,f6764]) ).

fof(f12351,plain,
    ( spl24_253
  <=> ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = X0
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),c_Polynomial_OpCons(t_a,X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_253])]) ).

fof(f12329,plain,
    ( ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = X0
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),c_Polynomial_OpCons(t_a,X1,X0))
        | ~ class_Rings_Ocomm__semiring__0(t_a) )
    | ~ spl24_92 ),
    inference(superposition,[],[f4606,f7192]) ).

fof(f12349,plain,
    ( ~ spl24_251
    | spl24_252
    | ~ spl24_92 ),
    inference(avatar_split_clause,[],[f12331,f6764,f12347,f12343]) ).

fof(f12347,plain,
    ( spl24_252
  <=> ! [X4,X5] :
        ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(t_a),X5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))
        | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(t_a),X5,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_252])]) ).

fof(f12331,plain,
    ( ! [X4,X5] :
        ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(t_a),X5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))
        | ~ class_Rings_Ocomm__semiring__1(t_a)
        | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(t_a),X5,X4) )
    | ~ spl24_92 ),
    inference(superposition,[],[f5403,f7192]) ).

fof(f12341,plain,
    ( spl24_250
    | ~ spl24_92
    | ~ spl24_92 ),
    inference(avatar_split_clause,[],[f12333,f6764,f6764,f12339]) ).

fof(f12339,plain,
    ( spl24_250
  <=> ! [X8] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Polynomial_Odegree(t_a,X8)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_250])]) ).

fof(f12333,plain,
    ( ! [X8] :
        ( ~ class_Rings_Ocomm__semiring__0(t_a)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Polynomial_Odegree(t_a,X8)) )
    | ~ spl24_92 ),
    inference(superposition,[],[f5260,f7192]) ).

fof(f12337,plain,
    ( ~ spl24_92
    | spl24_249
    | ~ spl24_92 ),
    inference(avatar_split_clause,[],[f12330,f6764,f12335,f6764]) ).

fof(f12335,plain,
    ( spl24_249
  <=> ! [X2,X3] :
        ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) != c_Polynomial_OpCons(t_a,X3,X2)
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_249])]) ).

fof(f12330,plain,
    ( ! [X2,X3] :
        ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) != c_Polynomial_OpCons(t_a,X3,X2)
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = X2
        | ~ class_Rings_Ocomm__semiring__0(t_a) )
    | ~ spl24_92 ),
    inference(superposition,[],[f4596,f7192]) ).

fof(f12164,plain,
    ( spl24_248
    | ~ spl24_121
    | ~ spl24_9 ),
    inference(avatar_split_clause,[],[f12156,f6248,f6941,f12162]) ).

fof(f12162,plain,
    ( spl24_248
  <=> ! [X2,X3] :
        ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Int_Oint),X2,c_Polynomial_OpCons(tc_Int_Oint,X3,X2)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint))
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_248])]) ).

fof(f12156,plain,
    ( ! [X2,X3] :
        ( ~ class_Rings_Ocomm__semiring__0(tc_Int_Oint)
        | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Int_Oint),X2,c_Polynomial_OpCons(tc_Int_Oint,X3,X2)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint))
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)) = X2 )
    | ~ spl24_9 ),
    inference(superposition,[],[f4606,f7085]) ).

fof(f7085,plain,
    ( ! [X1] : c_Polynomial_Osmult(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1) = X1
    | ~ spl24_9 ),
    inference(resolution,[],[f4998,f6250]) ).

fof(f12160,plain,
    ( ~ spl24_15
    | spl24_247
    | ~ spl24_5 ),
    inference(avatar_split_clause,[],[f12155,f6228,f12158,f6277]) ).

fof(f12158,plain,
    ( spl24_247
  <=> ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)) = X0
        | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Nat_Onat),X0,c_Polynomial_OpCons(tc_Nat_Onat,X1,X0)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_247])]) ).

fof(f12155,plain,
    ( ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)) = X0
        | ~ class_Rings_Ocomm__semiring__0(tc_Nat_Onat)
        | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Nat_Onat),X0,c_Polynomial_OpCons(tc_Nat_Onat,X1,X0)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)) )
    | ~ spl24_5 ),
    inference(superposition,[],[f4606,f7084]) ).

fof(f7084,plain,
    ( ! [X0] : c_Polynomial_Osmult(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) = X0
    | ~ spl24_5 ),
    inference(resolution,[],[f4998,f6230]) ).

fof(f12041,plain,
    ( spl24_246
    | spl24_137 ),
    inference(avatar_split_clause,[],[f12030,f7320,f12038]) ).

fof(f12038,plain,
    ( spl24_246
  <=> ! [X0,X1] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) != X0
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_246])]) ).

fof(f12030,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
      | X0 = X1
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) != X0 ),
    inference(superposition,[],[f5710,f4499]) ).

fof(f4499,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,[],[f1385]) ).

fof(f1385,plain,
    ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) = X0,
    inference(rectify,[],[f287]) ).

fof(f287,axiom,
    ! [X17] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X17) = X17,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__1) ).

fof(f12040,plain,
    ( spl24_137
    | spl24_246 ),
    inference(avatar_split_clause,[],[f12024,f12038,f7320]) ).

fof(f12024,plain,
    ! [X0,X1] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) != X0
      | X0 = X1
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(superposition,[],[f5710,f4499]) ).

fof(f11986,plain,
    spl24_245,
    inference(avatar_split_clause,[],[f11970,f11983]) ).

fof(f11983,plain,
    ( spl24_245
  <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = sK4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_245])]) ).

fof(f11970,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = sK4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(superposition,[],[f5628,f7452]) ).

fof(f11981,plain,
    ~ spl24_244,
    inference(avatar_split_clause,[],[f11975,f11978]) ).

fof(f11978,plain,
    ( spl24_244
  <=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = sK4(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_244])]) ).

fof(f11975,plain,
    c_Groups_Oone__class_Oone(tc_Nat_Onat) != sK4(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(superposition,[],[f5990,f7452]) ).

fof(f11926,plain,
    spl24_243,
    inference(avatar_split_clause,[],[f11914,f11922]) ).

fof(f11922,plain,
    ( spl24_243
  <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = sK5(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_243])]) ).

fof(f11914,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = sK5(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(superposition,[],[f5628,f7451]) ).

fof(f11925,plain,
    spl24_243,
    inference(avatar_split_clause,[],[f11890,f11922]) ).

fof(f11890,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = sK5(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(superposition,[],[f7451,f5628]) ).

fof(f11789,plain,
    ~ spl24_242,
    inference(avatar_split_clause,[],[f11780,f11786]) ).

fof(f11780,plain,
    ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(superposition,[],[f5924,f4540]) ).

fof(f11655,plain,
    ( spl24_241
    | ~ spl24_153 ),
    inference(avatar_split_clause,[],[f11650,f9279,f11652]) ).

fof(f11650,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_153 ),
    inference(forward_demodulation,[],[f11649,f7545]) ).

fof(f11649,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_153 ),
    inference(resolution,[],[f6872,f9280]) ).

fof(f11601,plain,
    ( ~ spl24_121
    | spl24_240
    | ~ spl24_9 ),
    inference(avatar_split_clause,[],[f11594,f6248,f11599,f6941]) ).

fof(f11599,plain,
    ( spl24_240
  <=> ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)) = X0
        | c_Polynomial_OpCons(tc_Int_Oint,X1,X0) != X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_240])]) ).

fof(f11594,plain,
    ( ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)) = X0
        | c_Polynomial_OpCons(tc_Int_Oint,X1,X0) != X0
        | ~ class_Rings_Ocomm__semiring__0(tc_Int_Oint) )
    | ~ spl24_9 ),
    inference(superposition,[],[f4596,f7085]) ).

fof(f11580,plain,
    ( ~ spl24_15
    | spl24_239
    | ~ spl24_5 ),
    inference(avatar_split_clause,[],[f11573,f6228,f11578,f6277]) ).

fof(f11578,plain,
    ( spl24_239
  <=> ! [X0,X1] :
        ( c_Polynomial_OpCons(tc_Nat_Onat,X1,X0) != X0
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_239])]) ).

fof(f11573,plain,
    ( ! [X0,X1] :
        ( c_Polynomial_OpCons(tc_Nat_Onat,X1,X0) != X0
        | ~ class_Rings_Ocomm__semiring__0(tc_Nat_Onat)
        | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)) = X0 )
    | ~ spl24_5 ),
    inference(superposition,[],[f4596,f7084]) ).

fof(f11239,plain,
    ( spl24_238
    | ~ spl24_235 ),
    inference(avatar_split_clause,[],[f11223,f11215,f11236]) ).

fof(f11223,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ spl24_235 ),
    inference(resolution,[],[f11217,f5678]) ).

fof(f11234,plain,
    ( ~ spl24_236
    | spl24_237
    | ~ spl24_235 ),
    inference(avatar_split_clause,[],[f11225,f11215,f11231,f11227]) ).

fof(f11225,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ spl24_235 ),
    inference(resolution,[],[f11217,f5243]) ).

fof(f11218,plain,
    ( spl24_235
    | ~ spl24_233 ),
    inference(avatar_split_clause,[],[f11213,f11143,f11215]) ).

fof(f11213,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ spl24_233 ),
    inference(resolution,[],[f11145,f5695]) ).

fof(f11155,plain,
    ( spl24_234
    | ~ spl24_191 ),
    inference(avatar_split_clause,[],[f11148,f9854,f11152]) ).

fof(f11148,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ spl24_191 ),
    inference(resolution,[],[f9855,f5678]) ).

fof(f11147,plain,
    ( spl24_163
    | ~ spl24_153 ),
    inference(avatar_split_clause,[],[f11051,f9279,f9358]) ).

fof(f11051,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_153 ),
    inference(resolution,[],[f9280,f5695]) ).

fof(f11146,plain,
    ( spl24_233
    | ~ spl24_163 ),
    inference(avatar_split_clause,[],[f11141,f9358,f11143]) ).

fof(f11141,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ spl24_163 ),
    inference(forward_demodulation,[],[f11139,f4706]) ).

fof(f11139,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ spl24_163 ),
    inference(resolution,[],[f5678,f9360]) ).

fof(f11121,plain,
    ( spl24_232
    | ~ spl24_6 ),
    inference(avatar_split_clause,[],[f11104,f6233,f11118]) ).

fof(f11118,plain,
    ( spl24_232
  <=> c_fequal = c_HOL_Oequal__class_Oequal(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_232])]) ).

fof(f11104,plain,
    ( c_fequal = c_HOL_Oequal__class_Oequal(tc_Int_Oint)
    | ~ spl24_6 ),
    inference(resolution,[],[f4657,f6235]) ).

fof(f6235,plain,
    ( class_HOL_Oequal(tc_Int_Oint)
    | ~ spl24_6 ),
    inference(avatar_component_clause,[],[f6233]) ).

fof(f11116,plain,
    ( spl24_231
    | ~ spl24_94 ),
    inference(avatar_split_clause,[],[f11106,f6774,f11113]) ).

fof(f11113,plain,
    ( spl24_231
  <=> c_fequal = c_HOL_Oequal__class_Oequal(tc_HOL_Obool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_231])]) ).

fof(f11106,plain,
    ( c_fequal = c_HOL_Oequal__class_Oequal(tc_HOL_Obool)
    | ~ spl24_94 ),
    inference(resolution,[],[f4657,f6776]) ).

fof(f11111,plain,
    ( spl24_230
    | ~ spl24_50 ),
    inference(avatar_split_clause,[],[f11105,f6475,f11108]) ).

fof(f11108,plain,
    ( spl24_230
  <=> c_fequal = c_HOL_Oequal__class_Oequal(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_230])]) ).

fof(f11105,plain,
    ( c_fequal = c_HOL_Oequal__class_Oequal(tc_Nat_Onat)
    | ~ spl24_50 ),
    inference(resolution,[],[f4657,f6477]) ).

fof(f6477,plain,
    ( class_HOL_Oequal(tc_Nat_Onat)
    | ~ spl24_50 ),
    inference(avatar_component_clause,[],[f6475]) ).

fof(f11098,plain,
    ( ~ spl24_9
    | spl24_175 ),
    inference(avatar_split_clause,[],[f11097,f9542,f6248]) ).

fof(f9542,plain,
    ( spl24_175
  <=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_175])]) ).

fof(f11097,plain,
    ( ~ class_Rings_Ocomm__semiring__1(tc_Int_Oint)
    | spl24_175 ),
    inference(resolution,[],[f9544,f5375]) ).

fof(f9544,plain,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | spl24_175 ),
    inference(avatar_component_clause,[],[f9542]) ).

fof(f11079,plain,
    ( ~ spl24_5
    | spl24_169 ),
    inference(avatar_split_clause,[],[f11074,f9437,f6228]) ).

fof(f9437,plain,
    ( spl24_169
  <=> c_Rings_Odvd__class_Odvd(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,[spl24_169])]) ).

fof(f11074,plain,
    ( ~ class_Rings_Ocomm__semiring__1(tc_Nat_Onat)
    | spl24_169 ),
    inference(resolution,[],[f9439,f5705]) ).

fof(f9439,plain,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | spl24_169 ),
    inference(avatar_component_clause,[],[f9437]) ).

fof(f11078,plain,
    ( ~ spl24_5
    | spl24_169 ),
    inference(avatar_split_clause,[],[f11075,f9437,f6228]) ).

fof(f11075,plain,
    ( ~ class_Rings_Ocomm__semiring__1(tc_Nat_Onat)
    | spl24_169 ),
    inference(resolution,[],[f9439,f5375]) ).

fof(f11077,plain,
    spl24_169,
    inference(avatar_contradiction_clause,[],[f11073]) ).

fof(f11073,plain,
    ( $false
    | spl24_169 ),
    inference(resolution,[],[f9439,f4537]) ).

fof(f4537,plain,
    ! [X0] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,X0),
    inference(cnf_transformation,[],[f1208]) ).

fof(f1208,plain,
    ! [X0] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,X0),
    inference(rectify,[],[f656]) ).

fof(f656,axiom,
    ! [X19] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X19,X19),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oorder__refl) ).

fof(f11076,plain,
    spl24_169,
    inference(avatar_contradiction_clause,[],[f11072]) ).

fof(f11072,plain,
    ( $false
    | spl24_169 ),
    inference(resolution,[],[f9439,f5240]) ).

fof(f5240,plain,
    ! [X0] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(cnf_transformation,[],[f1497]) ).

fof(f1497,plain,
    ! [X0] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(rectify,[],[f702]) ).

fof(f702,axiom,
    ! [X19] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X19,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gcd__lcm__complete__lattice__nat_Otop__greatest) ).

fof(f11043,plain,
    ( spl24_172
    | ~ spl24_163
    | spl24_153 ),
    inference(avatar_split_clause,[],[f11040,f9279,f9358,f9476]) ).

fof(f11040,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | spl24_153 ),
    inference(resolution,[],[f9281,f5693]) ).

fof(f9281,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | spl24_153 ),
    inference(avatar_component_clause,[],[f9279]) ).

fof(f10917,plain,
    ( spl24_163
    | spl24_191 ),
    inference(avatar_split_clause,[],[f10915,f9854,f9358]) ).

fof(f10915,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | spl24_191 ),
    inference(resolution,[],[f9856,f5360]) ).

fof(f9856,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | spl24_191 ),
    inference(avatar_component_clause,[],[f9854]) ).

fof(f10916,plain,
    ( spl24_163
    | spl24_191 ),
    inference(avatar_split_clause,[],[f10914,f9854,f9358]) ).

fof(f10914,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | spl24_191 ),
    inference(resolution,[],[f9856,f5360]) ).

fof(f10913,plain,
    spl24_148,
    inference(avatar_contradiction_clause,[],[f10910]) ).

fof(f10910,plain,
    ( $false
    | spl24_148 ),
    inference(resolution,[],[f9188,f5775]) ).

fof(f9188,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | spl24_148 ),
    inference(avatar_component_clause,[],[f9186]) ).

fof(f9186,plain,
    ( spl24_148
  <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_148])]) ).

fof(f10857,plain,
    ( spl24_228
    | spl24_229
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f10850,f7320,f7317,f10855,f10852]) ).

fof(f10852,plain,
    ( spl24_228
  <=> ! [X1,X3] : c_Orderings_Oord__class_Oless__eq(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1,X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_228])]) ).

fof(f10855,plain,
    ( spl24_229
  <=> ! [X2] :
        ( ~ class_Orderings_Oord(X2)
        | ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_229])]) ).

fof(f7317,plain,
    ( spl24_136
  <=> ! [X1] : c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_136])]) ).

fof(f10850,plain,
    ( ! [X2,X3,X1] :
        ( ~ class_Orderings_Oord(X2)
        | ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | c_Orderings_Oord__class_Oless__eq(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1,X3) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f10849,f7321]) ).

fof(f7321,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ spl24_137 ),
    inference(avatar_component_clause,[],[f7320]) ).

fof(f10849,plain,
    ( ! [X2,X3,X1] :
        ( c_Orderings_Oord__class_Oless__eq(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1,X3)
        | ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ class_Orderings_Oord(X2) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f10848,f7318]) ).

fof(f7318,plain,
    ( ! [X1] : c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
    | ~ spl24_136 ),
    inference(avatar_component_clause,[],[f7317]) ).

fof(f10848,plain,
    ( ! [X2,X3,X1] :
        ( ~ class_Orderings_Oord(X2)
        | c_Orderings_Oord__class_Oless__eq(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1,X3)
        | ~ c_Orderings_Oord__class_Oless__eq(X2,hAPP(X1,sK3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f10847,f7321]) ).

fof(f10847,plain,
    ( ! [X2,X3,X1] :
        ( ~ class_Orderings_Oord(X2)
        | ~ c_Orderings_Oord__class_Oless__eq(X2,hAPP(X1,sK3(X1,X2,X3)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | c_Orderings_Oord__class_Oless__eq(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1,X3) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f10846,f7321]) ).

fof(f10846,plain,
    ( ! [X2,X3,X1] :
        ( c_Orderings_Oord__class_Oless__eq(c_Groups_Oone__class_Oone(tc_Nat_Onat),X1,X3)
        | ~ c_Orderings_Oord__class_Oless__eq(X2,hAPP(X1,sK3(X1,X2,X3)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ class_Orderings_Oord(X2) )
    | ~ spl24_136 ),
    inference(forward_demodulation,[],[f8117,f7318]) ).

fof(f8117,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_fun(X0,X2),X1,X3)
        | ~ class_Orderings_Oord(X2)
        | ~ c_Orderings_Oord__class_Oless__eq(X2,hAPP(X1,sK3(X1,X2,X3)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f4789,f7318]) ).

fof(f4789,plain,
    ! [X2,X3,X0,X1] :
      ( ~ class_Orderings_Oord(X2)
      | c_Orderings_Oord__class_Oless__eq(tc_fun(X0,X2),X1,X3)
      | ~ c_Orderings_Oord__class_Oless__eq(X2,hAPP(X1,sK3(X1,X2,X3)),hAPP(X3,sK3(X1,X2,X3))) ),
    inference(cnf_transformation,[],[f3708]) ).

fof(f3708,plain,
    ! [X0,X1,X2,X3] :
      ( ~ class_Orderings_Oord(X2)
      | ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X0,X2),X1,X3)
          | ~ c_Orderings_Oord__class_Oless__eq(X2,hAPP(X1,sK3(X1,X2,X3)),hAPP(X3,sK3(X1,X2,X3))) )
        & ( ! [X5] : c_Orderings_Oord__class_Oless__eq(X2,hAPP(X1,X5),hAPP(X3,X5))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X0,X2),X1,X3) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f3706,f3707]) ).

fof(f3707,plain,
    ! [X1,X2,X3] :
      ( ? [X4] : ~ c_Orderings_Oord__class_Oless__eq(X2,hAPP(X1,X4),hAPP(X3,X4))
     => ~ c_Orderings_Oord__class_Oless__eq(X2,hAPP(X1,sK3(X1,X2,X3)),hAPP(X3,sK3(X1,X2,X3))) ),
    introduced(choice_axiom,[]) ).

fof(f3706,plain,
    ! [X0,X1,X2,X3] :
      ( ~ class_Orderings_Oord(X2)
      | ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X0,X2),X1,X3)
          | ? [X4] : ~ c_Orderings_Oord__class_Oless__eq(X2,hAPP(X1,X4),hAPP(X3,X4)) )
        & ( ! [X5] : c_Orderings_Oord__class_Oless__eq(X2,hAPP(X1,X5),hAPP(X3,X5))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X0,X2),X1,X3) ) ) ),
    inference(rectify,[],[f3705]) ).

fof(f3705,plain,
    ! [X3,X0,X1,X2] :
      ( ~ class_Orderings_Oord(X1)
      | ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,X1),X0,X2)
          | ? [X4] : ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X4),hAPP(X2,X4)) )
        & ( ! [X4] : c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X4),hAPP(X2,X4))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,X1),X0,X2) ) ) ),
    inference(nnf_transformation,[],[f3034]) ).

fof(f3034,plain,
    ! [X3,X0,X1,X2] :
      ( ~ class_Orderings_Oord(X1)
      | ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,X1),X0,X2)
      <=> ! [X4] : c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X4),hAPP(X2,X4)) ) ),
    inference(ennf_transformation,[],[f2141]) ).

fof(f2141,plain,
    ! [X1,X0,X3,X2] :
      ( class_Orderings_Oord(X1)
     => ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,X1),X0,X2)
      <=> ! [X4] : c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X4),hAPP(X2,X4)) ) ),
    inference(rectify,[],[f355]) ).

fof(f355,axiom,
    ! [X1,X12,X0,X8] :
      ( class_Orderings_Oord(X12)
     => ( ! [X2] : c_Orderings_Oord__class_Oless__eq(X12,hAPP(X1,X2),hAPP(X0,X2))
      <=> c_Orderings_Oord__class_Oless__eq(tc_fun(X8,X12),X1,X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__fun__def) ).

fof(f10841,plain,
    ( spl24_152
    | spl24_227
    | ~ spl24_136 ),
    inference(avatar_split_clause,[],[f10837,f7317,f10839,f9263]) ).

fof(f9263,plain,
    ( spl24_152
  <=> ! [X0,X1] : X0 = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_152])]) ).

fof(f10839,plain,
    ( spl24_227
  <=> ! [X2] : ~ class_Groups_Ogroup__add(X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_227])]) ).

fof(f10837,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Groups_Ogroup__add(X2)
        | X0 = X1 )
    | ~ spl24_136 ),
    inference(trivial_inequality_removal,[],[f10836]) ).

fof(f10836,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Groups_Ogroup__add(X2)
        | X0 = X1
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
    | ~ spl24_136 ),
    inference(forward_demodulation,[],[f9026,f7318]) ).

fof(f9026,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Groups_Ogroup__add(X2)
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ouminus__class_Ouminus(X2,X0)
        | X0 = X1 )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f5092,f7318]) ).

fof(f5092,plain,
    ! [X2,X0,X1] :
      ( ~ class_Groups_Ogroup__add(X2)
      | X0 = X1
      | c_Groups_Ouminus__class_Ouminus(X2,X1) != c_Groups_Ouminus__class_Ouminus(X2,X0) ),
    inference(cnf_transformation,[],[f3901]) ).

fof(f3901,plain,
    ! [X0,X1,X2] :
      ( ~ class_Groups_Ogroup__add(X2)
      | ( ( X0 = X1
          | c_Groups_Ouminus__class_Ouminus(X2,X1) != c_Groups_Ouminus__class_Ouminus(X2,X0) )
        & ( c_Groups_Ouminus__class_Ouminus(X2,X1) = c_Groups_Ouminus__class_Ouminus(X2,X0)
          | X0 != X1 ) ) ),
    inference(rectify,[],[f3900]) ).

fof(f3900,plain,
    ! [X2,X0,X1] :
      ( ~ class_Groups_Ogroup__add(X1)
      | ( ( X0 = X2
          | c_Groups_Ouminus__class_Ouminus(X1,X0) != c_Groups_Ouminus__class_Ouminus(X1,X2) )
        & ( c_Groups_Ouminus__class_Ouminus(X1,X0) = c_Groups_Ouminus__class_Ouminus(X1,X2)
          | X0 != X2 ) ) ),
    inference(nnf_transformation,[],[f2457]) ).

fof(f2457,plain,
    ! [X2,X0,X1] :
      ( ~ class_Groups_Ogroup__add(X1)
      | ( X0 = X2
      <=> c_Groups_Ouminus__class_Ouminus(X1,X0) = c_Groups_Ouminus__class_Ouminus(X1,X2) ) ),
    inference(ennf_transformation,[],[f1751]) ).

fof(f1751,plain,
    ! [X2,X1,X0] :
      ( class_Groups_Ogroup__add(X1)
     => ( X0 = X2
      <=> c_Groups_Ouminus__class_Ouminus(X1,X0) = c_Groups_Ouminus__class_Ouminus(X1,X2) ) ),
    inference(rectify,[],[f211]) ).

fof(f211,axiom,
    ! [X10,X8,X7] :
      ( class_Groups_Ogroup__add(X8)
     => ( X7 = X10
      <=> c_Groups_Ouminus__class_Ouminus(X8,X7) = c_Groups_Ouminus__class_Ouminus(X8,X10) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__equal__iff__equal) ).

fof(f10832,plain,
    ( spl24_155
    | spl24_149
    | ~ spl24_191
    | spl24_226
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f10828,f7320,f7317,f10830,f9854,f9190,f9289]) ).

fof(f9289,plain,
    ( spl24_155
  <=> ! [X1] : ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_155])]) ).

fof(f9190,plain,
    ( spl24_149
  <=> ! [X4,X1] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_149])]) ).

fof(f10830,plain,
    ( spl24_226
  <=> ! [X5,X2,X0] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X2)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_226])]) ).

fof(f10828,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X0)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X4)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X2)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f10827,f7321]) ).

fof(f10827,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X2)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X4)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X0) )
    | ~ spl24_136 ),
    inference(trivial_inequality_removal,[],[f10826]) ).

fof(f10826,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X2)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X4) )
    | ~ spl24_136 ),
    inference(forward_demodulation,[],[f10825,f7318]) ).

fof(f10825,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X2)
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X4),X5)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X0)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X4)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
    | ~ spl24_136 ),
    inference(forward_demodulation,[],[f10824,f7318]) ).

fof(f10824,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X4),X5))
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X4),X5)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X0)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X4)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X2) )
    | ~ spl24_136 ),
    inference(forward_demodulation,[],[f8221,f7318]) ).

fof(f8221,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X2)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
        | c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X4),X5) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X0)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X4)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X4),X5))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f4591,f7318]) ).

fof(f4591,plain,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
      | c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X4),X5) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3),X1)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X2)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X4)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X4),X5))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X0) ),
    inference(cnf_transformation,[],[f3573]) ).

fof(f3573,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X2)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X0)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X4)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X4),X5))
      | c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X4),X5) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3),X1)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
    inference(rectify,[],[f2454]) ).

fof(f2454,plain,
    ! [X3,X4,X2,X0,X1,X5] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X2)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X3)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X5))
      | c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X5) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X0),X4)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
    inference(flattening,[],[f2453]) ).

fof(f2453,plain,
    ! [X1,X3,X2,X5,X4,X0] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X3)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
      | ~ 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,X5,X2)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X5))
      | c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X5) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X0),X4) ),
    inference(ennf_transformation,[],[f1616]) ).

fof(f1616,plain,
    ! [X1,X3,X2,X5,X4,X0] :
      ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X5) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X0),X4)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X5))
       => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X2)
         => ( 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)
             => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X3)
               => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1) ) ) ) ) ) ),
    inference(rectify,[],[f835]) ).

fof(f835,axiom,
    ! [X21,X79,X50,X29,X28,X78] :
      ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X50),X79),X78) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X29),X21),X28)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X50),X79),X78))
       => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X78,X50)
         => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X28)
           => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X50)
             => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X50,X29)
               => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X21,X79) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono2__lemma) ).

fof(f10803,plain,
    ( spl24_224
    | spl24_225
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f10795,f7320,f7317,f10801,f10797]) ).

fof(f10797,plain,
    ( spl24_224
  <=> class_Groups_Ouminus(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_224])]) ).

fof(f10801,plain,
    ( spl24_225
  <=> ! [X1] : ~ class_Groups_Ouminus(X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_225])]) ).

fof(f10795,plain,
    ( ! [X1] :
        ( ~ class_Groups_Ouminus(X1)
        | class_Groups_Ouminus(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f9063,f7321]) ).

fof(f9063,plain,
    ( ! [X1] :
        ( ~ class_Groups_Ouminus(X1)
        | class_Groups_Ouminus(c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f4711,f7318]) ).

fof(f4711,plain,
    ! [X0,X1] :
      ( class_Groups_Ouminus(tc_fun(X0,X1))
      | ~ class_Groups_Ouminus(X1) ),
    inference(cnf_transformation,[],[f2603]) ).

fof(f2603,plain,
    ! [X0,X1] :
      ( class_Groups_Ouminus(tc_fun(X0,X1))
      | ~ class_Groups_Ouminus(X1) ),
    inference(ennf_transformation,[],[f1893]) ).

fof(f1893,plain,
    ! [X1,X0] :
      ( class_Groups_Ouminus(X1)
     => class_Groups_Ouminus(tc_fun(X0,X1)) ),
    inference(rectify,[],[f1014]) ).

fof(f1014,axiom,
    ! [X95,X94] :
      ( class_Groups_Ouminus(X94)
     => class_Groups_Ouminus(tc_fun(X95,X94)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Groups_Ouminus) ).

fof(f10773,plain,
    ( spl24_167
    | spl24_223
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f10769,f7320,f7317,f10771,f9408]) ).

fof(f9408,plain,
    ( spl24_167
  <=> ! [X2,X1] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_167])]) ).

fof(f10771,plain,
    ( spl24_223
  <=> ! [X1,X3] :
        ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ class_Rings_Olinordered__semidom(X1)
        | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_223])]) ).

fof(f10769,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X3)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
        | ~ class_Rings_Olinordered__semidom(X1) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f10768,f7321]) ).

fof(f10768,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X3)
        | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
        | ~ class_Rings_Olinordered__semidom(X1) )
    | ~ spl24_136 ),
    inference(forward_demodulation,[],[f8491,f7318]) ).

fof(f8491,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X3)
        | ~ class_Rings_Olinordered__semidom(X1)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
        | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X0)) )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f4680,f7318]) ).

fof(f4680,plain,
    ! [X2,X3,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X0))
      | ~ class_Rings_Olinordered__semidom(X1)
      | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X3)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0) ),
    inference(cnf_transformation,[],[f3635]) ).

fof(f3635,plain,
    ! [X0,X1,X2,X3] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X0))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0) )
        & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
          | ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X0)) ) )
      | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X3)
      | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(rectify,[],[f3634]) ).

fof(f3634,plain,
    ! [X1,X2,X3,X0] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),X1))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X1) )
        & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X1)
          | ~ c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),X1)) ) )
      | ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X0)
      | ~ class_Rings_Olinordered__semidom(X2) ),
    inference(nnf_transformation,[],[f2839]) ).

fof(f2839,plain,
    ! [X1,X2,X3,X0] :
      ( ( c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),X1))
      <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X1) )
      | ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X0)
      | ~ class_Rings_Olinordered__semidom(X2) ),
    inference(flattening,[],[f2838]) ).

fof(f2838,plain,
    ! [X3,X1,X2,X0] :
      ( ( c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),X1))
      <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X1) )
      | ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X0)
      | ~ class_Rings_Olinordered__semidom(X2) ),
    inference(ennf_transformation,[],[f1752]) ).

fof(f1752,plain,
    ! [X3,X1,X2,X0] :
      ( class_Rings_Olinordered__semidom(X2)
     => ( c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X0)
       => ( c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),X1))
        <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X1) ) ) ),
    inference(rectify,[],[f760]) ).

fof(f760,axiom,
    ! [X10,X20,X8,X13] :
      ( class_Rings_Olinordered__semidom(X8)
     => ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oone__class_Oone(X8),X10)
       => ( c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X10),X13),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X10),X20))
        <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X13,X20) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__increasing__iff) ).

fof(f10760,plain,
    ( spl24_152
    | spl24_166
    | ~ spl24_136 ),
    inference(avatar_split_clause,[],[f10759,f7317,f9398,f9263]) ).

fof(f9398,plain,
    ( spl24_166
  <=> ! [X2] : ~ class_Groups_Ozero(X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_166])]) ).

fof(f10759,plain,
    ( ! [X3,X0,X1] :
        ( ~ class_Groups_Ozero(X3)
        | X0 = X1 )
    | ~ spl24_136 ),
    inference(trivial_inequality_removal,[],[f10758]) ).

fof(f10758,plain,
    ( ! [X3,X0,X1] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | X0 = X1
        | ~ class_Groups_Ozero(X3) )
    | ~ spl24_136 ),
    inference(forward_demodulation,[],[f8692,f7318]) ).

fof(f8692,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Polynomial_Omonom(X3,X0,X2)
        | X0 = X1
        | ~ class_Groups_Ozero(X3) )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f5535,f7318]) ).

fof(f5535,plain,
    ! [X2,X3,X0,X1] :
      ( ~ class_Groups_Ozero(X3)
      | X0 = X1
      | c_Polynomial_Omonom(X3,X1,X2) != c_Polynomial_Omonom(X3,X0,X2) ),
    inference(cnf_transformation,[],[f4175]) ).

fof(f4175,plain,
    ! [X0,X1,X2,X3] :
      ( ~ class_Groups_Ozero(X3)
      | ( ( c_Polynomial_Omonom(X3,X1,X2) = c_Polynomial_Omonom(X3,X0,X2)
          | X0 != X1 )
        & ( X0 = X1
          | c_Polynomial_Omonom(X3,X1,X2) != c_Polynomial_Omonom(X3,X0,X2) ) ) ),
    inference(rectify,[],[f4174]) ).

fof(f4174,plain,
    ! [X2,X3,X0,X1] :
      ( ~ class_Groups_Ozero(X1)
      | ( ( c_Polynomial_Omonom(X1,X3,X0) = c_Polynomial_Omonom(X1,X2,X0)
          | X2 != X3 )
        & ( X2 = X3
          | c_Polynomial_Omonom(X1,X3,X0) != c_Polynomial_Omonom(X1,X2,X0) ) ) ),
    inference(nnf_transformation,[],[f2883]) ).

fof(f2883,plain,
    ! [X2,X3,X0,X1] :
      ( ~ class_Groups_Ozero(X1)
      | ( c_Polynomial_Omonom(X1,X3,X0) = c_Polynomial_Omonom(X1,X2,X0)
      <=> X2 = X3 ) ),
    inference(ennf_transformation,[],[f1276]) ).

fof(f1276,plain,
    ! [X0,X1,X2,X3] :
      ( class_Groups_Ozero(X1)
     => ( c_Polynomial_Omonom(X1,X3,X0) = c_Polynomial_Omonom(X1,X2,X0)
      <=> X2 = X3 ) ),
    inference(rectify,[],[f16]) ).

fof(f16,axiom,
    ! [X18,X8,X7,X10] :
      ( class_Groups_Ozero(X8)
     => ( X7 = X10
      <=> c_Polynomial_Omonom(X8,X7,X18) = c_Polynomial_Omonom(X8,X10,X18) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_monom__eq__iff) ).

fof(f10757,plain,
    ( ~ spl24_169
    | spl24_161
    | spl24_170
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f10756,f7320,f7317,f9441,f9332,f9437]) ).

fof(f9441,plain,
    ( spl24_170
  <=> ! [X0,X1] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_170])]) ).

fof(f10756,plain,
    ( ! [X2,X0,X1] :
        ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X0)
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f10755,f7321]) ).

fof(f10755,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X0) )
    | ~ spl24_136 ),
    inference(forward_demodulation,[],[f8529,f7318]) ).

fof(f8529,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1))
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X0)
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f5712,f7318]) ).

fof(f5712,plain,
    ! [X2,X0,X1] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1))
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X0) ),
    inference(cnf_transformation,[],[f4292]) ).

fof(f4292,plain,
    ! [X0,X1,X2] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
      | ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X0)
          | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1)) )
        & ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1))
          | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X0) ) ) ),
    inference(rectify,[],[f4291]) ).

fof(f4291,plain,
    ! [X1,X0,X2] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
      | ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
          | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0)) )
        & ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0))
          | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ) ) ),
    inference(nnf_transformation,[],[f3288]) ).

fof(f3288,plain,
    ! [X1,X0,X2] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
      | ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
      <=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0)) ) ),
    inference(ennf_transformation,[],[f2128]) ).

fof(f2128,plain,
    ! [X1,X2,X0] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
      <=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0)) ) ),
    inference(rectify,[],[f709]) ).

fof(f709,axiom,
    ! [X18,X10,X7] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X18
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X7),X18),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X10),X18))
      <=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X7,X10) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pow__divides__eq__nat) ).

fof(f10744,plain,
    ( spl24_153
    | spl24_205
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f10743,f7320,f7317,f10228,f9279]) ).

fof(f10228,plain,
    ( spl24_205
  <=> ! [X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X1
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_205])]) ).

fof(f10743,plain,
    ( ! [X2] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X2 )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f8956,f7321]) ).

fof(f8956,plain,
    ( ! [X2] :
        ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X2
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f7689,f7318]) ).

fof(f7689,plain,
    ! [X2] :
      ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X2
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
    inference(resolution,[],[f6872,f5285]) ).

fof(f10731,plain,
    ( ~ spl24_222
    | spl24_85
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f10726,f7320,f7317,f6721,f10728]) ).

fof(f10728,plain,
    ( spl24_222
  <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_OpCons(t_a,v_a,v_p) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_222])]) ).

fof(f10726,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Polynomial_OpCons(t_a,v_a,v_p)
    | spl24_85
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f8666,f7321]) ).

fof(f8666,plain,
    ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Polynomial_OpCons(t_a,v_a,v_p)
    | spl24_85
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f6723,f7318]) ).

fof(f10705,plain,
    ( spl24_144
    | spl24_170
    | ~ spl24_169
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f10704,f7320,f7317,f9437,f9441,f9145]) ).

fof(f10704,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f10703,f7321]) ).

fof(f10703,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f10702,f7318]) ).

fof(f10702,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f8187,f7321]) ).

fof(f8187,plain,
    ( ! [X2,X0,X1] :
        ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f5606,f7318]) ).

fof(f5606,plain,
    ! [X2,X0,X1] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
    inference(cnf_transformation,[],[f4218]) ).

fof(f4218,plain,
    ! [X0,X1,X2] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
      | ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0))
          | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0) )
        & ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0)
          | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,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,[],[f4217]) ).

fof(f4217,plain,
    ! [X1,X2,X0] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
      | ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
          | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) )
        & ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
          | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)) ) ) ),
    inference(nnf_transformation,[],[f2971]) ).

fof(f2971,plain,
    ! [X1,X2,X0] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
      | ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
      <=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ) ),
    inference(ennf_transformation,[],[f1545]) ).

fof(f1545,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
      <=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ) ),
    inference(rectify,[],[f627]) ).

fof(f627,axiom,
    ! [X44,X18,X43] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X44)
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X43,X18)
      <=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X44),X43),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X44),X18)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__dvd__cancel1) ).

fof(f10701,plain,
    ( spl24_219
    | spl24_221
    | spl24_219
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f10696,f7320,f7317,f10552,f10698,f10552]) ).

fof(f10698,plain,
    ( spl24_221
  <=> class_Enum_Oenum(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_221])]) ).

fof(f10552,plain,
    ( spl24_219
  <=> ! [X1] : ~ class_Enum_Oenum(X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_219])]) ).

fof(f10696,plain,
    ( ! [X0,X1] :
        ( ~ class_Enum_Oenum(X1)
        | class_Enum_Oenum(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ class_Enum_Oenum(X0) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f9069,f7321]) ).

fof(f9069,plain,
    ( ! [X0,X1] :
        ( ~ class_Enum_Oenum(X1)
        | class_Enum_Oenum(c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ class_Enum_Oenum(X0) )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f5323,f7318]) ).

fof(f5323,plain,
    ! [X0,X1] :
      ( class_Enum_Oenum(tc_fun(X1,X0))
      | ~ class_Enum_Oenum(X1)
      | ~ class_Enum_Oenum(X0) ),
    inference(cnf_transformation,[],[f4017]) ).

fof(f4017,plain,
    ! [X0,X1] :
      ( ~ class_Enum_Oenum(X1)
      | ~ class_Enum_Oenum(X0)
      | class_Enum_Oenum(tc_fun(X1,X0)) ),
    inference(rectify,[],[f3030]) ).

fof(f3030,plain,
    ! [X1,X0] :
      ( ~ class_Enum_Oenum(X0)
      | ~ class_Enum_Oenum(X1)
      | class_Enum_Oenum(tc_fun(X0,X1)) ),
    inference(flattening,[],[f3029]) ).

fof(f3029,plain,
    ! [X0,X1] :
      ( class_Enum_Oenum(tc_fun(X0,X1))
      | ~ class_Enum_Oenum(X0)
      | ~ class_Enum_Oenum(X1) ),
    inference(ennf_transformation,[],[f1824]) ).

fof(f1824,plain,
    ! [X0,X1] :
      ( ( class_Enum_Oenum(X0)
        & class_Enum_Oenum(X1) )
     => class_Enum_Oenum(tc_fun(X0,X1)) ),
    inference(rectify,[],[f1009]) ).

fof(f1009,axiom,
    ! [X95,X94] :
      ( ( class_Enum_Oenum(X95)
        & class_Enum_Oenum(X94) )
     => class_Enum_Oenum(tc_fun(X95,X94)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Enum_Oenum) ).

fof(f10613,plain,
    ( ~ spl24_148
    | spl24_205
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f10612,f7320,f7317,f10228,f9186]) ).

fof(f10612,plain,
    ( ! [X0] :
        ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f10611,f7321]) ).

fof(f10611,plain,
    ( ! [X0] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | 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) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f10610,f7318]) ).

fof(f10610,plain,
    ( ! [X0] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
        | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f8976,f7321]) ).

fof(f8976,plain,
    ( ! [X0] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
        | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f7422,f7318]) ).

fof(f7422,plain,
    ! [X0] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(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) ),
    inference(resolution,[],[f4658,f5094]) ).

fof(f10595,plain,
    ( ~ spl24_163
    | spl24_133
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f10594,f7320,f7317,f7107,f9358]) ).

fof(f10594,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | spl24_133
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f9054,f7321]) ).

fof(f9054,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | spl24_133
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f7109,f7318]) ).

fof(f7109,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | spl24_133 ),
    inference(avatar_component_clause,[],[f7107]) ).

fof(f10587,plain,
    ( spl24_162
    | spl24_161
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f10586,f7320,f7317,f9332,f9335]) ).

fof(f10586,plain,
    ( ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f8210,f7321]) ).

fof(f8210,plain,
    ( ! [X0,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_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(backward_demodulation,[],[f7825,f7318]) ).

fof(f7825,plain,
    ( ! [X0,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_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0),X1) )
    | ~ spl24_137 ),
    inference(backward_demodulation,[],[f4418,f7321]) ).

fof(f10576,plain,
    ( spl24_144
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f10575,f7320,f7317,f9145]) ).

fof(f10575,plain,
    ( ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f8843,f7321]) ).

fof(f8843,plain,
    ( ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f5755,f7318]) ).

fof(f10558,plain,
    ( spl24_219
    | spl24_86
    | spl24_220
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f10550,f7320,f7317,f10555,f6727,f10552]) ).

fof(f6727,plain,
    ( spl24_86
  <=> ! [X1] : ~ class_HOL_Oequal(X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_86])]) ).

fof(f10555,plain,
    ( spl24_220
  <=> class_HOL_Oequal(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_220])]) ).

fof(f10550,plain,
    ( ! [X0,X1] :
        ( class_HOL_Oequal(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ class_HOL_Oequal(X0)
        | ~ class_Enum_Oenum(X1) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f9064,f7321]) ).

fof(f9064,plain,
    ( ! [X0,X1] :
        ( class_HOL_Oequal(c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ class_Enum_Oenum(X1)
        | ~ class_HOL_Oequal(X0) )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f4724,f7318]) ).

fof(f4724,plain,
    ! [X0,X1] :
      ( class_HOL_Oequal(tc_fun(X1,X0))
      | ~ class_Enum_Oenum(X1)
      | ~ class_HOL_Oequal(X0) ),
    inference(cnf_transformation,[],[f3665]) ).

fof(f3665,plain,
    ! [X0,X1] :
      ( class_HOL_Oequal(tc_fun(X1,X0))
      | ~ class_Enum_Oenum(X1)
      | ~ class_HOL_Oequal(X0) ),
    inference(rectify,[],[f2741]) ).

fof(f2741,plain,
    ! [X1,X0] :
      ( class_HOL_Oequal(tc_fun(X0,X1))
      | ~ class_Enum_Oenum(X0)
      | ~ class_HOL_Oequal(X1) ),
    inference(flattening,[],[f2740]) ).

fof(f2740,plain,
    ! [X1,X0] :
      ( class_HOL_Oequal(tc_fun(X0,X1))
      | ~ class_HOL_Oequal(X1)
      | ~ class_Enum_Oenum(X0) ),
    inference(ennf_transformation,[],[f1246]) ).

fof(f1246,plain,
    ! [X1,X0] :
      ( ( class_HOL_Oequal(X1)
        & class_Enum_Oenum(X0) )
     => class_HOL_Oequal(tc_fun(X0,X1)) ),
    inference(rectify,[],[f1015]) ).

fof(f1015,axiom,
    ! [X95,X94] :
      ( ( class_Enum_Oenum(X95)
        & class_HOL_Oequal(X94) )
     => class_HOL_Oequal(tc_fun(X95,X94)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__HOL_Oequal) ).

fof(f10545,plain,
    ( spl24_195
    | spl24_218
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f10541,f7320,f7317,f10543,f9952]) ).

fof(f9952,plain,
    ( spl24_195
  <=> ! [X5,X3] :
        ( c_Groups_Ozero__class_Ozero(X5) = X3
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_195])]) ).

fof(f10543,plain,
    ( spl24_218
  <=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_218])]) ).

fof(f10541,plain,
    ( ! [X2,X0,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
        | c_Groups_Ozero__class_Ozero(X1) = X2 )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f8729,f7321]) ).

fof(f8729,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != X0
        | c_Groups_Ozero__class_Ozero(X1) = X2 )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f4466,f7318]) ).

fof(f4466,plain,
    ! [X2,X0,X1] :
      ( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
      | c_Groups_Oplus__class_Oplus(X1,X0,X2) != X0
      | c_Groups_Ozero__class_Ozero(X1) = X2 ),
    inference(cnf_transformation,[],[f3497]) ).

fof(f3497,plain,
    ! [X0,X1,X2] :
      ( ( ( c_Groups_Oplus__class_Oplus(X1,X0,X2) = X0
          | c_Groups_Ozero__class_Ozero(X1) != X2 )
        & ( c_Groups_Ozero__class_Ozero(X1) = X2
          | c_Groups_Oplus__class_Oplus(X1,X0,X2) != X0 ) )
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1) ),
    inference(nnf_transformation,[],[f2541]) ).

fof(f2541,plain,
    ! [X0,X1,X2] :
      ( ( c_Groups_Oplus__class_Oplus(X1,X0,X2) = X0
      <=> c_Groups_Ozero__class_Ozero(X1) = X2 )
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1) ),
    inference(ennf_transformation,[],[f1982]) ).

fof(f1982,plain,
    ! [X0,X2,X1] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
     => ( c_Groups_Oplus__class_Oplus(X1,X0,X2) = X0
      <=> c_Groups_Ozero__class_Ozero(X1) = X2 ) ),
    inference(rectify,[],[f82]) ).

fof(f82,axiom,
    ! [X10,X8,X7] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X8)
     => ( c_Groups_Oplus__class_Oplus(X8,X10,X7) = X10
      <=> c_Groups_Ozero__class_Ozero(X8) = X7 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__iff) ).

fof(f10536,plain,
    ( spl24_217
    | spl24_152
    | ~ spl24_136 ),
    inference(avatar_split_clause,[],[f10532,f7317,f9263,f10534]) ).

fof(f10534,plain,
    ( spl24_217
  <=> ! [X0] :
        ( ~ class_Rings_Oidom(X0)
        | ~ class_Int_Oring__char__0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_217])]) ).

fof(f10532,plain,
    ( ! [X2,X0,X1] :
        ( X1 = X2
        | ~ class_Rings_Oidom(X0)
        | ~ class_Int_Oring__char__0(X0) )
    | ~ spl24_136 ),
    inference(trivial_inequality_removal,[],[f10531]) ).

fof(f10531,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Rings_Oidom(X0)
        | ~ class_Int_Oring__char__0(X0)
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | X1 = X2 )
    | ~ spl24_136 ),
    inference(forward_demodulation,[],[f8694,f7318]) ).

fof(f8694,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Int_Oring__char__0(X0)
        | ~ class_Rings_Oidom(X0)
        | X1 = X2
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Polynomial_Opoly(X0,X2) )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f5825,f7318]) ).

fof(f5825,plain,
    ! [X2,X0,X1] :
      ( X1 = X2
      | c_Polynomial_Opoly(X0,X1) != c_Polynomial_Opoly(X0,X2)
      | ~ class_Rings_Oidom(X0)
      | ~ class_Int_Oring__char__0(X0) ),
    inference(cnf_transformation,[],[f4367]) ).

fof(f4367,plain,
    ! [X0,X1,X2] :
      ( ~ class_Int_Oring__char__0(X0)
      | ( ( c_Polynomial_Opoly(X0,X1) = c_Polynomial_Opoly(X0,X2)
          | X1 != X2 )
        & ( X1 = X2
          | c_Polynomial_Opoly(X0,X1) != c_Polynomial_Opoly(X0,X2) ) )
      | ~ class_Rings_Oidom(X0) ),
    inference(rectify,[],[f4366]) ).

fof(f4366,plain,
    ! [X2,X0,X1] :
      ( ~ class_Int_Oring__char__0(X2)
      | ( ( c_Polynomial_Opoly(X2,X0) = c_Polynomial_Opoly(X2,X1)
          | X0 != X1 )
        & ( X0 = X1
          | c_Polynomial_Opoly(X2,X0) != c_Polynomial_Opoly(X2,X1) ) )
      | ~ class_Rings_Oidom(X2) ),
    inference(nnf_transformation,[],[f2746]) ).

fof(f2746,plain,
    ! [X2,X0,X1] :
      ( ~ class_Int_Oring__char__0(X2)
      | ( c_Polynomial_Opoly(X2,X0) = c_Polynomial_Opoly(X2,X1)
      <=> X0 = X1 )
      | ~ class_Rings_Oidom(X2) ),
    inference(flattening,[],[f2745]) ).

fof(f2745,plain,
    ! [X2,X0,X1] :
      ( ( c_Polynomial_Opoly(X2,X0) = c_Polynomial_Opoly(X2,X1)
      <=> X0 = X1 )
      | ~ class_Int_Oring__char__0(X2)
      | ~ class_Rings_Oidom(X2) ),
    inference(ennf_transformation,[],[f1261]) ).

fof(f1261,plain,
    ! [X2,X0,X1] :
      ( ( class_Int_Oring__char__0(X2)
        & class_Rings_Oidom(X2) )
     => ( c_Polynomial_Opoly(X2,X0) = c_Polynomial_Opoly(X2,X1)
      <=> X0 = X1 ) ),
    inference(rectify,[],[f34]) ).

fof(f34,axiom,
    ! [X9,X6,X8] :
      ( ( class_Int_Oring__char__0(X8)
        & class_Rings_Oidom(X8) )
     => ( c_Polynomial_Opoly(X8,X6) = c_Polynomial_Opoly(X8,X9)
      <=> X6 = X9 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__eq__iff) ).

fof(f10525,plain,
    ( spl24_144
    | spl24_203
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f10524,f7320,f7317,f10157,f9145]) ).

fof(f10157,plain,
    ( spl24_203
  <=> ! [X1] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_203])]) ).

fof(f10524,plain,
    ( ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f8216,f7321]) ).

fof(f8216,plain,
    ( ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(backward_demodulation,[],[f7991,f7318]) ).

fof(f7991,plain,
    ( ! [X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) )
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f7921,f7321]) ).

fof(f7921,plain,
    ( ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) )
    | ~ spl24_137 ),
    inference(backward_demodulation,[],[f6976,f7321]) ).

fof(f6976,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)) ),
    inference(forward_demodulation,[],[f6975,f5628]) ).

fof(f6975,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) ),
    inference(forward_demodulation,[],[f6974,f4806]) ).

fof(f6974,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)) ),
    inference(forward_demodulation,[],[f6973,f5628]) ).

fof(f6973,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),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)),X1)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)) ),
    inference(forward_demodulation,[],[f5917,f4806]) ).

fof(f5917,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ),
    inference(definition_unfolding,[],[f4966,f4877,f4877]) ).

fof(f4966,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0) ),
    inference(cnf_transformation,[],[f3823]) ).

fof(f3823,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0) ),
    inference(rectify,[],[f3432]) ).

fof(f3432,plain,
    ! [X1,X0] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ),
    inference(flattening,[],[f3431]) ).

fof(f3431,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ),
    inference(ennf_transformation,[],[f1713]) ).

fof(f1713,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ) ),
    inference(rectify,[],[f606]) ).

fof(f606,axiom,
    ! [X23,X17] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X23)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__less__n__mult__m) ).

fof(f10505,plain,
    ( spl24_215
    | spl24_216
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f10498,f7320,f7317,f10503,f10500]) ).

fof(f10500,plain,
    ( spl24_215
  <=> ! [X2] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_215])]) ).

fof(f10503,plain,
    ( spl24_216
  <=> ! [X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_216])]) ).

fof(f10498,plain,
    ( ! [X2,X0,X1] :
        ( ~ 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_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f10497,f7321]) ).

fof(f10497,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f10496,f7321]) ).

fof(f10496,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != X0
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) )
    | ~ spl24_136 ),
    inference(forward_demodulation,[],[f10495,f7318]) ).

fof(f10495,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
        | c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X0
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) )
    | ~ spl24_136 ),
    inference(forward_demodulation,[],[f8241,f7318]) ).

fof(f8241,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2)
        | c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X0
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f5485,f7318]) ).

fof(f10485,plain,
    ( spl24_152
    | spl24_214
    | ~ spl24_136 ),
    inference(avatar_split_clause,[],[f10481,f7317,f10483,f9263]) ).

fof(f10483,plain,
    ( spl24_214
  <=> ! [X3] : ~ class_Groups_Ocancel__ab__semigroup__add(X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_214])]) ).

fof(f10481,plain,
    ( ! [X2,X3,X1] :
        ( ~ class_Groups_Ocancel__ab__semigroup__add(X3)
        | X1 = X2 )
    | ~ spl24_136 ),
    inference(trivial_inequality_removal,[],[f10480]) ).

fof(f10480,plain,
    ( ! [X2,X3,X1] :
        ( ~ class_Groups_Ocancel__ab__semigroup__add(X3)
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | X1 = X2 )
    | ~ spl24_136 ),
    inference(forward_demodulation,[],[f8771,f7318]) ).

fof(f8771,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ class_Groups_Ocancel__ab__semigroup__add(X3)
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(X3,X0,X2)
        | X1 = X2 )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f5625,f7318]) ).

fof(f5625,plain,
    ! [X2,X3,X0,X1] :
      ( ~ class_Groups_Ocancel__ab__semigroup__add(X3)
      | c_Groups_Oplus__class_Oplus(X3,X0,X1) != c_Groups_Oplus__class_Oplus(X3,X0,X2)
      | X1 = X2 ),
    inference(cnf_transformation,[],[f4230]) ).

fof(f4230,plain,
    ! [X0,X1,X2,X3] :
      ( c_Groups_Oplus__class_Oplus(X3,X0,X1) != c_Groups_Oplus__class_Oplus(X3,X0,X2)
      | X1 = X2
      | ~ class_Groups_Ocancel__ab__semigroup__add(X3) ),
    inference(rectify,[],[f2518]) ).

fof(f2518,plain,
    ! [X0,X2,X3,X1] :
      ( c_Groups_Oplus__class_Oplus(X1,X0,X2) != c_Groups_Oplus__class_Oplus(X1,X0,X3)
      | X2 = X3
      | ~ class_Groups_Ocancel__ab__semigroup__add(X1) ),
    inference(flattening,[],[f2517]) ).

fof(f2517,plain,
    ! [X0,X3,X2,X1] :
      ( X2 = X3
      | c_Groups_Oplus__class_Oplus(X1,X0,X2) != c_Groups_Oplus__class_Oplus(X1,X0,X3)
      | ~ class_Groups_Ocancel__ab__semigroup__add(X1) ),
    inference(ennf_transformation,[],[f1477]) ).

fof(f1477,plain,
    ! [X0,X3,X2,X1] :
      ( class_Groups_Ocancel__ab__semigroup__add(X1)
     => ( c_Groups_Oplus__class_Oplus(X1,X0,X2) = c_Groups_Oplus__class_Oplus(X1,X0,X3)
       => X2 = X3 ) ),
    inference(rectify,[],[f54]) ).

fof(f54,axiom,
    ! [X5,X4,X29,X22] :
      ( class_Groups_Ocancel__ab__semigroup__add(X4)
     => ( c_Groups_Oplus__class_Oplus(X4,X5,X29) = c_Groups_Oplus__class_Oplus(X4,X5,X22)
       => X22 = X29 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__imp__eq) ).

fof(f10446,plain,
    ( ~ spl24_213
    | spl24_14
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f10441,f7320,f7317,f6272,f10443]) ).

fof(f10441,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)
    | spl24_14
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f8665,f7321]) ).

fof(f8665,plain,
    ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)
    | spl24_14
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f6274,f7318]) ).

fof(f6274,plain,
    ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
    | spl24_14 ),
    inference(avatar_component_clause,[],[f6272]) ).

fof(f10429,plain,
    ( spl24_153
    | spl24_212
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f10425,f7320,f7317,f10427,f9279]) ).

fof(f10427,plain,
    ( spl24_212
  <=> ! [X0] :
        ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_212])]) ).

fof(f10425,plain,
    ( ! [X0] :
        ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f8955,f7321]) ).

fof(f8955,plain,
    ( ! [X0] :
        ( ~ 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,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f7687,f7318]) ).

fof(f7687,plain,
    ! [X0] :
      ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(resolution,[],[f6872,f5693]) ).

fof(f10410,plain,
    ( spl24_210
    | spl24_211
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f10402,f7320,f7317,f10408,f10404]) ).

fof(f10404,plain,
    ( spl24_210
  <=> class_Orderings_Oorder(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_210])]) ).

fof(f10408,plain,
    ( spl24_211
  <=> ! [X1] : ~ class_Orderings_Oorder(X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_211])]) ).

fof(f10402,plain,
    ( ! [X1] :
        ( ~ class_Orderings_Oorder(X1)
        | class_Orderings_Oorder(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f9068,f7321]) ).

fof(f9068,plain,
    ( ! [X1] :
        ( ~ class_Orderings_Oorder(X1)
        | class_Orderings_Oorder(c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f5020,f7318]) ).

fof(f5020,plain,
    ! [X0,X1] :
      ( class_Orderings_Oorder(tc_fun(X0,X1))
      | ~ class_Orderings_Oorder(X1) ),
    inference(cnf_transformation,[],[f2849]) ).

fof(f2849,plain,
    ! [X0,X1] :
      ( ~ class_Orderings_Oorder(X1)
      | class_Orderings_Oorder(tc_fun(X0,X1)) ),
    inference(ennf_transformation,[],[f1376]) ).

fof(f1376,plain,
    ! [X1,X0] :
      ( class_Orderings_Oorder(X1)
     => class_Orderings_Oorder(tc_fun(X0,X1)) ),
    inference(rectify,[],[f1012]) ).

fof(f1012,axiom,
    ! [X95,X94] :
      ( class_Orderings_Oorder(X94)
     => class_Orderings_Oorder(tc_fun(X95,X94)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oorder) ).

fof(f10388,plain,
    ( spl24_183
    | spl24_209
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f10384,f7320,f7317,f10386,f9723]) ).

fof(f9723,plain,
    ( spl24_183
  <=> ! [X0] : ~ class_Orderings_Oord(X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_183])]) ).

fof(f10386,plain,
    ( spl24_209
  <=> ! [X2,X1] :
        ( c_Orderings_Oord__class_Oless(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1,X2)
        | ~ c_Orderings_Oord__class_Oless__eq(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1,X2)
        | c_Orderings_Oord__class_Oless__eq(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_209])]) ).

fof(f10384,plain,
    ( ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1,X2)
        | c_Orderings_Oord__class_Oless__eq(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2,X1)
        | ~ c_Orderings_Oord__class_Oless__eq(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1,X2)
        | ~ class_Orderings_Oord(X0) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f10383,f7321]) ).

fof(f10383,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Orderings_Oord(X0)
        | c_Orderings_Oord__class_Oless__eq(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2,X1)
        | c_Orderings_Oord__class_Oless(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1,X2)
        | ~ c_Orderings_Oord__class_Oless__eq(c_Groups_Oone__class_Oone(tc_Nat_Onat),X1,X2) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f10382,f7321]) ).

fof(f10382,plain,
    ( ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1,X2)
        | ~ class_Orderings_Oord(X0)
        | c_Orderings_Oord__class_Oless__eq(c_Groups_Oone__class_Oone(tc_Nat_Onat),X2,X1)
        | ~ c_Orderings_Oord__class_Oless__eq(c_Groups_Oone__class_Oone(tc_Nat_Onat),X1,X2) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f10381,f7318]) ).

fof(f10381,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ class_Orderings_Oord(X0)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,X0),X1,X2)
        | c_Orderings_Oord__class_Oless__eq(c_Groups_Oone__class_Oone(tc_Nat_Onat),X2,X1)
        | c_Orderings_Oord__class_Oless(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1,X2) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f10380,f7321]) ).

fof(f10380,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_Orderings_Oord__class_Oless(c_Groups_Oone__class_Oone(tc_Nat_Onat),X1,X2)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,X0),X1,X2)
        | c_Orderings_Oord__class_Oless__eq(c_Groups_Oone__class_Oone(tc_Nat_Onat),X2,X1)
        | ~ class_Orderings_Oord(X0) )
    | ~ spl24_136 ),
    inference(forward_demodulation,[],[f9065,f7318]) ).

fof(f9065,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ class_Orderings_Oord(X0)
        | c_Orderings_Oord__class_Oless(tc_fun(X3,X0),X1,X2)
        | c_Orderings_Oord__class_Oless__eq(c_Groups_Oone__class_Oone(tc_Nat_Onat),X2,X1)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,X0),X1,X2) )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f4773,f7318]) ).

fof(f4773,plain,
    ! [X2,X3,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,X0),X2,X1)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,X0),X1,X2)
      | c_Orderings_Oord__class_Oless(tc_fun(X3,X0),X1,X2)
      | ~ class_Orderings_Oord(X0) ),
    inference(cnf_transformation,[],[f3699]) ).

fof(f3699,plain,
    ! [X0,X1,X2,X3] :
      ( ~ class_Orderings_Oord(X0)
      | ( ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,X0),X2,X1)
            & c_Orderings_Oord__class_Oless__eq(tc_fun(X3,X0),X1,X2) )
          | ~ c_Orderings_Oord__class_Oless(tc_fun(X3,X0),X1,X2) )
        & ( c_Orderings_Oord__class_Oless(tc_fun(X3,X0),X1,X2)
          | c_Orderings_Oord__class_Oless__eq(tc_fun(X3,X0),X2,X1)
          | ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,X0),X1,X2) ) ) ),
    inference(rectify,[],[f3698]) ).

fof(f3698,plain,
    ! [X1,X2,X0,X3] :
      ( ~ class_Orderings_Oord(X1)
      | ( ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,X1),X0,X2)
            & c_Orderings_Oord__class_Oless__eq(tc_fun(X3,X1),X2,X0) )
          | ~ c_Orderings_Oord__class_Oless(tc_fun(X3,X1),X2,X0) )
        & ( c_Orderings_Oord__class_Oless(tc_fun(X3,X1),X2,X0)
          | c_Orderings_Oord__class_Oless__eq(tc_fun(X3,X1),X0,X2)
          | ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,X1),X2,X0) ) ) ),
    inference(flattening,[],[f3697]) ).

fof(f3697,plain,
    ! [X1,X2,X0,X3] :
      ( ~ class_Orderings_Oord(X1)
      | ( ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,X1),X0,X2)
            & c_Orderings_Oord__class_Oless__eq(tc_fun(X3,X1),X2,X0) )
          | ~ c_Orderings_Oord__class_Oless(tc_fun(X3,X1),X2,X0) )
        & ( c_Orderings_Oord__class_Oless(tc_fun(X3,X1),X2,X0)
          | c_Orderings_Oord__class_Oless__eq(tc_fun(X3,X1),X0,X2)
          | ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,X1),X2,X0) ) ) ),
    inference(nnf_transformation,[],[f3447]) ).

fof(f3447,plain,
    ! [X1,X2,X0,X3] :
      ( ~ class_Orderings_Oord(X1)
      | ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,X1),X0,X2)
          & c_Orderings_Oord__class_Oless__eq(tc_fun(X3,X1),X2,X0) )
      <=> c_Orderings_Oord__class_Oless(tc_fun(X3,X1),X2,X0) ) ),
    inference(ennf_transformation,[],[f2103]) ).

fof(f2103,plain,
    ! [X3,X2,X1,X0] :
      ( class_Orderings_Oord(X1)
     => ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,X1),X0,X2)
          & c_Orderings_Oord__class_Oless__eq(tc_fun(X3,X1),X2,X0) )
      <=> c_Orderings_Oord__class_Oless(tc_fun(X3,X1),X2,X0) ) ),
    inference(rectify,[],[f620]) ).

fof(f620,axiom,
    ! [X0,X12,X1,X8] :
      ( class_Orderings_Oord(X12)
     => ( c_Orderings_Oord__class_Oless(tc_fun(X8,X12),X1,X0)
      <=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X8,X12),X0,X1)
          & c_Orderings_Oord__class_Oless__eq(tc_fun(X8,X12),X1,X0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__fun__def) ).

fof(f10360,plain,
    ( spl24_143
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f10359,f7320,f7317,f9142]) ).

fof(f10359,plain,
    ( ! [X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f8903,f7321]) ).

fof(f8903,plain,
    ( ! [X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(backward_demodulation,[],[f8007,f7318]) ).

fof(f8007,plain,
    ( ! [X0,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f7889,f5628]) ).

fof(f7889,plain,
    ( ! [X0,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)))
    | ~ spl24_137 ),
    inference(backward_demodulation,[],[f5993,f7321]) ).

fof(f10317,plain,
    ( spl24_183
    | spl24_208
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f10313,f7320,f7317,f10315,f9723]) ).

fof(f10315,plain,
    ( spl24_208
  <=> ! [X2,X1] :
        ( ~ c_Orderings_Oord__class_Oless(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1,X2)
        | ~ c_Orderings_Oord__class_Oless__eq(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_208])]) ).

fof(f10313,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1,X2)
        | ~ c_Orderings_Oord__class_Oless__eq(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2,X1)
        | ~ class_Orderings_Oord(X0) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f10312,f7321]) ).

fof(f10312,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless(c_Groups_Oone__class_Oone(tc_Nat_Onat),X1,X2)
        | ~ c_Orderings_Oord__class_Oless__eq(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2,X1)
        | ~ class_Orderings_Oord(X0) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f10311,f7318]) ).

fof(f10311,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless__eq(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2,X1)
        | ~ c_Orderings_Oord__class_Oless(tc_fun(X3,X0),X1,X2)
        | ~ class_Orderings_Oord(X0) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f9067,f7321]) ).

fof(f9067,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless__eq(c_Groups_Oone__class_Oone(tc_Nat_Onat),X2,X1)
        | ~ class_Orderings_Oord(X0)
        | ~ c_Orderings_Oord__class_Oless(tc_fun(X3,X0),X1,X2) )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f4775,f7318]) ).

fof(f4775,plain,
    ! [X2,X3,X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(tc_fun(X3,X0),X1,X2)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,X0),X2,X1)
      | ~ class_Orderings_Oord(X0) ),
    inference(cnf_transformation,[],[f3699]) ).

fof(f10296,plain,
    ( spl24_144
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f10295,f7320,f7317,f9145]) ).

fof(f10295,plain,
    ( ! [X27] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X27)
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f10294,f7321]) ).

fof(f10294,plain,
    ( ! [X27] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X27)
    | ~ spl24_136 ),
    inference(forward_demodulation,[],[f8870,f7318]) ).

fof(f8870,plain,
    ( ! [X27,X25] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X25,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X27)
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f7403,f7318]) ).

fof(f10281,plain,
    ( spl24_161
    | spl24_194
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f10280,f7320,f7317,f9939,f9332]) ).

fof(f10280,plain,
    ( ! [X48,X47] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X48,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X47 )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f8884,f7321]) ).

fof(f8884,plain,
    ( ! [X48,X47] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X48,c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X47 )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f7502,f7318]) ).

fof(f7502,plain,
    ! [X48,X49,X47] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X48,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X47,X49))
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X47 ),
    inference(superposition,[],[f5474,f5318]) ).

fof(f5474,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) = X1 ),
    inference(cnf_transformation,[],[f4126]) ).

fof(f10266,plain,
    ( ~ spl24_148
    | spl24_189
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f10265,f7320,f7317,f9848,f9186]) ).

fof(f10265,plain,
    ( ! [X0] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f10264,f7321]) ).

fof(f10264,plain,
    ( ! [X0] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f10263,f7318]) ).

fof(f10263,plain,
    ( ! [X0] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f8973,f7321]) ).

fof(f8973,plain,
    ( ! [X0] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f7266,f7318]) ).

fof(f7266,plain,
    ! [X0] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
    inference(resolution,[],[f5679,f5094]) ).

fof(f10256,plain,
    ( spl24_197
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f10255,f7320,f7317,f9979]) ).

fof(f9979,plain,
    ( spl24_197
  <=> ! [X2,X1,X3] :
        ( ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X3)
        | ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
        | X1 = X3
        | ~ class_Rings_Olinordered__semidom(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_197])]) ).

fof(f10255,plain,
    ( ! [X2,X3,X0] :
        ( ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
        | X0 = X2
        | ~ class_Rings_Olinordered__semidom(X3)
        | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(trivial_inequality_removal,[],[f10254]) ).

fof(f10254,plain,
    ( ! [X2,X3,X0] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | X0 = X2
        | ~ class_Rings_Olinordered__semidom(X3)
        | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
        | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f8508,f7318]) ).

fof(f8508,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1)
        | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
        | ~ class_Rings_Olinordered__semidom(X3)
        | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
        | X0 = X2 )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(backward_demodulation,[],[f7956,f7318]) ).

fof(f7956,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ class_Rings_Olinordered__semidom(X3)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1) != hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1)
        | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
        | X0 = X2
        | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2) )
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f7855,f5628]) ).

fof(f7855,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ class_Rings_Olinordered__semidom(X3)
        | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)) != hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1))
        | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
        | X0 = X2 )
    | ~ spl24_137 ),
    inference(backward_demodulation,[],[f5908,f7321]) ).

fof(f5908,plain,
    ! [X2,X3,X0,X1] :
      ( ~ class_Rings_Olinordered__semidom(X3)
      | X0 = X2
      | hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)) != hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1))
      | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
      | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0) ),
    inference(definition_unfolding,[],[f4880,f4877,f4877]) ).

fof(f4880,plain,
    ! [X2,X3,X0,X1] :
      ( X0 = X2
      | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),c_Nat_OSuc(X1)) != hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),c_Nat_OSuc(X1))
      | ~ class_Rings_Olinordered__semidom(X3)
      | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0) ),
    inference(cnf_transformation,[],[f3768]) ).

fof(f3768,plain,
    ! [X0,X1,X2,X3] :
      ( X0 = X2
      | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),c_Nat_OSuc(X1)) != hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),c_Nat_OSuc(X1))
      | ~ class_Rings_Olinordered__semidom(X3)
      | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0) ),
    inference(rectify,[],[f2680]) ).

fof(f2680,plain,
    ! [X3,X1,X2,X0] :
      ( X2 = X3
      | ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X2)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),c_Nat_OSuc(X1)) != hAPP(hAPP(c_Power_Opower__class_Opower(X0),X3),c_Nat_OSuc(X1))
      | ~ class_Rings_Olinordered__semidom(X0)
      | ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X3) ),
    inference(flattening,[],[f2679]) ).

fof(f2679,plain,
    ! [X2,X1,X0,X3] :
      ( X2 = X3
      | ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X2)
      | ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X3)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),c_Nat_OSuc(X1)) != hAPP(hAPP(c_Power_Opower__class_Opower(X0),X3),c_Nat_OSuc(X1))
      | ~ class_Rings_Olinordered__semidom(X0) ),
    inference(ennf_transformation,[],[f1320]) ).

fof(f1320,plain,
    ! [X2,X1,X0,X3] :
      ( class_Rings_Olinordered__semidom(X0)
     => ( hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),c_Nat_OSuc(X1)) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),X3),c_Nat_OSuc(X1))
       => ( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X3)
         => ( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X2)
           => X2 = X3 ) ) ) ),
    inference(rectify,[],[f745]) ).

fof(f745,axiom,
    ! [X4,X17,X29,X5] :
      ( class_Rings_Olinordered__semidom(X4)
     => ( hAPP(hAPP(c_Power_Opower__class_Opower(X4),X5),c_Nat_OSuc(X17)) = hAPP(hAPP(c_Power_Opower__class_Opower(X4),X29),c_Nat_OSuc(X17))
       => ( c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X5)
         => ( c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X29)
           => X5 = X29 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__inject__base) ).

fof(f10246,plain,
    ( spl24_153
    | spl24_164
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f10245,f7320,f7317,f9362,f9279]) ).

fof(f9362,plain,
    ( spl24_164
  <=> ! [X1] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_164])]) ).

fof(f10245,plain,
    ( ! [X0] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f8952,f7321]) ).

fof(f8952,plain,
    ( ! [X0] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f6872,f7318]) ).

fof(f10244,plain,
    ( spl24_206
    | spl24_207
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f10237,f7320,f7317,f10242,f10239]) ).

fof(f10239,plain,
    ( spl24_206
  <=> ! [X4,X3] : ~ c_Orderings_Oord__class_Oless__eq(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3,X4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_206])]) ).

fof(f10242,plain,
    ( spl24_207
  <=> ! [X0] :
        ( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ class_Orderings_Oord(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_207])]) ).

fof(f10237,plain,
    ( ! [X3,X0,X4] :
        ( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ class_Orderings_Oord(X0)
        | ~ c_Orderings_Oord__class_Oless__eq(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3,X4) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f10236,f7321]) ).

fof(f10236,plain,
    ( ! [X3,X0,X4] :
        ( ~ c_Orderings_Oord__class_Oless__eq(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3,X4)
        | c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ class_Orderings_Oord(X0) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f10235,f7318]) ).

fof(f10235,plain,
    ( ! [X2,X3,X0,X4] :
        ( c_Orderings_Oord__class_Oless__eq(X0,hAPP(X3,X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ c_Orderings_Oord__class_Oless__eq(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3,X4)
        | ~ class_Orderings_Oord(X0) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f10234,f7321]) ).

fof(f10234,plain,
    ( ! [X2,X3,X0,X4] :
        ( c_Orderings_Oord__class_Oless__eq(X0,hAPP(X3,X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ c_Orderings_Oord__class_Oless__eq(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3,X4)
        | ~ class_Orderings_Oord(X0) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f10233,f7321]) ).

fof(f10233,plain,
    ( ! [X2,X3,X0,X4] :
        ( ~ c_Orderings_Oord__class_Oless__eq(c_Groups_Oone__class_Oone(tc_Nat_Onat),X3,X4)
        | ~ class_Orderings_Oord(X0)
        | c_Orderings_Oord__class_Oless__eq(X0,hAPP(X3,X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
    | ~ spl24_136 ),
    inference(forward_demodulation,[],[f8061,f7318]) ).

fof(f8061,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X0),X3,X4)
        | c_Orderings_Oord__class_Oless__eq(X0,hAPP(X3,X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ class_Orderings_Oord(X0) )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f5466,f7318]) ).

fof(f5466,plain,
    ! [X2,X3,X0,X1,X4] :
      ( c_Orderings_Oord__class_Oless__eq(X0,hAPP(X3,X2),hAPP(X4,X2))
      | ~ class_Orderings_Oord(X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X0),X3,X4) ),
    inference(cnf_transformation,[],[f4120]) ).

fof(f4120,plain,
    ! [X0,X1,X2,X3,X4] :
      ( c_Orderings_Oord__class_Oless__eq(X0,hAPP(X3,X2),hAPP(X4,X2))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X0),X3,X4)
      | ~ class_Orderings_Oord(X0) ),
    inference(rectify,[],[f2892]) ).

fof(f2892,plain,
    ! [X1,X0,X3,X2,X4] :
      ( c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X3),hAPP(X4,X3))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X0,X1),X2,X4)
      | ~ class_Orderings_Oord(X1) ),
    inference(flattening,[],[f2891]) ).

fof(f2891,plain,
    ! [X4,X3,X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X3),hAPP(X4,X3))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X0,X1),X2,X4)
      | ~ class_Orderings_Oord(X1) ),
    inference(ennf_transformation,[],[f1823]) ).

fof(f1823,plain,
    ! [X4,X3,X2,X0,X1] :
      ( class_Orderings_Oord(X1)
     => ( c_Orderings_Oord__class_Oless__eq(tc_fun(X0,X1),X2,X4)
       => c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X3),hAPP(X4,X3)) ) ),
    inference(rectify,[],[f359]) ).

fof(f359,axiom,
    ! [X8,X12,X1,X13,X0] :
      ( class_Orderings_Oord(X12)
     => ( c_Orderings_Oord__class_Oless__eq(tc_fun(X8,X12),X1,X0)
       => c_Orderings_Oord__class_Oless__eq(X12,hAPP(X1,X13),hAPP(X0,X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__funD) ).

fof(f10230,plain,
    ( spl24_163
    | spl24_205
    | spl24_177
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f10226,f7320,f7317,f9552,f10228,f9358]) ).

fof(f9552,plain,
    ( spl24_177
  <=> hBOOL(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_177])]) ).

fof(f10226,plain,
    ( ! [X1] :
        ( hBOOL(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X1
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f10225,f7321]) ).

fof(f10225,plain,
    ( ! [X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X1
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
        | hBOOL(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f10224,f7321]) ).

fof(f10224,plain,
    ( ! [X1] :
        ( hBOOL(c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X1
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) )
    | ~ spl24_136 ),
    inference(forward_demodulation,[],[f8103,f7318]) ).

fof(f8103,plain,
    ( ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK11(X0,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | hBOOL(c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
        | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X1 )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f5181,f7318]) ).

fof(f5181,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
      | hBOOL(hAPP(X0,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))
      | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X1
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK11(X0,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(cnf_transformation,[],[f3944]) ).

fof(f3944,plain,
    ! [X0,X1,X2] :
      ( ( hBOOL(hAPP(X0,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))
        | ( ~ hBOOL(hAPP(X0,X2))
          & c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X1 )
        | ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
          & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sK8(X0,X1,X2))
          & c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),sK9(X0,X1,X2)),sK8(X0,X1,X2)) = X2
          & c_Orderings_Oord__class_Oless(tc_Int_Oint,sK8(X0,X1,X2),X1)
          & ~ hBOOL(hAPP(X0,sK8(X0,X1,X2))) )
        | ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,sK11(X0,X1,X2))
          & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK11(X0,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
          & ~ hBOOL(hAPP(X0,sK11(X0,X1,X2)))
          & c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),sK10(X0,X1,X2)),sK11(X0,X1,X2)) = X2
          & c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) )
      & ( ( ( hBOOL(hAPP(X0,X2))
            | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X1 )
          & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
            | ! [X7,X8] :
                ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X7)
                | c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X8),X7) != X2
                | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X7,X1)
                | hBOOL(hAPP(X0,X7)) ) )
          & ( ! [X9,X10] :
                ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X10)
                | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X10,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
                | hBOOL(hAPP(X0,X10))
                | c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X9),X10) != X2 )
            | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) )
        | ~ hBOOL(hAPP(X0,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1))) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11])],[f3941,f3943,f3942]) ).

fof(f3942,plain,
    ! [X0,X1,X2] :
      ( ? [X3,X4] :
          ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
          & c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X4),X3) = X2
          & c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X1)
          & ~ hBOOL(hAPP(X0,X3)) )
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sK8(X0,X1,X2))
        & c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),sK9(X0,X1,X2)),sK8(X0,X1,X2)) = X2
        & c_Orderings_Oord__class_Oless(tc_Int_Oint,sK8(X0,X1,X2),X1)
        & ~ hBOOL(hAPP(X0,sK8(X0,X1,X2))) ) ),
    introduced(choice_axiom,[]) ).

fof(f3943,plain,
    ! [X0,X1,X2] :
      ( ? [X5,X6] :
          ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X6)
          & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X6,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
          & ~ hBOOL(hAPP(X0,X6))
          & c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X5),X6) = X2 )
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,sK11(X0,X1,X2))
        & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK11(X0,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        & ~ hBOOL(hAPP(X0,sK11(X0,X1,X2)))
        & c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),sK10(X0,X1,X2)),sK11(X0,X1,X2)) = X2 ) ),
    introduced(choice_axiom,[]) ).

fof(f3941,plain,
    ! [X0,X1,X2] :
      ( ( hBOOL(hAPP(X0,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))
        | ( ~ hBOOL(hAPP(X0,X2))
          & c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X1 )
        | ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
          & ? [X3,X4] :
              ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
              & c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X4),X3) = X2
              & c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X1)
              & ~ hBOOL(hAPP(X0,X3)) ) )
        | ( ? [X5,X6] :
              ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X6)
              & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X6,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
              & ~ hBOOL(hAPP(X0,X6))
              & c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X5),X6) = X2 )
          & c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) )
      & ( ( ( hBOOL(hAPP(X0,X2))
            | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X1 )
          & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
            | ! [X7,X8] :
                ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X7)
                | c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X8),X7) != X2
                | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X7,X1)
                | hBOOL(hAPP(X0,X7)) ) )
          & ( ! [X9,X10] :
                ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X10)
                | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X10,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
                | hBOOL(hAPP(X0,X10))
                | c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X9),X10) != X2 )
            | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) )
        | ~ hBOOL(hAPP(X0,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1))) ) ),
    inference(rectify,[],[f3940]) ).

fof(f3940,plain,
    ! [X0,X2,X1] :
      ( ( hBOOL(hAPP(X0,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)))
        | ( ~ hBOOL(hAPP(X0,X1))
          & c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X2 )
        | ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
          & ? [X5,X6] :
              ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
              & c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X6),X5) = X1
              & c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X2)
              & ~ hBOOL(hAPP(X0,X5)) ) )
        | ( ? [X3,X4] :
              ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X4)
              & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
              & ~ hBOOL(hAPP(X0,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,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) )
      & ( ( ( hBOOL(hAPP(X0,X1))
            | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X2 )
          & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
            | ! [X5,X6] :
                ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
                | c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X6),X5) != X1
                | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X2)
                | hBOOL(hAPP(X0,X5)) ) )
          & ( ! [X3,X4] :
                ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X4)
                | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
                | hBOOL(hAPP(X0,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,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) )
        | ~ hBOOL(hAPP(X0,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2))) ) ),
    inference(flattening,[],[f3939]) ).

fof(f3939,plain,
    ! [X0,X2,X1] :
      ( ( hBOOL(hAPP(X0,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)))
        | ( ~ hBOOL(hAPP(X0,X1))
          & c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X2 )
        | ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
          & ? [X5,X6] :
              ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
              & c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X6),X5) = X1
              & c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X2)
              & ~ hBOOL(hAPP(X0,X5)) ) )
        | ( ? [X3,X4] :
              ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X4)
              & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
              & ~ hBOOL(hAPP(X0,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,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) )
      & ( ( ( hBOOL(hAPP(X0,X1))
            | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X2 )
          & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
            | ! [X5,X6] :
                ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
                | c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X6),X5) != X1
                | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X2)
                | hBOOL(hAPP(X0,X5)) ) )
          & ( ! [X3,X4] :
                ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X4)
                | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
                | hBOOL(hAPP(X0,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,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) )
        | ~ hBOOL(hAPP(X0,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2))) ) ),
    inference(nnf_transformation,[],[f2723]) ).

fof(f2723,plain,
    ! [X0,X2,X1] :
      ( hBOOL(hAPP(X0,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)))
    <=> ( ( hBOOL(hAPP(X0,X1))
          | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X2 )
        & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
          | ! [X5,X6] :
              ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
              | c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X6),X5) != X1
              | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X2)
              | hBOOL(hAPP(X0,X5)) ) )
        & ( ! [X3,X4] :
              ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X4)
              | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
              | hBOOL(hAPP(X0,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,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) ),
    inference(flattening,[],[f2722]) ).

fof(f2722,plain,
    ! [X1,X0,X2] :
      ( ( ( ! [X4,X3] :
              ( hBOOL(hAPP(X0,X4))
              | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
              | 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,X2,X4) )
          | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
        & ( hBOOL(hAPP(X0,X1))
          | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X2 )
        & ( ! [X6,X5] :
              ( hBOOL(hAPP(X0,X5))
              | c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X6),X5) != X1
              | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X2)
              | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5) )
          | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ) )
    <=> hBOOL(hAPP(X0,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2))) ),
    inference(ennf_transformation,[],[f1482]) ).

fof(f1482,plain,
    ! [X1,X0,X2] :
      ( ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
         => ! [X4,X3] :
              ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
                & 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,X2,X4) )
             => hBOOL(hAPP(X0,X4)) ) )
        & ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X2
         => hBOOL(hAPP(X0,X1)) )
        & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
         => ! [X6,X5] :
              ( ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X6),X5) = X1
                & c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X2)
                & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5) )
             => hBOOL(hAPP(X0,X5)) ) ) )
    <=> hBOOL(hAPP(X0,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2))) ),
    inference(rectify,[],[f926]) ).

fof(f926,axiom,
    ! [X14,X18,X44] :
      ( hBOOL(hAPP(X14,c_Divides_Odiv__class_Omod(tc_Int_Oint,X18,X44)))
    <=> ( ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X44
         => hBOOL(hAPP(X14,X18)) )
        & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X44,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
         => ! [X80,X64] :
              ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X44,X64)
                & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X64,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
                & c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X44),X80),X64) = X18 )
             => hBOOL(hAPP(X14,X64)) ) )
        & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X44)
         => ! [X64,X80] :
              ( ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X44),X80),X64) = X18
                & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X64)
                & c_Orderings_Oord__class_Oless(tc_Int_Oint,X64,X44) )
             => hBOOL(hAPP(X14,X64)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__zmod) ).

fof(f10199,plain,
    ( spl24_177
    | ~ spl24_87
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f10198,f7320,f7317,f6730,f9552]) ).

fof(f6730,plain,
    ( spl24_87
  <=> ! [X0] : hBOOL(hAPP(hAPP(c_fequal,X0),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_87])]) ).

fof(f10198,plain,
    ( hBOOL(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ spl24_87
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f8139,f7321]) ).

fof(f8139,plain,
    ( hBOOL(c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ spl24_87
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f6731,f7318]) ).

fof(f6731,plain,
    ( ! [X0] : hBOOL(hAPP(hAPP(c_fequal,X0),X0))
    | ~ spl24_87 ),
    inference(avatar_component_clause,[],[f6730]) ).

fof(f10168,plain,
    ( spl24_177
    | spl24_163
    | spl24_204
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f10164,f7320,f7317,f10166,f9358,f9552]) ).

fof(f10166,plain,
    ( spl24_204
  <=> ! [X1] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
        | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_204])]) ).

fof(f10164,plain,
    ( ! [X1] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X1
        | hBOOL(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f10163,f7321]) ).

fof(f10163,plain,
    ( ! [X1] :
        ( hBOOL(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
        | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X1 )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f10162,f7318]) ).

fof(f10162,plain,
    ( ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK11(X0,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
        | hBOOL(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X1 )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f10161,f7321]) ).

fof(f10161,plain,
    ( ! [X2,X0,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X1
        | hBOOL(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK11(X0,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f10160,f7321]) ).

fof(f10160,plain,
    ( ! [X2,X0,X1] :
        ( hBOOL(c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK11(X0,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)
        | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X1 )
    | ~ spl24_136 ),
    inference(forward_demodulation,[],[f8096,f7318]) ).

fof(f8096,plain,
    ( ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,sK8(X0,X1,X2),X1)
        | hBOOL(c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X1
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK11(X0,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f5166,f7318]) ).

fof(f5166,plain,
    ! [X2,X0,X1] :
      ( hBOOL(hAPP(X0,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))
      | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X1
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK11(X0,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,sK8(X0,X1,X2),X1) ),
    inference(cnf_transformation,[],[f3944]) ).

fof(f10159,plain,
    ( spl24_203
    | spl24_144
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f10155,f7320,f7317,f9145,f10157]) ).

fof(f10155,plain,
    ( ! [X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f8220,f7321]) ).

fof(f8220,plain,
    ( ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(backward_demodulation,[],[f8037,f7318]) ).

fof(f8037,plain,
    ( ! [X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)) )
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f7901,f7321]) ).

fof(f7901,plain,
    ( ! [X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)) )
    | ~ spl24_137 ),
    inference(backward_demodulation,[],[f6612,f7321]) ).

fof(f6612,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)) ),
    inference(forward_demodulation,[],[f6606,f5628]) ).

fof(f6606,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)) ),
    inference(backward_demodulation,[],[f6532,f5628]) ).

fof(f6532,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) ),
    inference(forward_demodulation,[],[f6531,f4806]) ).

fof(f6531,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) ),
    inference(forward_demodulation,[],[f5886,f4806]) ).

fof(f5886,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0) ),
    inference(definition_unfolding,[],[f4672,f4877,f4877]) ).

fof(f4672,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)) ),
    inference(cnf_transformation,[],[f3628]) ).

fof(f3628,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)) ),
    inference(rectify,[],[f3444]) ).

fof(f3444,plain,
    ! [X1,X0] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ),
    inference(flattening,[],[f3443]) ).

fof(f3443,plain,
    ! [X1,X0] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0) ),
    inference(ennf_transformation,[],[f1233]) ).

fof(f1233,plain,
    ! [X1,X0] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ) ),
    inference(rectify,[],[f605]) ).

fof(f605,axiom,
    ! [X17,X23] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23),X17)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__less__m__mult__n) ).

fof(f10147,plain,
    ( spl24_185
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f10146,f7320,f7317,f9773]) ).

fof(f9773,plain,
    ( spl24_185
  <=> ! [X0,X1] :
        ( ~ class_Rings_Olinordered__semidom(X1)
        | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X0)
        | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_185])]) ).

fof(f10146,plain,
    ( ! [X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Oone__class_Oone(X0),X1)
        | c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ class_Rings_Olinordered__semidom(X0) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f10145,f7321]) ).

fof(f10145,plain,
    ( ! [X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Oone__class_Oone(X0),X1)
        | c_Orderings_Oord__class_Oless(X0,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ class_Rings_Olinordered__semidom(X0) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f10144,f7318]) ).

fof(f10144,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Oone__class_Oone(X0),X1)
        | c_Orderings_Oord__class_Oless(X0,hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ class_Rings_Olinordered__semidom(X0) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f8405,f7321]) ).

fof(f8405,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Rings_Olinordered__semidom(X0)
        | c_Orderings_Oord__class_Oless(X0,hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Oone__class_Oone(X0),X1) )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f4817,f7318]) ).

fof(f4817,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless(X0,hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2)))
      | ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Oone__class_Oone(X0),X1)
      | ~ class_Rings_Olinordered__semidom(X0) ),
    inference(cnf_transformation,[],[f3728]) ).

fof(f3728,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(X0,hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2)))
      | ~ class_Rings_Olinordered__semidom(X0)
      | ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Oone__class_Oone(X0),X1) ),
    inference(rectify,[],[f2674]) ).

fof(f2674,plain,
    ! [X1,X2,X0] :
      ( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X0)))
      | ~ class_Rings_Olinordered__semidom(X1)
      | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2) ),
    inference(flattening,[],[f2673]) ).

fof(f2673,plain,
    ! [X1,X2,X0] :
      ( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X0)))
      | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
      | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(ennf_transformation,[],[f1950]) ).

fof(f1950,plain,
    ! [X1,X2,X0] :
      ( class_Rings_Olinordered__semidom(X1)
     => ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
       => c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X0))) ) ),
    inference(rectify,[],[f747]) ).

fof(f747,axiom,
    ! [X17,X4,X5] :
      ( class_Rings_Olinordered__semidom(X4)
     => ( c_Orderings_Oord__class_Oless(X4,c_Groups_Oone__class_Oone(X4),X5)
       => c_Orderings_Oord__class_Oless(X4,hAPP(hAPP(c_Power_Opower__class_Opower(X4),X5),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X5),X17))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__less__power__Suc) ).

fof(f10112,plain,
    ( ~ spl24_153
    | spl24_154
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f10111,f7320,f7317,f9283,f9279]) ).

fof(f9283,plain,
    ( spl24_154
  <=> ! [X1] : c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_154])]) ).

fof(f10111,plain,
    ( ! [X0] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f8951,f7321]) ).

fof(f8951,plain,
    ( ! [X0] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f6583,f7318]) ).

fof(f6583,plain,
    ! [X0] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(forward_demodulation,[],[f4748,f5830]) ).

fof(f4748,plain,
    ! [X0] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(cnf_transformation,[],[f3681]) ).

fof(f10093,plain,
    ( spl24_198
    | spl24_152
    | ~ spl24_136 ),
    inference(avatar_split_clause,[],[f10092,f7317,f9263,f10011]) ).

fof(f10011,plain,
    ( spl24_198
  <=> ! [X1] : ~ class_Lattices_Oboolean__algebra(X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_198])]) ).

fof(f10092,plain,
    ( ! [X2,X0,X1] :
        ( X0 = X1
        | ~ class_Lattices_Oboolean__algebra(X2) )
    | ~ spl24_136 ),
    inference(trivial_inequality_removal,[],[f10091]) ).

fof(f10091,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Lattices_Oboolean__algebra(X2)
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | X0 = X1 )
    | ~ spl24_136 ),
    inference(forward_demodulation,[],[f9016,f7318]) ).

fof(f9016,plain,
    ( ! [X2,X0,X1] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ouminus__class_Ouminus(X2,X0)
        | X0 = X1
        | ~ class_Lattices_Oboolean__algebra(X2) )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f4961,f7318]) ).

fof(f4961,plain,
    ! [X2,X0,X1] :
      ( ~ class_Lattices_Oboolean__algebra(X2)
      | X0 = X1
      | c_Groups_Ouminus__class_Ouminus(X2,X1) != c_Groups_Ouminus__class_Ouminus(X2,X0) ),
    inference(cnf_transformation,[],[f3819]) ).

fof(f3819,plain,
    ! [X0,X1,X2] :
      ( ~ class_Lattices_Oboolean__algebra(X2)
      | ( ( X0 = X1
          | c_Groups_Ouminus__class_Ouminus(X2,X1) != c_Groups_Ouminus__class_Ouminus(X2,X0) )
        & ( c_Groups_Ouminus__class_Ouminus(X2,X1) = c_Groups_Ouminus__class_Ouminus(X2,X0)
          | X0 != X1 ) ) ),
    inference(rectify,[],[f3818]) ).

fof(f3818,plain,
    ! [X0,X2,X1] :
      ( ~ class_Lattices_Oboolean__algebra(X1)
      | ( ( X0 = X2
          | c_Groups_Ouminus__class_Ouminus(X1,X0) != c_Groups_Ouminus__class_Ouminus(X1,X2) )
        & ( c_Groups_Ouminus__class_Ouminus(X1,X0) = c_Groups_Ouminus__class_Ouminus(X1,X2)
          | X0 != X2 ) ) ),
    inference(nnf_transformation,[],[f3249]) ).

fof(f3249,plain,
    ! [X0,X2,X1] :
      ( ~ class_Lattices_Oboolean__algebra(X1)
      | ( X0 = X2
      <=> c_Groups_Ouminus__class_Ouminus(X1,X0) = c_Groups_Ouminus__class_Ouminus(X1,X2) ) ),
    inference(ennf_transformation,[],[f1792]) ).

fof(f1792,plain,
    ! [X2,X1,X0] :
      ( class_Lattices_Oboolean__algebra(X1)
     => ( X0 = X2
      <=> c_Groups_Ouminus__class_Ouminus(X1,X0) = c_Groups_Ouminus__class_Ouminus(X1,X2) ) ),
    inference(rectify,[],[f376]) ).

fof(f376,axiom,
    ! [X13,X8,X20] :
      ( class_Lattices_Oboolean__algebra(X8)
     => ( c_Groups_Ouminus__class_Ouminus(X8,X13) = c_Groups_Ouminus__class_Ouminus(X8,X20)
      <=> X13 = X20 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__eq__compl__iff) ).

fof(f10090,plain,
    ( spl24_183
    | spl24_202
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f10085,f7320,f7317,f10087,f9723]) ).

fof(f10087,plain,
    ( spl24_202
  <=> class_Orderings_Oord(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_202])]) ).

fof(f10085,plain,
    ( ! [X0] :
        ( class_Orderings_Oord(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ class_Orderings_Oord(X0) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f9070,f7321]) ).

fof(f9070,plain,
    ( ! [X0] :
        ( ~ class_Orderings_Oord(X0)
        | class_Orderings_Oord(c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f5591,f7318]) ).

fof(f5591,plain,
    ! [X0,X1] :
      ( class_Orderings_Oord(tc_fun(X1,X0))
      | ~ class_Orderings_Oord(X0) ),
    inference(cnf_transformation,[],[f4207]) ).

fof(f4207,plain,
    ! [X0,X1] :
      ( ~ class_Orderings_Oord(X0)
      | class_Orderings_Oord(tc_fun(X1,X0)) ),
    inference(rectify,[],[f2937]) ).

fof(f2937,plain,
    ! [X1,X0] :
      ( ~ class_Orderings_Oord(X1)
      | class_Orderings_Oord(tc_fun(X0,X1)) ),
    inference(ennf_transformation,[],[f1577]) ).

fof(f1577,plain,
    ! [X0,X1] :
      ( class_Orderings_Oord(X1)
     => class_Orderings_Oord(tc_fun(X0,X1)) ),
    inference(rectify,[],[f1013]) ).

fof(f1013,axiom,
    ! [X95,X94] :
      ( class_Orderings_Oord(X94)
     => class_Orderings_Oord(tc_fun(X95,X94)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).

fof(f10082,plain,
    ( spl24_161
    | spl24_201
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f10078,f7320,f7317,f10080,f9332]) ).

fof(f10080,plain,
    ( spl24_201
  <=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_201])]) ).

fof(f10078,plain,
    ( ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f8588,f7321]) ).

fof(f8588,plain,
    ( ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(backward_demodulation,[],[f8000,f7318]) ).

fof(f8000,plain,
    ( ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f7903,f7321]) ).

fof(f7903,plain,
    ( ! [X0,X1] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
    | ~ spl24_137 ),
    inference(backward_demodulation,[],[f6616,f7321]) ).

fof(f10050,plain,
    ( spl24_144
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f10049,f7320,f7317,f9145]) ).

fof(f10049,plain,
    ( ! [X69] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X69)
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f10048,f7321]) ).

fof(f10048,plain,
    ( ! [X69] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X69)
    | ~ spl24_136 ),
    inference(forward_demodulation,[],[f8896,f7318]) ).

fof(f8896,plain,
    ( ! [X70,X69] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X70,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X69)
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f7531,f7318]) ).

fof(f10025,plain,
    ( spl24_146
    | spl24_200
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f10021,f7320,f7317,f10023,f9162]) ).

fof(f10023,plain,
    ( spl24_200
  <=> ! [X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ class_Rings_Olinordered__semidom(X0)
        | ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Oone__class_Oone(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_200])]) ).

fof(f10021,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Oone__class_Oone(X0),X1)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
        | ~ class_Rings_Olinordered__semidom(X0) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f10020,f7321]) ).

fof(f10020,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ class_Rings_Olinordered__semidom(X0)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
        | ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Oone__class_Oone(X0),X1)
        | ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f10019,f7318]) ).

fof(f10019,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
        | ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Oone__class_Oone(X0),X1)
        | ~ c_Orderings_Oord__class_Oless(X0,hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ class_Rings_Olinordered__semidom(X0) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f8505,f7321]) ).

fof(f8505,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Oone__class_Oone(X0),X1)
        | ~ c_Orderings_Oord__class_Oless(X0,hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ class_Rings_Olinordered__semidom(X0)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f5608,f7318]) ).

fof(f5608,plain,
    ! [X2,X3,X0,X1] :
      ( ~ class_Rings_Olinordered__semidom(X0)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
      | ~ c_Orderings_Oord__class_Oless(X0,hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3))
      | ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Oone__class_Oone(X0),X1) ),
    inference(cnf_transformation,[],[f4219]) ).

fof(f4219,plain,
    ! [X0,X1,X2,X3] :
      ( ~ class_Rings_Olinordered__semidom(X0)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
      | ~ c_Orderings_Oord__class_Oless(X0,hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3))
      | ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Oone__class_Oone(X0),X1) ),
    inference(rectify,[],[f2859]) ).

fof(f2859,plain,
    ! [X0,X3,X2,X1] :
      ( ~ class_Rings_Olinordered__semidom(X0)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
      | ~ c_Orderings_Oord__class_Oless(X0,hAPP(hAPP(c_Power_Opower__class_Opower(X0),X3),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X3),X1))
      | ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Oone__class_Oone(X0),X3) ),
    inference(flattening,[],[f2858]) ).

fof(f2858,plain,
    ! [X3,X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
      | ~ c_Orderings_Oord__class_Oless(X0,hAPP(hAPP(c_Power_Opower__class_Opower(X0),X3),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X3),X1))
      | ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Oone__class_Oone(X0),X3)
      | ~ class_Rings_Olinordered__semidom(X0) ),
    inference(ennf_transformation,[],[f1732]) ).

fof(f1732,plain,
    ! [X3,X2,X0,X1] :
      ( class_Rings_Olinordered__semidom(X0)
     => ( c_Orderings_Oord__class_Oless(X0,c_Groups_Oone__class_Oone(X0),X3)
       => ( c_Orderings_Oord__class_Oless(X0,hAPP(hAPP(c_Power_Opower__class_Opower(X0),X3),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X3),X1))
         => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ) ) ),
    inference(rectify,[],[f752]) ).

fof(f752,axiom,
    ! [X4,X17,X23,X5] :
      ( class_Rings_Olinordered__semidom(X4)
     => ( c_Orderings_Oord__class_Oless(X4,c_Groups_Oone__class_Oone(X4),X5)
       => ( c_Orderings_Oord__class_Oless(X4,hAPP(hAPP(c_Power_Opower__class_Opower(X4),X5),X23),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X5),X17))
         => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X23,X17) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__less__imp__less__exp) ).

fof(f10017,plain,
    ( spl24_198
    | spl24_199
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f10009,f7320,f7317,f10014,f10011]) ).

fof(f10014,plain,
    ( spl24_199
  <=> class_Lattices_Oboolean__algebra(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_199])]) ).

fof(f10009,plain,
    ( ! [X1] :
        ( class_Lattices_Oboolean__algebra(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ class_Lattices_Oboolean__algebra(X1) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f9071,f7321]) ).

fof(f9071,plain,
    ( ! [X1] :
        ( class_Lattices_Oboolean__algebra(c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ class_Lattices_Oboolean__algebra(X1) )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f5802,f7318]) ).

fof(f5802,plain,
    ! [X0,X1] :
      ( class_Lattices_Oboolean__algebra(tc_fun(X0,X1))
      | ~ class_Lattices_Oboolean__algebra(X1) ),
    inference(cnf_transformation,[],[f4351]) ).

fof(f4351,plain,
    ! [X0,X1] :
      ( class_Lattices_Oboolean__algebra(tc_fun(X0,X1))
      | ~ class_Lattices_Oboolean__algebra(X1) ),
    inference(rectify,[],[f2957]) ).

fof(f2957,plain,
    ! [X1,X0] :
      ( class_Lattices_Oboolean__algebra(tc_fun(X1,X0))
      | ~ class_Lattices_Oboolean__algebra(X0) ),
    inference(ennf_transformation,[],[f1437]) ).

fof(f1437,plain,
    ! [X0,X1] :
      ( class_Lattices_Oboolean__algebra(X0)
     => class_Lattices_Oboolean__algebra(tc_fun(X1,X0)) ),
    inference(rectify,[],[f1010]) ).

fof(f1010,axiom,
    ! [X94,X95] :
      ( class_Lattices_Oboolean__algebra(X94)
     => class_Lattices_Oboolean__algebra(tc_fun(X95,X94)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Oboolean__algebra) ).

fof(f9999,plain,
    ( spl24_178
    | spl24_152
    | ~ spl24_136 ),
    inference(avatar_split_clause,[],[f9998,f7317,f9263,f9567]) ).

fof(f9567,plain,
    ( spl24_178
  <=> ! [X2] : ~ class_Groups_Ocancel__semigroup__add(X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_178])]) ).

fof(f9998,plain,
    ( ! [X2,X0,X1] :
        ( X0 = X1
        | ~ class_Groups_Ocancel__semigroup__add(X2) )
    | ~ spl24_136 ),
    inference(trivial_inequality_removal,[],[f9997]) ).

fof(f9997,plain,
    ( ! [X2,X0,X1] :
        ( X0 = X1
        | ~ class_Groups_Ocancel__semigroup__add(X2)
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
    | ~ spl24_136 ),
    inference(forward_demodulation,[],[f8748,f7318]) ).

fof(f8748,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ class_Groups_Ocancel__semigroup__add(X2)
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(X2,X0,X3)
        | X0 = X1 )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f4898,f7318]) ).

fof(f4898,plain,
    ! [X2,X3,X0,X1] :
      ( X0 = X1
      | c_Groups_Oplus__class_Oplus(X2,X1,X3) != c_Groups_Oplus__class_Oplus(X2,X0,X3)
      | ~ class_Groups_Ocancel__semigroup__add(X2) ),
    inference(cnf_transformation,[],[f3780]) ).

fof(f3780,plain,
    ! [X0,X1,X2,X3] :
      ( ~ class_Groups_Ocancel__semigroup__add(X2)
      | ( ( c_Groups_Oplus__class_Oplus(X2,X1,X3) = c_Groups_Oplus__class_Oplus(X2,X0,X3)
          | X0 != X1 )
        & ( X0 = X1
          | c_Groups_Oplus__class_Oplus(X2,X1,X3) != c_Groups_Oplus__class_Oplus(X2,X0,X3) ) ) ),
    inference(rectify,[],[f3779]) ).

fof(f3779,plain,
    ! [X3,X0,X2,X1] :
      ( ~ class_Groups_Ocancel__semigroup__add(X2)
      | ( ( c_Groups_Oplus__class_Oplus(X2,X0,X1) = c_Groups_Oplus__class_Oplus(X2,X3,X1)
          | X0 != X3 )
        & ( X0 = X3
          | c_Groups_Oplus__class_Oplus(X2,X0,X1) != c_Groups_Oplus__class_Oplus(X2,X3,X1) ) ) ),
    inference(nnf_transformation,[],[f3233]) ).

fof(f3233,plain,
    ! [X3,X0,X2,X1] :
      ( ~ class_Groups_Ocancel__semigroup__add(X2)
      | ( c_Groups_Oplus__class_Oplus(X2,X0,X1) = c_Groups_Oplus__class_Oplus(X2,X3,X1)
      <=> X0 = X3 ) ),
    inference(ennf_transformation,[],[f2200]) ).

fof(f2200,plain,
    ! [X3,X1,X0,X2] :
      ( class_Groups_Ocancel__semigroup__add(X2)
     => ( c_Groups_Oplus__class_Oplus(X2,X0,X1) = c_Groups_Oplus__class_Oplus(X2,X3,X1)
      <=> X0 = X3 ) ),
    inference(rectify,[],[f56]) ).

fof(f56,axiom,
    ! [X10,X7,X8,X30] :
      ( class_Groups_Ocancel__semigroup__add(X8)
     => ( X10 = X30
      <=> c_Groups_Oplus__class_Oplus(X8,X10,X7) = c_Groups_Oplus__class_Oplus(X8,X30,X7) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__cancel) ).

fof(f9981,plain,
    ( spl24_197
    | spl24_144
    | ~ spl24_136 ),
    inference(avatar_split_clause,[],[f9977,f7317,f9145,f9979]) ).

fof(f9977,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
        | ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X3)
        | ~ class_Rings_Olinordered__semidom(X2)
        | X1 = X3
        | ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1) )
    | ~ spl24_136 ),
    inference(trivial_inequality_removal,[],[f9976]) ).

fof(f9976,plain,
    ( ! [X2,X3,X0,X1] :
        ( X1 = X3
        | ~ class_Rings_Olinordered__semidom(X2)
        | ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
        | ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X3)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
    | ~ spl24_136 ),
    inference(forward_demodulation,[],[f8492,f7318]) ).

fof(f8492,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X3)
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)
        | X1 = X3
        | ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
        | ~ class_Rings_Olinordered__semidom(X2) )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f4703,f7318]) ).

fof(f4703,plain,
    ! [X2,X3,X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X3)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
      | X1 = X3
      | hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),X0) != hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)
      | ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
      | ~ class_Rings_Olinordered__semidom(X2) ),
    inference(cnf_transformation,[],[f3652]) ).

fof(f3652,plain,
    ! [X0,X1,X2,X3] :
      ( ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
      | X1 = X3
      | ~ class_Rings_Olinordered__semidom(X2)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),X0) != hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)
      | ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X3) ),
    inference(rectify,[],[f3401]) ).

fof(f3401,plain,
    ! [X3,X1,X0,X2] :
      ( ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1)
      | X1 = X2
      | ~ class_Rings_Olinordered__semidom(X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3) != hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X3)
      | ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X2) ),
    inference(flattening,[],[f3400]) ).

fof(f3400,plain,
    ! [X3,X1,X2,X0] :
      ( X1 = X2
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
      | ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1)
      | ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X2)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3) != hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X3)
      | ~ class_Rings_Olinordered__semidom(X0) ),
    inference(ennf_transformation,[],[f1318]) ).

fof(f1318,plain,
    ! [X3,X1,X2,X0] :
      ( class_Rings_Olinordered__semidom(X0)
     => ( hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X3)
       => ( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X2)
         => ( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1)
           => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
             => X1 = X2 ) ) ) ) ),
    inference(rectify,[],[f758]) ).

fof(f758,axiom,
    ! [X4,X29,X5,X17] :
      ( class_Rings_Olinordered__semidom(X4)
     => ( hAPP(hAPP(c_Power_Opower__class_Opower(X4),X5),X17) = hAPP(hAPP(c_Power_Opower__class_Opower(X4),X29),X17)
       => ( c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X5)
         => ( c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X29)
           => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X17)
             => X5 = X29 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__eq__imp__eq__base) ).

fof(f9975,plain,
    ( spl24_166
    | spl24_152
    | ~ spl24_136 ),
    inference(avatar_split_clause,[],[f9974,f7317,f9263,f9398]) ).

fof(f9974,plain,
    ( ! [X2,X3,X4] :
        ( X3 = X4
        | ~ class_Groups_Ozero(X2) )
    | ~ spl24_136 ),
    inference(trivial_inequality_removal,[],[f9973]) ).

fof(f9973,plain,
    ( ! [X2,X3,X4] :
        ( ~ class_Groups_Ozero(X2)
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | X3 = X4 )
    | ~ spl24_136 ),
    inference(forward_demodulation,[],[f8681,f7318]) ).

fof(f8681,plain,
    ( ! [X2,X3,X1,X4] :
        ( X3 = X4
        | ~ class_Groups_Ozero(X2)
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Polynomial_OpCons(X2,X4,X1) )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f4842,f7318]) ).

fof(f9972,plain,
    ( spl24_149
    | ~ spl24_191
    | spl24_196
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f9968,f7320,f7317,f9970,f9854,f9190]) ).

fof(f9970,plain,
    ( spl24_196
  <=> ! [X2,X0,X4] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X2)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_196])]) ).

fof(f9968,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X2)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X1)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X2) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f9967,f9844]) ).

fof(f9844,plain,
    ( ! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f9002,f7321]) ).

fof(f9002,plain,
    ( ! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f5009,f7318]) ).

fof(f9967,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X2)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X1)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X2) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f9966,f7321]) ).

fof(f9966,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X2)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X1)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X2) )
    | ~ spl24_136 ),
    inference(forward_demodulation,[],[f8240,f7318]) ).

fof(f8240,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X2)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X1)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X2)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X4)) )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f5452,f7318]) ).

fof(f5452,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X2)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X1)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X2)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3),X0),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X4)) ),
    inference(cnf_transformation,[],[f4110]) ).

fof(f4110,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X2)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3),X0),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X4))
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X1)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X2) ),
    inference(rectify,[],[f3361]) ).

fof(f3361,plain,
    ! [X1,X3,X0,X4,X2] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X4),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3),X2))
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,X3)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X0) ),
    inference(flattening,[],[f3360]) ).

fof(f3360,plain,
    ! [X4,X0,X1,X2,X3] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,X3)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X4),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3),X2)) ),
    inference(ennf_transformation,[],[f1765]) ).

fof(f1765,plain,
    ! [X4,X0,X1,X2,X3] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X4),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3),X2))
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
       => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
         => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X0)
           => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,X3) ) ) ) ),
    inference(rectify,[],[f834]) ).

fof(f834,axiom,
    ! [X29,X78,X28,X21,X79] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X29),X79),X78),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X29),X21),X28))
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X78)
       => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X78,X29)
         => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X28,X29)
           => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X79,X21) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unique__quotient__lemma) ).

fof(f9954,plain,
    ( spl24_195
    | spl24_152
    | ~ spl24_136 ),
    inference(avatar_split_clause,[],[f9950,f7317,f9263,f9952]) ).

fof(f9950,plain,
    ( ! [X2,X3,X1,X5] :
        ( X1 = X2
        | c_Groups_Ozero__class_Ozero(X5) = X3
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5) )
    | ~ spl24_136 ),
    inference(trivial_inequality_removal,[],[f9949]) ).

fof(f9949,plain,
    ( ! [X2,X3,X1,X5] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | c_Groups_Ozero__class_Ozero(X5) = X3
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5)
        | X1 = X2 )
    | ~ spl24_136 ),
    inference(forward_demodulation,[],[f9948,f7318]) ).

fof(f9948,plain,
    ( ! [X2,X3,X1,X4,X5] :
        ( c_Groups_Ozero__class_Ozero(X5) = X3
        | X1 = X2
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5)
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(X5,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X3),X1)) )
    | ~ spl24_136 ),
    inference(forward_demodulation,[],[f8397,f7318]) ).

fof(f8397,plain,
    ( ! [X2,X3,X1,X4,X5] :
        ( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5)
        | c_Groups_Oplus__class_Oplus(X5,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X3),X1)) != c_Groups_Oplus__class_Oplus(X5,X4,c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | X1 = X2
        | c_Groups_Ozero__class_Ozero(X5) = X3 )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f6026,f7318]) ).

fof(f6026,plain,
    ! [X2,X3,X1,X4,X5] :
      ( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5)
      | X1 = X2
      | c_Groups_Oplus__class_Oplus(X5,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X3),X1)) != c_Groups_Oplus__class_Oplus(X5,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X3),X2))
      | c_Groups_Ozero__class_Ozero(X5) = X3 ),
    inference(equality_resolution,[],[f4534]) ).

fof(f4534,plain,
    ! [X2,X3,X0,X1,X4,X5] :
      ( c_Groups_Oplus__class_Oplus(X5,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X3),X1)) != c_Groups_Oplus__class_Oplus(X5,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X3),X2))
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5)
      | X1 = X2
      | c_Groups_Ozero__class_Ozero(X5) = X3
      | X0 != X4 ),
    inference(cnf_transformation,[],[f3537]) ).

fof(f3537,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( c_Groups_Oplus__class_Oplus(X5,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X3),X1)) != c_Groups_Oplus__class_Oplus(X5,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X3),X2))
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5)
      | X1 = X2
      | c_Groups_Ozero__class_Ozero(X5) = X3
      | X0 != X4 ),
    inference(rectify,[],[f3278]) ).

fof(f3278,plain,
    ! [X1,X5,X4,X3,X0,X2] :
      ( c_Groups_Oplus__class_Oplus(X2,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X4)) != c_Groups_Oplus__class_Oplus(X2,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X5))
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2)
      | X4 = X5
      | c_Groups_Ozero__class_Ozero(X2) = X3
      | X0 != X1 ),
    inference(flattening,[],[f3277]) ).

fof(f3277,plain,
    ! [X2,X5,X1,X4,X3,X0] :
      ( c_Groups_Oplus__class_Oplus(X2,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X4)) != c_Groups_Oplus__class_Oplus(X2,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X5))
      | X4 = X5
      | X0 != X1
      | c_Groups_Ozero__class_Ozero(X2) = X3
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ),
    inference(ennf_transformation,[],[f1544]) ).

fof(f1544,plain,
    ! [X2,X5,X1,X4,X3,X0] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2)
     => ( c_Groups_Ozero__class_Ozero(X2) != X3
       => ( ( X4 != X5
            & X0 = X1 )
         => c_Groups_Oplus__class_Oplus(X2,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X4)) != c_Groups_Oplus__class_Oplus(X2,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X5)) ) ) ),
    inference(rectify,[],[f132]) ).

fof(f132,axiom,
    ! [X5,X29,X4,X28,X45,X22] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4)
     => ( c_Groups_Ozero__class_Ozero(X4) != X28
       => ( ( X5 = X29
            & X22 != X45 )
         => c_Groups_Oplus__class_Oplus(X4,X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X28),X22)) != c_Groups_Oplus__class_Oplus(X4,X29,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X28),X45)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__scale__eq__noteq) ).

fof(f9947,plain,
    ( spl24_179
    | spl24_152
    | ~ spl24_177
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f9946,f7320,f7317,f9552,f9263,f9671]) ).

fof(f9671,plain,
    ( spl24_179
  <=> ! [X2] :
        ( ~ class_HOL_Oequal(X2)
        | ~ class_Groups_Ozero(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_179])]) ).

fof(f9946,plain,
    ( ! [X2,X0,X1] :
        ( ~ hBOOL(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | X0 = X1
        | ~ class_HOL_Oequal(X2)
        | ~ class_Groups_Ozero(X2) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f8147,f7321]) ).

fof(f8147,plain,
    ( ! [X2,X0,X1] :
        ( ~ hBOOL(c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ class_Groups_Ozero(X2)
        | ~ class_HOL_Oequal(X2)
        | X0 = X1 )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f5344,f7318]) ).

fof(f5344,plain,
    ! [X2,X0,X1] :
      ( ~ class_Groups_Ozero(X2)
      | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Polynomial_Opoly(X2)),X1),X0))
      | ~ class_HOL_Oequal(X2)
      | X0 = X1 ),
    inference(cnf_transformation,[],[f4034]) ).

fof(f4034,plain,
    ! [X0,X1,X2] :
      ( ~ class_Groups_Ozero(X2)
      | ( ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Polynomial_Opoly(X2)),X1),X0))
          | X0 != X1 )
        & ( X0 = X1
          | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Polynomial_Opoly(X2)),X1),X0)) ) )
      | ~ class_HOL_Oequal(X2) ),
    inference(rectify,[],[f4033]) ).

fof(f4033,plain,
    ! [X1,X2,X0] :
      ( ~ class_Groups_Ozero(X0)
      | ( ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Polynomial_Opoly(X0)),X2),X1))
          | X1 != X2 )
        & ( X1 = X2
          | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Polynomial_Opoly(X0)),X2),X1)) ) )
      | ~ class_HOL_Oequal(X0) ),
    inference(nnf_transformation,[],[f3435]) ).

fof(f3435,plain,
    ! [X1,X2,X0] :
      ( ~ class_Groups_Ozero(X0)
      | ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Polynomial_Opoly(X0)),X2),X1))
      <=> X1 = X2 )
      | ~ class_HOL_Oequal(X0) ),
    inference(flattening,[],[f3434]) ).

fof(f3434,plain,
    ! [X0,X1,X2] :
      ( ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Polynomial_Opoly(X0)),X2),X1))
      <=> X1 = X2 )
      | ~ class_Groups_Ozero(X0)
      | ~ class_HOL_Oequal(X0) ),
    inference(ennf_transformation,[],[f1221]) ).

fof(f1221,plain,
    ! [X0,X1,X2] :
      ( ( class_Groups_Ozero(X0)
        & class_HOL_Oequal(X0) )
     => ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Polynomial_Opoly(X0)),X2),X1))
      <=> X1 = X2 ) ),
    inference(rectify,[],[f15]) ).

fof(f15,axiom,
    ! [X8,X9,X6] :
      ( ( class_Groups_Ozero(X8)
        & class_HOL_Oequal(X8) )
     => ( X6 = X9
      <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Polynomial_Opoly(X8)),X6),X9)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equal__poly__def) ).

fof(f9941,plain,
    ( spl24_194
    | spl24_161
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f9937,f7320,f7317,f9332,f9939]) ).

fof(f9937,plain,
    ( ! [X50,X48] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X50
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X48,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f8873,f7321]) ).

fof(f8873,plain,
    ( ! [X50,X48] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X50
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X48,c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f7410,f7318]) ).

fof(f9917,plain,
    ( spl24_192
    | spl24_193
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f9909,f7320,f7317,f9914,f9911]) ).

fof(f9911,plain,
    ( spl24_192
  <=> ! [X1] : ~ class_Orderings_Opreorder(X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_192])]) ).

fof(f9914,plain,
    ( spl24_193
  <=> class_Orderings_Opreorder(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_193])]) ).

fof(f9909,plain,
    ( ! [X1] :
        ( class_Orderings_Opreorder(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ class_Orderings_Opreorder(X1) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f9062,f7321]) ).

fof(f9062,plain,
    ( ! [X1] :
        ( ~ class_Orderings_Opreorder(X1)
        | class_Orderings_Opreorder(c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f4707,f7318]) ).

fof(f4707,plain,
    ! [X0,X1] :
      ( class_Orderings_Opreorder(tc_fun(X0,X1))
      | ~ class_Orderings_Opreorder(X1) ),
    inference(cnf_transformation,[],[f3653]) ).

fof(f3653,plain,
    ! [X0,X1] :
      ( class_Orderings_Opreorder(tc_fun(X0,X1))
      | ~ class_Orderings_Opreorder(X1) ),
    inference(rectify,[],[f2867]) ).

fof(f2867,plain,
    ! [X1,X0] :
      ( class_Orderings_Opreorder(tc_fun(X1,X0))
      | ~ class_Orderings_Opreorder(X0) ),
    inference(ennf_transformation,[],[f2175]) ).

fof(f2175,plain,
    ! [X1,X0] :
      ( class_Orderings_Opreorder(X0)
     => class_Orderings_Opreorder(tc_fun(X1,X0)) ),
    inference(rectify,[],[f1011]) ).

fof(f1011,axiom,
    ! [X94,X95] :
      ( class_Orderings_Opreorder(X94)
     => class_Orderings_Opreorder(tc_fun(X95,X94)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Opreorder) ).

fof(f9903,plain,
    ( spl24_152
    | spl24_144
    | ~ spl24_136 ),
    inference(avatar_split_clause,[],[f9902,f7317,f9145,f9263]) ).

fof(f9902,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
        | X1 = X2 )
    | ~ spl24_136 ),
    inference(trivial_inequality_removal,[],[f9901]) ).

fof(f9901,plain,
    ( ! [X2,X0,X1] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | X1 = X2
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) )
    | ~ spl24_136 ),
    inference(forward_demodulation,[],[f8179,f7318]) ).

fof(f8179,plain,
    ( ! [X2,X0,X1] :
        ( X1 = X2
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2) )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f5069,f7318]) ).

fof(f5069,plain,
    ! [X2,X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
      | X1 = X2
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2) ),
    inference(cnf_transformation,[],[f3889]) ).

fof(f3889,plain,
    ! [X0,X1,X2] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
      | ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2)
          | X1 != X2 )
        & ( X1 = X2
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2) ) ) ),
    inference(nnf_transformation,[],[f3295]) ).

fof(f3295,plain,
    ! [X0,X1,X2] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
      | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2)
      <=> X1 = X2 ) ),
    inference(ennf_transformation,[],[f2137]) ).

fof(f2137,plain,
    ! [X2,X1,X0] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2)
      <=> X1 = X2 ) ),
    inference(rectify,[],[f569]) ).

fof(f569,axiom,
    ! [X44,X43,X18] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X44)
     => ( X18 = X43
      <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X44),X43) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X44),X18) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel1) ).

fof(f9898,plain,
    ( spl24_143
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f9897,f7320,f7317,f9142]) ).

fof(f9897,plain,
    ( ! [X0] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f8904,f7321]) ).

fof(f8904,plain,
    ( ! [X0] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(backward_demodulation,[],[f8033,f7318]) ).

fof(f8033,plain,
    ( ! [X0,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f7883,f5628]) ).

fof(f7883,plain,
    ( ! [X0,X1] : 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_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)))
    | ~ spl24_137 ),
    inference(backward_demodulation,[],[f5984,f7321]) ).

fof(f9857,plain,
    ( spl24_189
    | spl24_190
    | ~ spl24_191
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f9846,f7320,f7317,f9854,f9851,f9848]) ).

fof(f9851,plain,
    ( spl24_190
  <=> ! [X2,X1] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_190])]) ).

fof(f9846,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f9845,f7321]) ).

fof(f9845,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
        | c_Orderings_Oord__class_Oless__eq(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),X2) )
    | ~ spl24_136 ),
    inference(forward_demodulation,[],[f8231,f7318]) ).

fof(f8231,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
        | c_Orderings_Oord__class_Oless__eq(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),X2)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)) )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f4892,f7318]) ).

fof(f9833,plain,
    ( spl24_152
    | spl24_188
    | ~ spl24_136 ),
    inference(avatar_split_clause,[],[f9829,f7317,f9831,f9263]) ).

fof(f9831,plain,
    ( spl24_188
  <=> ! [X2,X3] :
        ( ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X3)
        | ~ class_Rings_Olinordered__semidom(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_188])]) ).

fof(f9829,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X3)
        | ~ class_Rings_Olinordered__semidom(X2)
        | X0 = X1 )
    | ~ spl24_136 ),
    inference(trivial_inequality_removal,[],[f9828]) ).

fof(f9828,plain,
    ( ! [X2,X3,X0,X1] :
        ( X0 = X1
        | ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X3)
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ class_Rings_Olinordered__semidom(X2) )
    | ~ spl24_136 ),
    inference(forward_demodulation,[],[f8489,f7318]) ).

fof(f8489,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X3)
        | X0 = X1
        | ~ class_Rings_Olinordered__semidom(X2)
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),X0) )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f4645,f7318]) ).

fof(f4645,plain,
    ! [X2,X3,X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X3)
      | ~ class_Rings_Olinordered__semidom(X2)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),X1) != hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),X0)
      | X0 = X1 ),
    inference(cnf_transformation,[],[f3611]) ).

fof(f3611,plain,
    ! [X0,X1,X2,X3] :
      ( ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X3)
      | ( ( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),X0)
          | X0 != X1 )
        & ( X0 = X1
          | hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),X1) != hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),X0) ) )
      | ~ class_Rings_Olinordered__semidom(X2) ),
    inference(rectify,[],[f3610]) ).

fof(f3610,plain,
    ! [X3,X2,X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Oone__class_Oone(X0),X1)
      | ( ( hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2)
          | X2 != X3 )
        & ( X2 = X3
          | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3) != hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2) ) )
      | ~ class_Rings_Olinordered__semidom(X0) ),
    inference(nnf_transformation,[],[f2715]) ).

fof(f2715,plain,
    ! [X3,X2,X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Oone__class_Oone(X0),X1)
      | ( hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2)
      <=> X2 = X3 )
      | ~ class_Rings_Olinordered__semidom(X0) ),
    inference(flattening,[],[f2714]) ).

fof(f2714,plain,
    ! [X1,X2,X0,X3] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2)
      <=> X2 = X3 )
      | ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Oone__class_Oone(X0),X1)
      | ~ class_Rings_Olinordered__semidom(X0) ),
    inference(ennf_transformation,[],[f1753]) ).

fof(f1753,plain,
    ! [X1,X2,X0,X3] :
      ( class_Rings_Olinordered__semidom(X0)
     => ( c_Orderings_Oord__class_Oless(X0,c_Groups_Oone__class_Oone(X0),X1)
       => ( hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2)
        <=> X2 = X3 ) ) ),
    inference(rectify,[],[f733]) ).

fof(f733,axiom,
    ! [X8,X7,X18,X43] :
      ( class_Rings_Olinordered__semidom(X8)
     => ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oone__class_Oone(X8),X7)
       => ( hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X18) = hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X43)
        <=> X18 = X43 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__inject__exp) ).

fof(f9823,plain,
    ( spl24_173
    | spl24_161
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f9822,f7320,f7317,f9332,f9510]) ).

fof(f9510,plain,
    ( spl24_173
  <=> ! [X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_173])]) ).

fof(f9822,plain,
    ( ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f8600,f7321]) ).

fof(f8600,plain,
    ( ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(backward_demodulation,[],[f8001,f7318]) ).

fof(f8001,plain,
    ( ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1) )
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f7909,f7321]) ).

fof(f7909,plain,
    ( ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1) )
    | ~ spl24_137 ),
    inference(backward_demodulation,[],[f6645,f7321]) ).

fof(f6645,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_Oone__class_Oone(tc_Nat_Onat) = X0
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 ),
    inference(forward_demodulation,[],[f6644,f5628]) ).

fof(f6644,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = 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)) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1) ),
    inference(forward_demodulation,[],[f6643,f4806]) ).

fof(f6643,plain,
    ! [X0,X1] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),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))
      | c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 ),
    inference(forward_demodulation,[],[f6642,f5628]) ).

fof(f6642,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
      | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),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))
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 ),
    inference(forward_demodulation,[],[f6005,f4806]) ).

fof(f6005,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
      | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),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))
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 ),
    inference(definition_unfolding,[],[f5817,f4877,f4877]) ).

fof(f5817,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
      | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
      | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1) ),
    inference(cnf_transformation,[],[f4361]) ).

fof(f9809,plain,
    ( ~ spl24_177
    | spl24_187
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f9805,f7320,f7317,f9807,f9552]) ).

fof(f9807,plain,
    ( spl24_187
  <=> ! [X2,X1] :
        ( ~ class_Rings_Odvd(X2)
        | c_Rings_Odvd__class_Odvd(X2,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ class_Rings_Osemiring__0(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_187])]) ).

fof(f9805,plain,
    ( ! [X2,X1] :
        ( ~ class_Rings_Odvd(X2)
        | ~ hBOOL(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ class_Rings_Osemiring__0(X2)
        | c_Rings_Odvd__class_Odvd(X2,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f9804,f7321]) ).

fof(f9804,plain,
    ( ! [X2,X1] :
        ( ~ class_Rings_Osemiring__0(X2)
        | ~ hBOOL(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | c_Rings_Odvd__class_Odvd(X2,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ class_Rings_Odvd(X2) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f9803,f7318]) ).

fof(f9803,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Rings_Osemiring__0(X2)
        | ~ hBOOL(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ class_Rings_Odvd(X2)
        | c_Rings_Odvd__class_Odvd(X2,X1,c_Groups_Oplus__class_Oplus(X2,sK16(X0,X1,X2),c_Groups_Ozero__class_Ozero(X2))) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f8088,f7321]) ).

fof(f8088,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Rings_Osemiring__0(X2)
        | ~ hBOOL(c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ class_Rings_Odvd(X2)
        | c_Rings_Odvd__class_Odvd(X2,X1,c_Groups_Oplus__class_Oplus(X2,sK16(X0,X1,X2),c_Groups_Ozero__class_Ozero(X2))) )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f5499,f7318]) ).

fof(f5499,plain,
    ! [X2,X0,X1,X4] :
      ( ~ class_Rings_Osemiring__0(X2)
      | c_Rings_Odvd__class_Odvd(X2,X1,c_Groups_Oplus__class_Oplus(X2,sK16(X0,X1,X2),c_Groups_Ozero__class_Ozero(X2)))
      | ~ hBOOL(hAPP(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X4)))
      | ~ class_Rings_Odvd(X2) ),
    inference(cnf_transformation,[],[f4152]) ).

fof(f4152,plain,
    ! [X0,X1,X2] :
      ( ~ class_Rings_Osemiring__0(X2)
      | ( ( ( hBOOL(hAPP(X0,sK16(X0,X1,X2)))
            & c_Rings_Odvd__class_Odvd(X2,X1,c_Groups_Oplus__class_Oplus(X2,sK16(X0,X1,X2),c_Groups_Ozero__class_Ozero(X2))) )
          | ! [X4] : ~ hBOOL(hAPP(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X4))) )
        & ( hBOOL(hAPP(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),sK17(X0,X1,X2))))
          | ! [X6] :
              ( ~ hBOOL(hAPP(X0,X6))
              | ~ c_Rings_Odvd__class_Odvd(X2,X1,c_Groups_Oplus__class_Oplus(X2,X6,c_Groups_Ozero__class_Ozero(X2))) ) ) )
      | ~ class_Rings_Odvd(X2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK16,sK17])],[f4149,f4151,f4150]) ).

fof(f4150,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( hBOOL(hAPP(X0,X3))
          & c_Rings_Odvd__class_Odvd(X2,X1,c_Groups_Oplus__class_Oplus(X2,X3,c_Groups_Ozero__class_Ozero(X2))) )
     => ( hBOOL(hAPP(X0,sK16(X0,X1,X2)))
        & c_Rings_Odvd__class_Odvd(X2,X1,c_Groups_Oplus__class_Oplus(X2,sK16(X0,X1,X2),c_Groups_Ozero__class_Ozero(X2))) ) ),
    introduced(choice_axiom,[]) ).

fof(f4151,plain,
    ! [X0,X1,X2] :
      ( ? [X5] : hBOOL(hAPP(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X5)))
     => hBOOL(hAPP(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),sK17(X0,X1,X2)))) ),
    introduced(choice_axiom,[]) ).

fof(f4149,plain,
    ! [X0,X1,X2] :
      ( ~ class_Rings_Osemiring__0(X2)
      | ( ( ? [X3] :
              ( hBOOL(hAPP(X0,X3))
              & c_Rings_Odvd__class_Odvd(X2,X1,c_Groups_Oplus__class_Oplus(X2,X3,c_Groups_Ozero__class_Ozero(X2))) )
          | ! [X4] : ~ hBOOL(hAPP(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X4))) )
        & ( ? [X5] : hBOOL(hAPP(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X5)))
          | ! [X6] :
              ( ~ hBOOL(hAPP(X0,X6))
              | ~ c_Rings_Odvd__class_Odvd(X2,X1,c_Groups_Oplus__class_Oplus(X2,X6,c_Groups_Ozero__class_Ozero(X2))) ) ) )
      | ~ class_Rings_Odvd(X2) ),
    inference(rectify,[],[f4148]) ).

fof(f4148,plain,
    ! [X2,X1,X0] :
      ( ~ class_Rings_Osemiring__0(X0)
      | ( ( ? [X4] :
              ( hBOOL(hAPP(X2,X4))
              & c_Rings_Odvd__class_Odvd(X0,X1,c_Groups_Oplus__class_Oplus(X0,X4,c_Groups_Ozero__class_Ozero(X0))) )
          | ! [X3] : ~ hBOOL(hAPP(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X3))) )
        & ( ? [X3] : hBOOL(hAPP(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X3)))
          | ! [X4] :
              ( ~ hBOOL(hAPP(X2,X4))
              | ~ c_Rings_Odvd__class_Odvd(X0,X1,c_Groups_Oplus__class_Oplus(X0,X4,c_Groups_Ozero__class_Ozero(X0))) ) ) )
      | ~ class_Rings_Odvd(X0) ),
    inference(nnf_transformation,[],[f2591]) ).

fof(f2591,plain,
    ! [X2,X1,X0] :
      ( ~ class_Rings_Osemiring__0(X0)
      | ( ? [X4] :
            ( hBOOL(hAPP(X2,X4))
            & c_Rings_Odvd__class_Odvd(X0,X1,c_Groups_Oplus__class_Oplus(X0,X4,c_Groups_Ozero__class_Ozero(X0))) )
      <=> ? [X3] : hBOOL(hAPP(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X3))) )
      | ~ class_Rings_Odvd(X0) ),
    inference(flattening,[],[f2590]) ).

fof(f2590,plain,
    ! [X2,X1,X0] :
      ( ( ? [X4] :
            ( hBOOL(hAPP(X2,X4))
            & c_Rings_Odvd__class_Odvd(X0,X1,c_Groups_Oplus__class_Oplus(X0,X4,c_Groups_Ozero__class_Ozero(X0))) )
      <=> ? [X3] : hBOOL(hAPP(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X3))) )
      | ~ class_Rings_Odvd(X0)
      | ~ class_Rings_Osemiring__0(X0) ),
    inference(ennf_transformation,[],[f1354]) ).

fof(f1354,plain,
    ! [X2,X1,X0] :
      ( ( class_Rings_Odvd(X0)
        & class_Rings_Osemiring__0(X0) )
     => ( ? [X4] :
            ( hBOOL(hAPP(X2,X4))
            & c_Rings_Odvd__class_Odvd(X0,X1,c_Groups_Oplus__class_Oplus(X0,X4,c_Groups_Ozero__class_Ozero(X0))) )
      <=> ? [X3] : hBOOL(hAPP(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X3))) ) ),
    inference(rectify,[],[f653]) ).

fof(f653,axiom,
    ! [X8,X59,X14] :
      ( ( class_Rings_Odvd(X8)
        & class_Rings_Osemiring__0(X8) )
     => ( ? [X2] : hBOOL(hAPP(X14,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X59),X2)))
      <=> ? [X2] :
            ( hBOOL(hAPP(X14,X2))
            & c_Rings_Odvd__class_Odvd(X8,X59,c_Groups_Oplus__class_Oplus(X8,X2,c_Groups_Ozero__class_Ozero(X8))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unity__coeff__ex) ).

fof(f9802,plain,
    ( spl24_167
    | spl24_186
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f9798,f7320,f7317,f9800,f9408]) ).

fof(f9800,plain,
    ( spl24_186
  <=> ! [X0,X3] :
        ( ~ class_Rings_Olinordered__semidom(X3)
        | c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
        | ~ c_Orderings_Oord__class_Oless__eq(X3,X0,c_Groups_Oone__class_Oone(X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_186])]) ).

fof(f9798,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ class_Rings_Olinordered__semidom(X3)
        | ~ c_Orderings_Oord__class_Oless__eq(X3,X0,c_Groups_Oone__class_Oone(X3))
        | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
        | c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f9797,f7321]) ).

fof(f9797,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ class_Rings_Olinordered__semidom(X3)
        | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
        | c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
        | ~ c_Orderings_Oord__class_Oless__eq(X3,X0,c_Groups_Oone__class_Oone(X3)) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f9796,f7318]) ).

fof(f9796,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless__eq(X3,X0,c_Groups_Oone__class_Oone(X3))
        | c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
        | ~ class_Rings_Olinordered__semidom(X3)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f8485,f7321]) ).

fof(f8485,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
        | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
        | ~ c_Orderings_Oord__class_Oless__eq(X3,X0,c_Groups_Oone__class_Oone(X3))
        | c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ class_Rings_Olinordered__semidom(X3) )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f4530,f7318]) ).

fof(f4530,plain,
    ! [X2,X3,X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
      | ~ c_Orderings_Oord__class_Oless__eq(X3,X0,c_Groups_Oone__class_Oone(X3))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
      | ~ class_Rings_Olinordered__semidom(X3)
      | c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X2)) ),
    inference(cnf_transformation,[],[f3534]) ).

fof(f3534,plain,
    ! [X0,X1,X2,X3] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
      | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
      | ~ class_Rings_Olinordered__semidom(X3)
      | ~ c_Orderings_Oord__class_Oless__eq(X3,X0,c_Groups_Oone__class_Oone(X3))
      | c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X2)) ),
    inference(rectify,[],[f2513]) ).

fof(f2513,plain,
    ! [X0,X3,X2,X1] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
      | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
      | ~ class_Rings_Olinordered__semidom(X1)
      | ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Oone__class_Oone(X1))
      | c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),X2)) ),
    inference(flattening,[],[f2512]) ).

fof(f2512,plain,
    ! [X2,X1,X3,X0] :
      ( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),X2))
      | ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Oone__class_Oone(X1))
      | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
      | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(ennf_transformation,[],[f2007]) ).

fof(f2007,plain,
    ! [X2,X1,X3,X0] :
      ( class_Rings_Olinordered__semidom(X1)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
       => ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
         => ( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Oone__class_Oone(X1))
           => c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),X2)) ) ) ) ),
    inference(rectify,[],[f759]) ).

fof(f759,axiom,
    ! [X5,X4,X17,X65] :
      ( class_Rings_Olinordered__semidom(X4)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X65)
       => ( c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X5)
         => ( c_Orderings_Oord__class_Oless__eq(X4,X5,c_Groups_Oone__class_Oone(X4))
           => c_Orderings_Oord__class_Oless__eq(X4,hAPP(hAPP(c_Power_Opower__class_Opower(X4),X5),X65),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X5),X17)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__decreasing) ).

fof(f9775,plain,
    ( spl24_147
    | spl24_185
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f9771,f7320,f7317,f9773,f9165]) ).

fof(f9771,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ class_Rings_Olinordered__semidom(X1)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
        | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X0) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f9770,f7321]) ).

fof(f9770,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
        | ~ class_Rings_Olinordered__semidom(X1)
        | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X0) )
    | ~ spl24_136 ),
    inference(forward_demodulation,[],[f8490,f7318]) ).

fof(f8490,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ class_Rings_Olinordered__semidom(X1)
        | c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),X2))
        | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2) )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f4650,f7318]) ).

fof(f4650,plain,
    ! [X2,X3,X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X0)
      | c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),X2))
      | ~ class_Rings_Olinordered__semidom(X1)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2) ),
    inference(cnf_transformation,[],[f3614]) ).

fof(f3614,plain,
    ! [X0,X1,X2,X3] :
      ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X0)
      | c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),X2))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
      | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(rectify,[],[f2508]) ).

fof(f2508,plain,
    ! [X0,X2,X3,X1] :
      ( ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X0)
      | c_Orderings_Oord__class_Oless(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),X3))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3)
      | ~ class_Rings_Olinordered__semidom(X2) ),
    inference(flattening,[],[f2507]) ).

fof(f2507,plain,
    ! [X1,X0,X3,X2] :
      ( c_Orderings_Oord__class_Oless(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),X3))
      | ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3)
      | ~ class_Rings_Olinordered__semidom(X2) ),
    inference(ennf_transformation,[],[f2016]) ).

fof(f2016,plain,
    ! [X1,X0,X3,X2] :
      ( class_Rings_Olinordered__semidom(X2)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3)
       => ( c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X0)
         => c_Orderings_Oord__class_Oless(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),X3)) ) ) ),
    inference(rectify,[],[f753]) ).

fof(f753,axiom,
    ! [X5,X17,X4,X65] :
      ( class_Rings_Olinordered__semidom(X4)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X65)
       => ( c_Orderings_Oord__class_Oless(X4,c_Groups_Oone__class_Oone(X4),X5)
         => c_Orderings_Oord__class_Oless(X4,hAPP(hAPP(c_Power_Opower__class_Opower(X4),X5),X17),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X5),X65)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__increasing) ).

fof(f9728,plain,
    ( spl24_183
    | spl24_184
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f9721,f7320,f7317,f9726,f9723]) ).

fof(f9726,plain,
    ( spl24_184
  <=> ! [X2,X1] :
        ( ~ c_Orderings_Oord__class_Oless(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1,X2)
        | c_Orderings_Oord__class_Oless__eq(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_184])]) ).

fof(f9721,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1,X2)
        | c_Orderings_Oord__class_Oless__eq(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1,X2)
        | ~ class_Orderings_Oord(X0) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f9720,f7321]) ).

fof(f9720,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1,X2)
        | ~ class_Orderings_Oord(X0)
        | c_Orderings_Oord__class_Oless__eq(c_Groups_Oone__class_Oone(tc_Nat_Onat),X1,X2) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f9719,f7321]) ).

fof(f9719,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless(c_Groups_Oone__class_Oone(tc_Nat_Onat),X1,X2)
        | c_Orderings_Oord__class_Oless__eq(c_Groups_Oone__class_Oone(tc_Nat_Onat),X1,X2)
        | ~ class_Orderings_Oord(X0) )
    | ~ spl24_136 ),
    inference(forward_demodulation,[],[f9066,f7318]) ).

fof(f9066,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless(tc_fun(X3,X0),X1,X2)
        | ~ class_Orderings_Oord(X0)
        | c_Orderings_Oord__class_Oless__eq(c_Groups_Oone__class_Oone(tc_Nat_Onat),X1,X2) )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f4774,f7318]) ).

fof(f4774,plain,
    ! [X2,X3,X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(tc_fun(X3,X0),X1,X2)
      | c_Orderings_Oord__class_Oless__eq(tc_fun(X3,X0),X1,X2)
      | ~ class_Orderings_Oord(X0) ),
    inference(cnf_transformation,[],[f3699]) ).

fof(f9705,plain,
    ( ~ spl24_153
    | ~ spl24_136
    | ~ spl24_137
    | spl24_139 ),
    inference(avatar_split_clause,[],[f9704,f7676,f7320,f7317,f9279]) ).

fof(f7676,plain,
    ( spl24_139
  <=> 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,[spl24_139])]) ).

fof(f9704,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_136
    | ~ spl24_137
    | spl24_139 ),
    inference(forward_demodulation,[],[f9061,f7321]) ).

fof(f9061,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl24_136
    | spl24_139 ),
    inference(backward_demodulation,[],[f7678,f7318]) ).

fof(f7678,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))
    | spl24_139 ),
    inference(avatar_component_clause,[],[f7676]) ).

fof(f9700,plain,
    ( spl24_182
    | spl24_152
    | spl24_152
    | ~ spl24_136 ),
    inference(avatar_split_clause,[],[f9696,f7317,f9263,f9263,f9698]) ).

fof(f9698,plain,
    ( spl24_182
  <=> ! [X1] : ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_182])]) ).

fof(f9696,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( X0 = X4
        | X2 = X3
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1) )
    | ~ spl24_136 ),
    inference(trivial_inequality_removal,[],[f9695]) ).

fof(f9695,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( X0 = X4
        | X2 = X3
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
    | ~ spl24_136 ),
    inference(forward_demodulation,[],[f9694,f7318]) ).

fof(f9694,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | X0 = X4
        | X2 = X3 )
    | ~ spl24_136 ),
    inference(forward_demodulation,[],[f8308,f7318]) ).

fof(f8308,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( X0 = X4
        | c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3),c_Groups_Oone__class_Oone(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X3))
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
        | X2 = X3 )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f4870,f7318]) ).

fof(f4870,plain,
    ! [X2,X3,X0,X1,X4] :
      ( c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X3)) != c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X2))
      | X0 = X4
      | X2 = X3
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1) ),
    inference(cnf_transformation,[],[f3763]) ).

fof(f3763,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
      | ( ( c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X3)) != c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X2))
          | X0 = X4
          | X2 = X3 )
        & ( ( X0 != X4
            & X2 != X3 )
          | c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X3)) = c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X2)) ) ) ),
    inference(rectify,[],[f3762]) ).

fof(f3762,plain,
    ! [X4,X3,X2,X0,X1] :
      ( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3)
      | ( ( c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X4),X2)) != c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X4),X0))
          | X1 = X4
          | X0 = X2 )
        & ( ( X1 != X4
            & X0 != X2 )
          | c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X4),X2)) = c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X4),X0)) ) ) ),
    inference(flattening,[],[f3761]) ).

fof(f3761,plain,
    ! [X4,X3,X2,X0,X1] :
      ( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3)
      | ( ( c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X4),X2)) != c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X4),X0))
          | X1 = X4
          | X0 = X2 )
        & ( ( X1 != X4
            & X0 != X2 )
          | c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X4),X2)) = c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X4),X0)) ) ) ),
    inference(nnf_transformation,[],[f2800]) ).

fof(f2800,plain,
    ! [X4,X3,X2,X0,X1] :
      ( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3)
      | ( c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X4),X2)) != c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X4),X0))
      <=> ( X1 != X4
          & X0 != X2 ) ) ),
    inference(ennf_transformation,[],[f1538]) ).

fof(f1538,plain,
    ! [X3,X1,X0,X4,X2] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3)
     => ( c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X4),X2)) != c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X4),X0))
      <=> ( X1 != X4
          & X0 != X2 ) ) ),
    inference(rectify,[],[f111]) ).

fof(f111,axiom,
    ! [X30,X7,X41,X8,X10] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X8)
     => ( c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X30),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X41)) != c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X41),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X30))
      <=> ( X7 != X10
          & X30 != X41 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_crossproduct__noteq) ).

fof(f9692,plain,
    ( ~ spl24_175
    | spl24_181
    | spl24_176
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f9688,f7320,f7317,f9546,f9690,f9542]) ).

fof(f9690,plain,
    ( spl24_181
  <=> ! [X2] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_181])]) ).

fof(f9546,plain,
    ( spl24_176
  <=> ! [X2,X1] : c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_176])]) ).

fof(f9688,plain,
    ( ! [X2,X0,X1] :
        ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,X1)
        | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X2
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f9687,f7321]) ).

fof(f9687,plain,
    ( ! [X2,X0,X1] :
        ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,X1)
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X2 )
    | ~ spl24_136 ),
    inference(forward_demodulation,[],[f8222,f7318]) ).

fof(f8222,plain,
    ( ! [X2,X0,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X2
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1))
        | c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,X1) )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f4599,f7318]) ).

fof(f4599,plain,
    ! [X2,X0,X1] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1))
      | c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,X1)
      | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X2 ),
    inference(cnf_transformation,[],[f3579]) ).

fof(f3579,plain,
    ! [X0,X1,X2] :
      ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X2
      | ( ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1))
          | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,X1) )
        & ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,X1)
          | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1)) ) ) ),
    inference(rectify,[],[f3578]) ).

fof(f3578,plain,
    ! [X1,X0,X2] :
      ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X2
      | ( ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0))
          | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X0) )
        & ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X0)
          | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0)) ) ) ),
    inference(nnf_transformation,[],[f2987]) ).

fof(f2987,plain,
    ! [X1,X0,X2] :
      ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X2
      | ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0))
      <=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X0) ) ),
    inference(ennf_transformation,[],[f2192]) ).

fof(f2192,plain,
    ! [X0,X1,X2] :
      ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X2
     => ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0))
      <=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X0) ) ),
    inference(rectify,[],[f774]) ).

fof(f774,axiom,
    ! [X67,X43,X44] :
      ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X44
     => ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X43,X67)
      <=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X44),X43),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X44),X67)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__mono) ).

fof(f9680,plain,
    ( spl24_177
    | spl24_180
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f9676,f7320,f7317,f9678,f9552]) ).

fof(f9678,plain,
    ( spl24_180
  <=> ! [X1] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X1
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_180])]) ).

fof(f9676,plain,
    ( ! [X1] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
        | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X1
        | hBOOL(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f9675,f7321]) ).

fof(f9675,plain,
    ( ! [X1] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X1
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)
        | hBOOL(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f9674,f7318]) ).

fof(f9674,plain,
    ( ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,sK8(X0,X1,X2),X1)
        | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X1
        | hBOOL(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)) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f8094,f7321]) ).

fof(f8094,plain,
    ( ! [X2,X0,X1] :
        ( hBOOL(c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,sK8(X0,X1,X2),X1)
        | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X1
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f5163,f7318]) ).

fof(f5163,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,sK8(X0,X1,X2),X1)
      | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X1
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | hBOOL(hAPP(X0,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1))) ),
    inference(cnf_transformation,[],[f3944]) ).

fof(f9673,plain,
    ( spl24_179
    | spl24_177
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f9669,f7320,f7317,f9552,f9671]) ).

fof(f9669,plain,
    ( ! [X2] :
        ( hBOOL(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ class_HOL_Oequal(X2)
        | ~ class_Groups_Ozero(X2) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f8143,f7321]) ).

fof(f8143,plain,
    ( ! [X2] :
        ( ~ class_Groups_Ozero(X2)
        | ~ class_HOL_Oequal(X2)
        | hBOOL(c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f6119,f7318]) ).

fof(f6119,plain,
    ! [X2,X1] :
      ( ~ class_HOL_Oequal(X2)
      | ~ class_Groups_Ozero(X2)
      | hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Polynomial_Opoly(X2)),X1),X1)) ),
    inference(equality_resolution,[],[f5345]) ).

fof(f5345,plain,
    ! [X2,X0,X1] :
      ( ~ class_Groups_Ozero(X2)
      | hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Polynomial_Opoly(X2)),X1),X0))
      | X0 != X1
      | ~ class_HOL_Oequal(X2) ),
    inference(cnf_transformation,[],[f4034]) ).

fof(f9582,plain,
    ( spl24_172
    | ~ spl24_9
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f9581,f7320,f7317,f6248,f9476]) ).

fof(f9581,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ spl24_9
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f9580,f9473]) ).

fof(f9473,plain,
    ( ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f8592,f7321]) ).

fof(f8592,plain,
    ( ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f4924,f7318]) ).

fof(f9580,plain,
    ( ! [X1] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | ~ spl24_9
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f8596,f7321]) ).

fof(f8596,plain,
    ( ! [X1] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)
    | ~ spl24_9
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f7254,f7318]) ).

fof(f9579,plain,
    ( spl24_152
    | spl24_166
    | ~ spl24_136 ),
    inference(avatar_split_clause,[],[f9578,f7317,f9398,f9263]) ).

fof(f9578,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Groups_Ozero(X1)
        | X0 = X2 )
    | ~ spl24_136 ),
    inference(trivial_inequality_removal,[],[f9577]) ).

fof(f9577,plain,
    ( ! [X2,X0,X1] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | X0 = X2
        | ~ class_Groups_Ozero(X1) )
    | ~ spl24_136 ),
    inference(forward_demodulation,[],[f8578,f7318]) ).

fof(f8578,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Groups_Ozero(X1)
        | X0 = X2
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(c_Polynomial_Ocoeff(X1,X2),sK1(X0,X1,X2)) )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f4519,f7318]) ).

fof(f4519,plain,
    ! [X2,X0,X1] :
      ( X0 = X2
      | hAPP(c_Polynomial_Ocoeff(X1,X2),sK1(X0,X1,X2)) != hAPP(c_Polynomial_Ocoeff(X1,X0),sK1(X0,X1,X2))
      | ~ class_Groups_Ozero(X1) ),
    inference(cnf_transformation,[],[f3531]) ).

fof(f3531,plain,
    ! [X0,X1,X2] :
      ( ~ class_Groups_Ozero(X1)
      | ( ( ! [X3] : hAPP(c_Polynomial_Ocoeff(X1,X2),X3) = hAPP(c_Polynomial_Ocoeff(X1,X0),X3)
          | X0 != X2 )
        & ( X0 = X2
          | hAPP(c_Polynomial_Ocoeff(X1,X2),sK1(X0,X1,X2)) != hAPP(c_Polynomial_Ocoeff(X1,X0),sK1(X0,X1,X2)) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f3529,f3530]) ).

fof(f3530,plain,
    ! [X0,X1,X2] :
      ( ? [X4] : hAPP(c_Polynomial_Ocoeff(X1,X2),X4) != hAPP(c_Polynomial_Ocoeff(X1,X0),X4)
     => hAPP(c_Polynomial_Ocoeff(X1,X2),sK1(X0,X1,X2)) != hAPP(c_Polynomial_Ocoeff(X1,X0),sK1(X0,X1,X2)) ),
    introduced(choice_axiom,[]) ).

fof(f3529,plain,
    ! [X0,X1,X2] :
      ( ~ class_Groups_Ozero(X1)
      | ( ( ! [X3] : hAPP(c_Polynomial_Ocoeff(X1,X2),X3) = hAPP(c_Polynomial_Ocoeff(X1,X0),X3)
          | X0 != X2 )
        & ( X0 = X2
          | ? [X4] : hAPP(c_Polynomial_Ocoeff(X1,X2),X4) != hAPP(c_Polynomial_Ocoeff(X1,X0),X4) ) ) ),
    inference(rectify,[],[f3528]) ).

fof(f3528,plain,
    ! [X2,X0,X1] :
      ( ~ class_Groups_Ozero(X0)
      | ( ( ! [X3] : hAPP(c_Polynomial_Ocoeff(X0,X1),X3) = hAPP(c_Polynomial_Ocoeff(X0,X2),X3)
          | X1 != X2 )
        & ( X1 = X2
          | ? [X3] : hAPP(c_Polynomial_Ocoeff(X0,X1),X3) != hAPP(c_Polynomial_Ocoeff(X0,X2),X3) ) ) ),
    inference(nnf_transformation,[],[f3017]) ).

fof(f3017,plain,
    ! [X2,X0,X1] :
      ( ~ class_Groups_Ozero(X0)
      | ( ! [X3] : hAPP(c_Polynomial_Ocoeff(X0,X1),X3) = hAPP(c_Polynomial_Ocoeff(X0,X2),X3)
      <=> X1 = X2 ) ),
    inference(ennf_transformation,[],[f1715]) ).

fof(f1715,plain,
    ! [X0,X1,X2] :
      ( class_Groups_Ozero(X0)
     => ( ! [X3] : hAPP(c_Polynomial_Ocoeff(X0,X1),X3) = hAPP(c_Polynomial_Ocoeff(X0,X2),X3)
      <=> X1 = X2 ) ),
    inference(rectify,[],[f33]) ).

fof(f33,axiom,
    ! [X8,X9,X6] :
      ( class_Groups_Ozero(X8)
     => ( ! [X25] : hAPP(c_Polynomial_Ocoeff(X8,X6),X25) = hAPP(c_Polynomial_Ocoeff(X8,X9),X25)
      <=> X6 = X9 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_expand__poly__eq) ).

fof(f9569,plain,
    ( spl24_152
    | spl24_178
    | ~ spl24_136 ),
    inference(avatar_split_clause,[],[f9565,f7317,f9567,f9263]) ).

fof(f9565,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Groups_Ocancel__semigroup__add(X2)
        | X0 = X1 )
    | ~ spl24_136 ),
    inference(trivial_inequality_removal,[],[f9564]) ).

fof(f9564,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Groups_Ocancel__semigroup__add(X2)
        | X0 = X1
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
    | ~ spl24_136 ),
    inference(forward_demodulation,[],[f8731,f7318]) ).

fof(f8731,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(X2,X3,X0)
        | ~ class_Groups_Ocancel__semigroup__add(X2)
        | X0 = X1 )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f4491,f7318]) ).

fof(f4491,plain,
    ! [X2,X3,X0,X1] :
      ( c_Groups_Oplus__class_Oplus(X2,X3,X1) != c_Groups_Oplus__class_Oplus(X2,X3,X0)
      | ~ class_Groups_Ocancel__semigroup__add(X2)
      | X0 = X1 ),
    inference(cnf_transformation,[],[f3511]) ).

fof(f3511,plain,
    ! [X0,X1,X2,X3] :
      ( ~ class_Groups_Ocancel__semigroup__add(X2)
      | ( ( X0 = X1
          | c_Groups_Oplus__class_Oplus(X2,X3,X1) != c_Groups_Oplus__class_Oplus(X2,X3,X0) )
        & ( c_Groups_Oplus__class_Oplus(X2,X3,X1) = c_Groups_Oplus__class_Oplus(X2,X3,X0)
          | X0 != X1 ) ) ),
    inference(rectify,[],[f3510]) ).

fof(f3510,plain,
    ! [X3,X2,X0,X1] :
      ( ~ class_Groups_Ocancel__semigroup__add(X0)
      | ( ( X2 = X3
          | c_Groups_Oplus__class_Oplus(X0,X1,X2) != c_Groups_Oplus__class_Oplus(X0,X1,X3) )
        & ( c_Groups_Oplus__class_Oplus(X0,X1,X2) = c_Groups_Oplus__class_Oplus(X0,X1,X3)
          | X2 != X3 ) ) ),
    inference(nnf_transformation,[],[f2436]) ).

fof(f2436,plain,
    ! [X3,X2,X0,X1] :
      ( ~ class_Groups_Ocancel__semigroup__add(X0)
      | ( X2 = X3
      <=> c_Groups_Oplus__class_Oplus(X0,X1,X2) = c_Groups_Oplus__class_Oplus(X0,X1,X3) ) ),
    inference(ennf_transformation,[],[f1324]) ).

fof(f1324,plain,
    ! [X3,X1,X2,X0] :
      ( class_Groups_Ocancel__semigroup__add(X0)
     => ( X2 = X3
      <=> c_Groups_Oplus__class_Oplus(X0,X1,X2) = c_Groups_Oplus__class_Oplus(X0,X1,X3) ) ),
    inference(rectify,[],[f57]) ).

fof(f57,axiom,
    ! [X8,X7,X10,X30] :
      ( class_Groups_Ocancel__semigroup__add(X8)
     => ( c_Groups_Oplus__class_Oplus(X8,X7,X10) = c_Groups_Oplus__class_Oplus(X8,X7,X30)
      <=> X10 = X30 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__cancel) ).

fof(f9555,plain,
    ( spl24_152
    | ~ spl24_177
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f9550,f7320,f7317,f9552,f9263]) ).

fof(f9550,plain,
    ( ! [X0,X1] :
        ( ~ hBOOL(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | X0 = X1 )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f8138,f7321]) ).

fof(f8138,plain,
    ( ! [X0,X1] :
        ( X0 = X1
        | ~ hBOOL(c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f4416,f7318]) ).

fof(f4416,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP(hAPP(c_fequal,X0),X1))
      | X0 = X1 ),
    inference(cnf_transformation,[],[f1883]) ).

fof(f1883,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP(hAPP(c_fequal,X0),X1))
      | X0 = X1 ),
    inference(rectify,[],[f1176]) ).

fof(f1176,axiom,
    ! [X13,X20] :
      ( ~ hBOOL(hAPP(hAPP(c_fequal,X13),X20))
      | X13 = X20 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__1) ).

fof(f9548,plain,
    ( spl24_161
    | ~ spl24_175
    | spl24_176
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f9540,f7320,f7317,f9546,f9542,f9332]) ).

fof(f9540,plain,
    ( ! [X2,X0,X1] :
        ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X1)
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f9539,f7321]) ).

fof(f9539,plain,
    ( ! [X2,X0,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X1) )
    | ~ spl24_136 ),
    inference(forward_demodulation,[],[f8532,f7318]) ).

fof(f8532,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X0))
        | c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X1)
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f4661,f7318]) ).

fof(f4661,plain,
    ! [X2,X0,X1] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X1)
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X0))
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
    inference(cnf_transformation,[],[f3620]) ).

fof(f3620,plain,
    ! [X0,X1,X2] :
      ( ( ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X0))
          | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X1) )
        & ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X1)
          | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X0)) ) )
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
    inference(rectify,[],[f3619]) ).

fof(f3619,plain,
    ! [X2,X0,X1] :
      ( ( ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X0),X2))
          | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X0) )
        & ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X0)
          | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X0),X2)) ) )
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2 ),
    inference(nnf_transformation,[],[f2671]) ).

fof(f2671,plain,
    ! [X2,X0,X1] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X0),X2))
      <=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X0) )
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2 ),
    inference(ennf_transformation,[],[f2189]) ).

fof(f2189,plain,
    ! [X1,X2,X0] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2
     => ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X0),X2))
      <=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X0) ) ),
    inference(rectify,[],[f710]) ).

fof(f710,axiom,
    ! [X10,X7,X18] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X18
     => ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X7),X18),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X10),X18))
      <=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,X7,X10) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pow__divides__eq__int) ).

fof(f9537,plain,
    ( spl24_174
    | ~ spl24_92
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f9532,f7320,f7317,f6764,f9534]) ).

fof(f9534,plain,
    ( spl24_174
  <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(t_a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_174])]) ).

fof(f9532,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(t_a)
    | ~ spl24_92
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f9531,f9473]) ).

fof(f9531,plain,
    ( ! [X4] : hAPP(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4) = c_Groups_Ozero__class_Ozero(t_a)
    | ~ spl24_92
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f9530,f7321]) ).

fof(f9530,plain,
    ( ! [X4] : c_Groups_Ozero__class_Ozero(t_a) = hAPP(c_Groups_Oone__class_Oone(tc_Nat_Onat),X4)
    | ~ spl24_92
    | ~ spl24_136 ),
    inference(forward_demodulation,[],[f8671,f7318]) ).

fof(f8671,plain,
    ( ! [X4] : hAPP(c_Polynomial_Opoly(t_a,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X4) = c_Groups_Ozero__class_Ozero(t_a)
    | ~ spl24_92
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f7206,f7318]) ).

fof(f9516,plain,
    ( spl24_154
    | ~ spl24_153
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f9515,f7320,f7317,f9279,f9283]) ).

fof(f9515,plain,
    ( ! [X1] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f9514,f7321]) ).

fof(f9514,plain,
    ( ! [X1] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
    | ~ spl24_136 ),
    inference(forward_demodulation,[],[f8911,f7318]) ).

fof(f8911,plain,
    ( ! [X1] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f7665,f7318]) ).

fof(f7665,plain,
    ! [X1] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(superposition,[],[f6583,f5388]) ).

fof(f9512,plain,
    ( spl24_152
    | spl24_173
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f9508,f7320,f7317,f9510,f9263]) ).

fof(f9508,plain,
    ( ! [X2,X0,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
        | X0 = X2
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f9507,f7321]) ).

fof(f9507,plain,
    ( ! [X2,X0,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
        | X0 = X2
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(c_Groups_Oone__class_Oone(tc_Nat_Onat),X1) )
    | ~ spl24_136 ),
    inference(forward_demodulation,[],[f8185,f7318]) ).

fof(f8185,plain,
    ( ! [X2,X0,X1] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
        | X0 = X2 )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f5482,f7318]) ).

fof(f5482,plain,
    ! [X2,X0,X1] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
      | X0 = X2 ),
    inference(cnf_transformation,[],[f4132]) ).

fof(f4132,plain,
    ! [X0,X1,X2] :
      ( ( X0 = X2
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) )
      & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)
        | ( X0 != X2
          & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ) ) ),
    inference(rectify,[],[f4131]) ).

fof(f4131,plain,
    ! [X1,X2,X0] :
      ( ( X0 = X1
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2) )
      & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2)
        | ( X0 != X1
          & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2 ) ) ),
    inference(flattening,[],[f4130]) ).

fof(f4130,plain,
    ! [X1,X2,X0] :
      ( ( X0 = X1
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2) )
      & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2)
        | ( X0 != X1
          & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2 ) ) ),
    inference(nnf_transformation,[],[f1459]) ).

fof(f1459,plain,
    ! [X1,X2,X0] :
      ( ( X0 = X1
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2 )
    <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2) ),
    inference(rectify,[],[f122]) ).

fof(f122,axiom,
    ! [X43,X18,X44] :
      ( ( X18 = X43
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X44 )
    <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X43),X44) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18),X44) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__cancel2) ).

fof(f9484,plain,
    ( spl24_166
    | spl24_152
    | ~ spl24_136 ),
    inference(avatar_split_clause,[],[f9483,f7317,f9263,f9398]) ).

fof(f9483,plain,
    ( ! [X2,X0,X1] :
        ( X0 = X1
        | ~ class_Groups_Ozero(X2) )
    | ~ spl24_136 ),
    inference(trivial_inequality_removal,[],[f9482]) ).

fof(f9482,plain,
    ( ! [X2,X0,X1] :
        ( X0 = X1
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ class_Groups_Ozero(X2) )
    | ~ spl24_136 ),
    inference(forward_demodulation,[],[f8697,f7318]) ).

fof(f8697,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Groups_Ozero(X2)
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Polynomial_Ocoeff(X2,X0)
        | X0 = X1 )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f5414,f7318]) ).

fof(f5414,plain,
    ! [X2,X0,X1] :
      ( X0 = X1
      | c_Polynomial_Ocoeff(X2,X1) != c_Polynomial_Ocoeff(X2,X0)
      | ~ class_Groups_Ozero(X2) ),
    inference(cnf_transformation,[],[f4082]) ).

fof(f4082,plain,
    ! [X0,X1,X2] :
      ( ~ class_Groups_Ozero(X2)
      | ( ( X0 = X1
          | c_Polynomial_Ocoeff(X2,X1) != c_Polynomial_Ocoeff(X2,X0) )
        & ( c_Polynomial_Ocoeff(X2,X1) = c_Polynomial_Ocoeff(X2,X0)
          | X0 != X1 ) ) ),
    inference(nnf_transformation,[],[f2897]) ).

fof(f2897,plain,
    ! [X0,X1,X2] :
      ( ~ class_Groups_Ozero(X2)
      | ( X0 = X1
      <=> c_Polynomial_Ocoeff(X2,X1) = c_Polynomial_Ocoeff(X2,X0) ) ),
    inference(ennf_transformation,[],[f1783]) ).

fof(f1783,plain,
    ! [X2,X0,X1] :
      ( class_Groups_Ozero(X2)
     => ( X0 = X1
      <=> c_Polynomial_Ocoeff(X2,X1) = c_Polynomial_Ocoeff(X2,X0) ) ),
    inference(rectify,[],[f35]) ).

fof(f35,axiom,
    ! [X20,X13,X8] :
      ( class_Groups_Ozero(X8)
     => ( c_Polynomial_Ocoeff(X8,X13) = c_Polynomial_Ocoeff(X8,X20)
      <=> X13 = X20 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__inject) ).

fof(f9479,plain,
    ( spl24_172
    | ~ spl24_121
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f9474,f7320,f7317,f6941,f9476]) ).

fof(f9474,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ spl24_121
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(backward_demodulation,[],[f9349,f9473]) ).

fof(f9349,plain,
    ( ! [X3] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
    | ~ spl24_121
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f9348,f7321]) ).

fof(f9348,plain,
    ( ! [X3] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Groups_Oone__class_Oone(tc_Nat_Onat),X3)
    | ~ spl24_121
    | ~ spl24_136 ),
    inference(forward_demodulation,[],[f8663,f7318]) ).

fof(f8663,plain,
    ( ! [X3] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Polynomial_Opoly(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X3)
    | ~ spl24_121
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f7205,f7318]) ).

fof(f7205,plain,
    ( ! [X3] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Polynomial_Opoly(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint))),X3)
    | ~ spl24_121 ),
    inference(resolution,[],[f4404,f6943]) ).

fof(f9468,plain,
    ( spl24_171
    | spl24_161
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f9464,f7320,f7317,f9332,f9466]) ).

fof(f9466,plain,
    ( spl24_171
  <=> ! [X4] :
        ( hAPP(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4) != X4
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_171])]) ).

fof(f9464,plain,
    ( ! [X4,X5] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X5
        | hAPP(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4) != X4
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X4 )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f8586,f7321]) ).

fof(f8586,plain,
    ( ! [X4,X5] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X5
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X4
        | hAPP(c_Groups_Oone__class_Oone(tc_Nat_Onat),X4) != X4 )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(backward_demodulation,[],[f7930,f7318]) ).

fof(f7930,plain,
    ( ! [X4,X5] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X5
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X4
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5),X4) != X4 )
    | ~ spl24_137 ),
    inference(backward_demodulation,[],[f7630,f7321]) ).

fof(f7630,plain,
    ! [X4,X5] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5),X4) != X4
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X4
      | c_Groups_Oone__class_Oone(tc_Nat_Onat) = X5 ),
    inference(superposition,[],[f5763,f5329]) ).

fof(f9459,plain,
    ( spl24_143
    | spl24_144
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f9458,f7320,f7317,f9145,f9142]) ).

fof(f9458,plain,
    ( ! [X12,X13] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X12)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X13,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f8213,f7321]) ).

fof(f8213,plain,
    ( ! [X12,X13] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X13,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X12) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(backward_demodulation,[],[f7935,f7318]) ).

fof(f7935,plain,
    ( ! [X12,X13] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12),X13),X12)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X13,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
    | ~ spl24_137 ),
    inference(backward_demodulation,[],[f7729,f7321]) ).

fof(f7729,plain,
    ! [X12,X13] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12),X13),X12)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X13,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(superposition,[],[f4796,f4704]) ).

fof(f4704,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,[],[f1253]) ).

fof(f1253,plain,
    ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0,
    inference(rectify,[],[f285]) ).

fof(f285,axiom,
    ! [X17] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X17,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__1__right) ).

fof(f4796,plain,
    ! [X2,X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0))
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
    inference(cnf_transformation,[],[f3714]) ).

fof(f3714,plain,
    ! [X0,X1,X2] :
      ( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) )
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ) ),
    inference(rectify,[],[f3713]) ).

fof(f3713,plain,
    ! [X2,X1,X0] :
      ( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) )
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2)) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ) ),
    inference(flattening,[],[f3712]) ).

fof(f3712,plain,
    ! [X2,X1,X0] :
      ( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) )
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2)) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ) ),
    inference(nnf_transformation,[],[f1527]) ).

fof(f1527,plain,
    ! [X2,X1,X0] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
        & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) )
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2)) ),
    inference(rectify,[],[f573]) ).

fof(f573,axiom,
    ! [X44,X43,X18] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X44)
        & c_Orderings_Oord__class_Oless(tc_Nat_Onat,X43,X18) )
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X44),X43),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X44),X18)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel1) ).

fof(f9443,plain,
    ( ~ spl24_169
    | spl24_170
    | spl24_161
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f9435,f7320,f7317,f9332,f9441,f9437]) ).

fof(f9435,plain,
    ( ! [X2,X0,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,X1)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f9434,f7321]) ).

fof(f9434,plain,
    ( ! [X2,X0,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,X1)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
    | ~ spl24_136 ),
    inference(forward_demodulation,[],[f8180,f7318]) ).

fof(f8180,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1))
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,X1) )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f5257,f7318]) ).

fof(f5257,plain,
    ! [X2,X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1))
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,X1) ),
    inference(cnf_transformation,[],[f3979]) ).

fof(f9413,plain,
    ( spl24_167
    | spl24_168
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f9406,f7320,f7317,f9411,f9408]) ).

fof(f9411,plain,
    ( spl24_168
  <=> ! [X0,X3] :
        ( ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Oone__class_Oone(X0),X3)
        | c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ class_Rings_Olinordered__semidom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_168])]) ).

fof(f9406,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Oone__class_Oone(X0),X3)
        | ~ class_Rings_Olinordered__semidom(X0)
        | c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f9405,f7321]) ).

fof(f9405,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ class_Rings_Olinordered__semidom(X0)
        | ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Oone__class_Oone(X0),X3)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) )
    | ~ spl24_136 ),
    inference(forward_demodulation,[],[f8498,f7318]) ).

fof(f8498,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
        | ~ class_Rings_Olinordered__semidom(X0)
        | ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Oone__class_Oone(X0),X3)
        | c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X3),X1)) )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f4904,f7318]) ).

fof(f4904,plain,
    ! [X2,X3,X0,X1] :
      ( ~ class_Rings_Olinordered__semidom(X0)
      | c_Orderings_Oord__class_Oless__eq(X0,hAPP(hAPP(c_Power_Opower__class_Opower(X0),X3),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X3),X1))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
      | ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Oone__class_Oone(X0),X3) ),
    inference(cnf_transformation,[],[f3785]) ).

fof(f3785,plain,
    ! [X0,X1,X2,X3] :
      ( ~ class_Rings_Olinordered__semidom(X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
      | ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Oone__class_Oone(X0),X3)
      | c_Orderings_Oord__class_Oless__eq(X0,hAPP(hAPP(c_Power_Opower__class_Opower(X0),X3),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X3),X1)) ),
    inference(rectify,[],[f3022]) ).

fof(f3022,plain,
    ! [X2,X3,X1,X0] :
      ( ~ class_Rings_Olinordered__semidom(X2)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
      | ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oone__class_Oone(X2),X0)
      | c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),X3)) ),
    inference(flattening,[],[f3021]) ).

fof(f3021,plain,
    ! [X2,X3,X1,X0] :
      ( c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),X3))
      | ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oone__class_Oone(X2),X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
      | ~ class_Rings_Olinordered__semidom(X2) ),
    inference(ennf_transformation,[],[f2039]) ).

fof(f2039,plain,
    ! [X2,X3,X1,X0] :
      ( class_Rings_Olinordered__semidom(X2)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
       => ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oone__class_Oone(X2),X0)
         => c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),X3)) ) ) ),
    inference(rectify,[],[f754]) ).

fof(f754,axiom,
    ! [X5,X17,X4,X65] :
      ( class_Rings_Olinordered__semidom(X4)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X65)
       => ( c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Oone__class_Oone(X4),X5)
         => c_Orderings_Oord__class_Oless__eq(X4,hAPP(hAPP(c_Power_Opower__class_Opower(X4),X5),X17),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X5),X65)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__increasing) ).

fof(f9400,plain,
    ( spl24_166
    | spl24_152
    | ~ spl24_136 ),
    inference(avatar_split_clause,[],[f9396,f7317,f9263,f9398]) ).

fof(f9396,plain,
    ( ! [X2,X0,X1] :
        ( X0 = X1
        | ~ class_Groups_Ozero(X2) )
    | ~ spl24_136 ),
    inference(trivial_inequality_removal,[],[f9395]) ).

fof(f9395,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Groups_Ozero(X2)
        | X0 = X1
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
    | ~ spl24_136 ),
    inference(forward_demodulation,[],[f8680,f7318]) ).

fof(f8680,plain,
    ( ! [X2,X0,X1,X4] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Polynomial_OpCons(X2,X4,X1)
        | X0 = X1
        | ~ class_Groups_Ozero(X2) )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f4841,f7318]) ).

fof(f9383,plain,
    ( ~ spl24_153
    | spl24_155
    | spl24_165
    | spl24_149
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f9379,f7320,f7317,f9190,f9381,f9289,f9279]) ).

fof(f9381,plain,
    ( spl24_165
  <=> ! [X5,X2,X0] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_165])]) ).

fof(f9379,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X4)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X0)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X0)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(trivial_inequality_removal,[],[f9378]) ).

fof(f9378,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X4)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X0)
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f9377,f7318]) ).

fof(f9377,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X3)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X4)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X0)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f9376,f7321]) ).

fof(f9376,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X4)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X0)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X0)
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X3) )
    | ~ spl24_136 ),
    inference(forward_demodulation,[],[f9375,f7318]) ).

fof(f9375,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X0)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X0)
        | c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X3) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X4),X5)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X4) )
    | ~ spl24_136 ),
    inference(forward_demodulation,[],[f8237,f7318]) ).

fof(f8237,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Nat_Onat),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X3) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X4),X5)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X0)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X4) )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f5087,f7318]) ).

fof(f5087,plain,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X4)
      | c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X3) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X4),X5)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
    inference(cnf_transformation,[],[f3898]) ).

fof(f3898,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X4)
      | c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X3) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X4),X5)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X0) ),
    inference(rectify,[],[f2914]) ).

fof(f2914,plain,
    ! [X2,X0,X5,X4,X3,X1] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X3)
      | c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5),X0),X4) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3),X1)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,X2)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5),X0),X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(flattening,[],[f2913]) ).

fof(f2913,plain,
    ! [X5,X2,X3,X1,X0,X4] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X3)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,X2)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
      | ~ 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,X1,X2)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5),X0),X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5),X0),X4) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3),X1) ),
    inference(ennf_transformation,[],[f1322]) ).

fof(f1322,plain,
    ! [X5,X2,X3,X1,X0,X4] :
      ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5),X0),X4) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3),X1)
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5),X0),X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
       => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
         => ( 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),X5)
             => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,X2)
               => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X3) ) ) ) ) ) ),
    inference(rectify,[],[f837]) ).

fof(f837,axiom,
    ! [X79,X28,X29,X21,X78,X50] :
      ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X50),X79),X78) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X29),X21),X28)
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X50),X79),X78),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
       => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X28,X29)
         => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X78)
           => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X50)
             => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X50,X29)
               => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X79,X21) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono2__neg__lemma) ).

fof(f9364,plain,
    ( spl24_163
    | spl24_164
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f9356,f7320,f7317,f9362,f9358]) ).

fof(f9356,plain,
    ( ! [X1] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f9082,f7321]) ).

fof(f9082,plain,
    ( ! [X1] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f5410,f7318]) ).

fof(f9353,plain,
    ( spl24_143
    | spl24_144
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f9352,f7320,f7317,f9145,f9142]) ).

fof(f9352,plain,
    ( ! [X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f8212,f7321]) ).

fof(f8212,plain,
    ( ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(backward_demodulation,[],[f7933,f7318]) ).

fof(f7933,plain,
    ( ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0),X0) )
    | ~ spl24_137 ),
    inference(backward_demodulation,[],[f7709,f7321]) ).

fof(f7709,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0),X0)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(superposition,[],[f4726,f4499]) ).

fof(f4726,plain,
    ! [X2,X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2))
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
    inference(cnf_transformation,[],[f3668]) ).

fof(f3668,plain,
    ! [X0,X1,X2] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) )
      & ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) )
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2)) ) ),
    inference(rectify,[],[f3667]) ).

fof(f3667,plain,
    ! [X1,X2,X0] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) )
      & ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) )
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ) ),
    inference(flattening,[],[f3666]) ).

fof(f3666,plain,
    ! [X1,X2,X0] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) )
      & ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) )
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ) ),
    inference(nnf_transformation,[],[f1855]) ).

fof(f1855,plain,
    ! [X1,X2,X0] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
    <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
        & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ) ),
    inference(rectify,[],[f572]) ).

fof(f572,axiom,
    ! [X44,X18,X43] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X43,X18)
        & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X44) )
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X43),X44),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18),X44)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel2) ).

fof(f9337,plain,
    ( spl24_161
    | spl24_162
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f9330,f7320,f7317,f9335,f9332]) ).

fof(f9330,plain,
    ( ! [X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f8211,f7321]) ).

fof(f8211,plain,
    ( ! [X0,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_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(backward_demodulation,[],[f7832,f7318]) ).

fof(f7832,plain,
    ( ! [X0,X1] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1),X1)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) )
    | ~ spl24_137 ),
    inference(backward_demodulation,[],[f4911,f7321]) ).

fof(f9329,plain,
    ( spl24_152
    | spl24_160
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f9325,f7320,f7317,f9327,f9263]) ).

fof(f9327,plain,
    ( spl24_160
  <=> ! [X0] :
        ( ~ class_Groups_Oab__group__add(X0)
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_160])]) ).

fof(f9325,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Groups_Oab__group__add(X0)
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(X0)
        | X1 = X2 )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f9126,f7321]) ).

fof(f9126,plain,
    ( ! [X2,X0,X1] :
        ( X1 = X2
        | ~ class_Groups_Oab__group__add(X0)
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(X0) )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f4936,f7318]) ).

fof(f4936,plain,
    ! [X2,X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X0) != c_Groups_Ominus__class_Ominus(X0,X1,X2)
      | X1 = X2
      | ~ class_Groups_Oab__group__add(X0) ),
    inference(cnf_transformation,[],[f3806]) ).

fof(f3806,plain,
    ! [X0,X1,X2] :
      ( ( ( X1 = X2
          | c_Groups_Ozero__class_Ozero(X0) != c_Groups_Ominus__class_Ominus(X0,X1,X2) )
        & ( c_Groups_Ozero__class_Ozero(X0) = c_Groups_Ominus__class_Ominus(X0,X1,X2)
          | X1 != X2 ) )
      | ~ class_Groups_Oab__group__add(X0) ),
    inference(rectify,[],[f3805]) ).

fof(f3805,plain,
    ! [X2,X1,X0] :
      ( ( ( 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,[],[f2487]) ).

fof(f2487,plain,
    ! [X2,X1,X0] :
      ( ( 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,[],[f1914]) ).

fof(f1914,plain,
    ! [X2,X1,X0] :
      ( class_Groups_Oab__group__add(X2)
     => ( X0 = X1
      <=> c_Groups_Ozero__class_Ozero(X2) = c_Groups_Ominus__class_Ominus(X2,X1,X0) ) ),
    inference(rectify,[],[f990]) ).

fof(f990,axiom,
    ! [X10,X7,X8] :
      ( class_Groups_Oab__group__add(X8)
     => ( c_Groups_Ozero__class_Ozero(X8) = c_Groups_Ominus__class_Ominus(X8,X7,X10)
      <=> X7 = X10 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__iff__diff__eq__0) ).

fof(f9309,plain,
    ( spl24_157
    | spl24_158
    | spl24_159
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f9301,f7320,f7317,f9306,f9303,f9295]) ).

fof(f9295,plain,
    ( spl24_157
  <=> ! [X2] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_157])]) ).

fof(f9303,plain,
    ( spl24_158
  <=> ! [X1,X3] :
        ( ~ 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,X3,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_158])]) ).

fof(f9306,plain,
    ( spl24_159
  <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_159])]) ).

fof(f9301,plain,
    ( ! [X3,X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ 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,X3,X1)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f9300,f7321]) ).

fof(f9300,plain,
    ( ! [X3,X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X1) )
    | ~ spl24_136 ),
    inference(forward_demodulation,[],[f8243,f7318]) ).

fof(f8243,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ 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,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X1)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X0)),X1)) )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f5831,f7318]) ).

fof(f5831,plain,
    ! [X2,X3,X0,X1] :
      ( ~ 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,X3,X1)
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X0),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X0)),X1))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
    inference(cnf_transformation,[],[f4369]) ).

fof(f4369,plain,
    ! [X0,X1,X2,X3] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X1)
      | ~ 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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X0),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X0)),X1))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(rectify,[],[f2928]) ).

fof(f2928,plain,
    ! [X0,X3,X1,X2] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X3)
      | ~ 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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0)),X3))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(flattening,[],[f2927]) ).

fof(f2927,plain,
    ! [X1,X3,X2,X0] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0)),X3))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X3)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
    inference(ennf_transformation,[],[f1239]) ).

fof(f1239,plain,
    ! [X1,X3,X2,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,X2,X3)
       => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
         => c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0)),X3)) ) ) ),
    inference(rectify,[],[f929]) ).

fof(f929,axiom,
    ! [X22,X21,X29,X28] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X22)
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X29,X28)
       => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X28,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
         => c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X29),X22),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X29),c_Divides_Odiv__class_Omod(tc_Int_Oint,X21,X22)),X28)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult2__lemma__aux1) ).

fof(f9297,plain,
    ( spl24_155
    | spl24_156
    | spl24_157
    | ~ spl24_153
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f9287,f7320,f7317,f9279,f9295,f9292,f9289]) ).

fof(f9287,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f9286,f7321]) ).

fof(f9286,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
    | ~ spl24_136 ),
    inference(forward_demodulation,[],[f8244,f7318]) ).

fof(f8244,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f5865,f7318]) ).

fof(f5865,plain,
    ! [X2,X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(cnf_transformation,[],[f4394]) ).

fof(f4394,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
    inference(rectify,[],[f2792]) ).

fof(f2792,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(flattening,[],[f2791]) ).

fof(f2791,plain,
    ! [X0,X2,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(ennf_transformation,[],[f1869]) ).

fof(f1869,plain,
    ! [X0,X2,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
     => ( c_Orderings_Oord__class_Oless__eq(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),X1)
         => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) ),
    inference(rectify,[],[f833]) ).

fof(f833,axiom,
    ! [X78,X50,X79] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X50),X79),X78),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X78)
       => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X50)
         => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X79,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_q__neg__lemma) ).

fof(f9285,plain,
    ( ~ spl24_153
    | spl24_154
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f9277,f7320,f7317,f9283,f9279]) ).

fof(f9277,plain,
    ( ! [X1] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f8950,f7321]) ).

fof(f8950,plain,
    ( ! [X1] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f7660,f7318]) ).

fof(f7660,plain,
    ! [X1] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(superposition,[],[f6583,f5830]) ).

fof(f9265,plain,
    ( spl24_151
    | spl24_152
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f9258,f7320,f7317,f9263,f9260]) ).

fof(f9260,plain,
    ( spl24_151
  <=> ! [X2] :
        ( ~ class_Groups_Ogroup__add(X2)
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_151])]) ).

fof(f9258,plain,
    ( ! [X2,X0,X1] :
        ( X0 = X1
        | ~ class_Groups_Ogroup__add(X2)
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(X2) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f9127,f7321]) ).

fof(f9127,plain,
    ( ! [X2,X0,X1] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(X2)
        | ~ class_Groups_Ogroup__add(X2)
        | X0 = X1 )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f5701,f7318]) ).

fof(f5701,plain,
    ! [X2,X0,X1] :
      ( c_Groups_Ominus__class_Ominus(X2,X0,X1) != c_Groups_Ozero__class_Ozero(X2)
      | X0 = X1
      | ~ class_Groups_Ogroup__add(X2) ),
    inference(cnf_transformation,[],[f4284]) ).

fof(f4284,plain,
    ! [X0,X1,X2] :
      ( ( ( X0 = X1
          | c_Groups_Ominus__class_Ominus(X2,X0,X1) != c_Groups_Ozero__class_Ozero(X2) )
        & ( c_Groups_Ominus__class_Ominus(X2,X0,X1) = c_Groups_Ozero__class_Ozero(X2)
          | X0 != X1 ) )
      | ~ class_Groups_Ogroup__add(X2) ),
    inference(rectify,[],[f4283]) ).

fof(f4283,plain,
    ! [X1,X2,X0] :
      ( ( ( X1 = X2
          | c_Groups_Ozero__class_Ozero(X0) != c_Groups_Ominus__class_Ominus(X0,X1,X2) )
        & ( c_Groups_Ozero__class_Ozero(X0) = c_Groups_Ominus__class_Ominus(X0,X1,X2)
          | X1 != X2 ) )
      | ~ class_Groups_Ogroup__add(X0) ),
    inference(nnf_transformation,[],[f2765]) ).

fof(f2765,plain,
    ! [X1,X2,X0] :
      ( ( X1 = X2
      <=> c_Groups_Ozero__class_Ozero(X0) = c_Groups_Ominus__class_Ominus(X0,X1,X2) )
      | ~ class_Groups_Ogroup__add(X0) ),
    inference(ennf_transformation,[],[f1668]) ).

fof(f1668,plain,
    ! [X0,X2,X1] :
      ( class_Groups_Ogroup__add(X0)
     => ( X1 = X2
      <=> c_Groups_Ozero__class_Ozero(X0) = c_Groups_Ominus__class_Ominus(X0,X1,X2) ) ),
    inference(rectify,[],[f989]) ).

fof(f989,axiom,
    ! [X8,X7,X10] :
      ( class_Groups_Ogroup__add(X8)
     => ( X7 = X10
      <=> c_Groups_Ozero__class_Ozero(X8) = c_Groups_Ominus__class_Ominus(X8,X7,X10) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__minus__eq) ).

fof(f9231,plain,
    ( spl24_144
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f9230,f7320,f7317,f9145]) ).

fof(f9230,plain,
    ( ! [X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f8815,f7321]) ).

fof(f8815,plain,
    ( ! [X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f4777,f7318]) ).

fof(f9195,plain,
    ( ~ spl24_148
    | spl24_149
    | spl24_150
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f9184,f7320,f7317,f9193,f9190,f9186]) ).

fof(f9193,plain,
    ( spl24_150
  <=> ! [X2,X0,X3] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X2)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_150])]) ).

fof(f9184,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X0)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X4)
        | ~ 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,X3,X2)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f9183,f7321]) ).

fof(f9183,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X2)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X4)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ 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,X3,X0) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f9182,f7318]) ).

fof(f9182,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X0)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X4),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X4)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X2) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f9181,f7321]) ).

fof(f9181,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X2)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X4)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X4),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
    | ~ spl24_136 ),
    inference(forward_demodulation,[],[f8238,f7318]) ).

fof(f8238,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X0)
        | ~ 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,X3,X2)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X4)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X4),X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)) )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f5365,f7318]) ).

fof(f5365,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X4),X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1),X0))
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X4)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X2)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X0) ),
    inference(cnf_transformation,[],[f4044]) ).

fof(f4044,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X2)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X4),X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1),X0))
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X4) ),
    inference(rectify,[],[f3246]) ).

fof(f3246,plain,
    ! [X2,X1,X3,X4,X0] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X3)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X2)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X0),X3),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X1),X2))
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ),
    inference(flattening,[],[f3245]) ).

fof(f3245,plain,
    ! [X4,X0,X3,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X3)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X2)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X0),X3),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X1),X2)) ),
    inference(ennf_transformation,[],[f2093]) ).

fof(f2093,plain,
    ! [X4,X0,X3,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X0),X3),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X1),X2))
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
       => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X2)
         => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X3)
           => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ) ) ) ),
    inference(rectify,[],[f836]) ).

fof(f836,axiom,
    ! [X79,X21,X28,X78,X29] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X29),X79),X78),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X29),X21),X28))
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X28,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
       => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X29,X28)
         => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X29,X78)
           => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X21,X79) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unique__quotient__lemma__neg) ).

fof(f9167,plain,
    ( spl24_146
    | spl24_147
    | ~ spl24_136 ),
    inference(avatar_split_clause,[],[f9160,f7317,f9165,f9162]) ).

fof(f9160,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) )
    | ~ spl24_136 ),
    inference(trivial_inequality_removal,[],[f9159]) ).

fof(f9159,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
    | ~ spl24_136 ),
    inference(forward_demodulation,[],[f8821,f7318]) ).

fof(f8821,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f4982,f7318]) ).

fof(f4982,plain,
    ! [X2,X3,X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
    inference(cnf_transformation,[],[f3837]) ).

fof(f3837,plain,
    ! [X0,X1,X2,X3] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
    inference(rectify,[],[f3345]) ).

fof(f3345,plain,
    ! [X0,X3,X1,X2] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X3) ),
    inference(flattening,[],[f3344]) ).

fof(f3344,plain,
    ! [X1,X2,X3,X0] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X3)
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
    inference(ennf_transformation,[],[f1874]) ).

fof(f1874,plain,
    ! [X1,X2,X3,X0] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
     => ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X3) ) ),
    inference(rectify,[],[f494]) ).

fof(f494,axiom,
    ! [X23,X56,X51,X17] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X51,X56)
     => ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X23,X56) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X51,X17)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X23,X17) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__eq__less) ).

fof(f9155,plain,
    ( spl24_145
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f9150,f7320,f7317,f9152]) ).

fof(f9152,plain,
    ( spl24_145
  <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_145])]) ).

fof(f9150,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f8598,f7321]) ).

fof(f8598,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(backward_demodulation,[],[f7917,f7318]) ).

fof(f7917,plain,
    ( ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ spl24_137 ),
    inference(backward_demodulation,[],[f6880,f7321]) ).

fof(f9147,plain,
    ( spl24_143
    | spl24_144
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f9140,f7320,f7317,f9145,f9142]) ).

fof(f9140,plain,
    ( ! [X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f9139,f7321]) ).

fof(f9139,plain,
    ( ! [X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f9138,f7318]) ).

fof(f9138,plain,
    ( ! [X2,X0,X1] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) )
    | ~ spl24_136
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f8845,f7321]) ).

fof(f8845,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) )
    | ~ spl24_136 ),
    inference(backward_demodulation,[],[f5783,f7318]) ).

fof(f5783,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),X1) ),
    inference(cnf_transformation,[],[f4338]) ).

fof(f4338,plain,
    ! [X0,X1,X2] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),X1) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),X1)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) ) ),
    inference(nnf_transformation,[],[f1794]) ).

fof(f1794,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),X1) ),
    inference(rectify,[],[f963]) ).

fof(f963,axiom,
    ! [X92,X91,X44] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X92,X44),X91)
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X92,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X91,X44)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__diff__conv) ).

fof(f7978,plain,
    ( spl24_142
    | ~ spl24_129
    | ~ spl24_131
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f7973,f7320,f7015,f7003,f7975]) ).

fof(f7975,plain,
    ( spl24_142
  <=> c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_142])]) ).

fof(f7015,plain,
    ( spl24_131
  <=> c_Polynomial_OpCons(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_131])]) ).

fof(f7973,plain,
    ( c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat))
    | ~ spl24_129
    | ~ spl24_131
    | ~ spl24_137 ),
    inference(forward_demodulation,[],[f7922,f7017]) ).

fof(f7017,plain,
    ( c_Polynomial_OpCons(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat))
    | ~ spl24_131 ),
    inference(avatar_component_clause,[],[f7015]) ).

fof(f7922,plain,
    ( c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Nat_Onat)) = c_Polynomial_OpCons(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)))
    | ~ spl24_129
    | ~ spl24_137 ),
    inference(backward_demodulation,[],[f7005,f7321]) ).

fof(f7945,plain,
    ( spl24_141
    | ~ spl24_111
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f7918,f7320,f6883,f7942]) ).

fof(f7918,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ spl24_111
    | ~ spl24_137 ),
    inference(backward_demodulation,[],[f6885,f7321]) ).

fof(f7824,plain,
    ( spl24_137
    | spl24_140 ),
    inference(avatar_split_clause,[],[f7812,f7821,f7320]) ).

fof(f7821,plain,
    ( spl24_140
  <=> ! [X13,X12] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X13),c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X12
        | X12 = X13 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_140])]) ).

fof(f7812,plain,
    ! [X12,X13] :
      ( X12 = X13
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X13),c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X12 ),
    inference(superposition,[],[f5482,f4704]) ).

fof(f7823,plain,
    ( spl24_140
    | spl24_137 ),
    inference(avatar_split_clause,[],[f7818,f7320,f7821]) ).

fof(f7818,plain,
    ! [X12,X13] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X13),c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X12
      | X12 = X13 ),
    inference(superposition,[],[f5482,f4704]) ).

fof(f7679,plain,
    ( spl24_138
    | ~ spl24_139 ),
    inference(avatar_split_clause,[],[f7670,f7676,f7672]) ).

fof(f7670,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))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(forward_demodulation,[],[f7663,f4958]) ).

fof(f7663,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(superposition,[],[f6583,f4706]) ).

fof(f7323,plain,
    ( spl24_136
    | ~ spl24_137 ),
    inference(avatar_split_clause,[],[f7311,f7320,f7317]) ).

fof(f7311,plain,
    ! [X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
      | c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1 ),
    inference(superposition,[],[f5739,f4924]) ).

fof(f5739,plain,
    ! [X0,X1] :
      ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)
      | c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1 ),
    inference(cnf_transformation,[],[f4311]) ).

fof(f4311,plain,
    ! [X0,X1] :
      ( ( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
          & c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1 )
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1) )
      & ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != X0
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != X1 ) ),
    inference(rectify,[],[f4310]) ).

fof(f4310,plain,
    ! [X1,X0] :
      ( ( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
          & c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0 )
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) )
      & ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != X1
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != X0 ) ),
    inference(flattening,[],[f4309]) ).

fof(f4309,plain,
    ! [X1,X0] :
      ( ( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
          & c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0 )
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) )
      & ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != X1
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != X0 ) ),
    inference(nnf_transformation,[],[f1879]) ).

fof(f1879,plain,
    ! [X1,X0] :
      ( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
        & c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0 )
    <=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) ),
    inference(rectify,[],[f286]) ).

fof(f286,axiom,
    ! [X18,X43] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X43),X18) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    <=> ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X18
        & c_Groups_Oone__class_Oone(tc_Nat_Onat) = X43 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__1__eq__mult__iff) ).

fof(f7265,plain,
    ( spl24_135
    | ~ spl24_1 ),
    inference(avatar_split_clause,[],[f7259,f6208,f7262]) ).

fof(f7259,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ spl24_1 ),
    inference(resolution,[],[f5678,f6210]) ).

fof(f7181,plain,
    ~ spl24_134,
    inference(avatar_split_clause,[],[f7173,f7177]) ).

fof(f7173,plain,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(superposition,[],[f5615,f4958]) ).

fof(f7180,plain,
    ~ spl24_134,
    inference(avatar_split_clause,[],[f7170,f7177]) ).

fof(f7170,plain,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(superposition,[],[f5615,f4958]) ).

fof(f7110,plain,
    ~ spl24_133,
    inference(avatar_split_clause,[],[f7104,f7107]) ).

fof(f7104,plain,
    ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(resolution,[],[f5094,f6166]) ).

fof(f7023,plain,
    ( spl24_132
    | ~ spl24_23 ),
    inference(avatar_split_clause,[],[f7012,f6330,f7020]) ).

fof(f7020,plain,
    ( spl24_132
  <=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)) = c_Polynomial_OpCons(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_132])]) ).

fof(f7012,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)) = c_Polynomial_OpCons(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)))
    | ~ spl24_23 ),
    inference(resolution,[],[f5674,f6332]) ).

fof(f7018,plain,
    ( spl24_131
    | ~ spl24_24 ),
    inference(avatar_split_clause,[],[f7013,f6335,f7015]) ).

fof(f7013,plain,
    ( c_Polynomial_OpCons(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat))
    | ~ spl24_24 ),
    inference(resolution,[],[f5674,f6337]) ).

fof(f7011,plain,
    ( spl24_130
    | ~ spl24_9 ),
    inference(avatar_split_clause,[],[f7001,f6248,f7008]) ).

fof(f7001,plain,
    ( c_Polynomial_OpCons(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint))) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Int_Oint))
    | ~ spl24_9 ),
    inference(resolution,[],[f4567,f6250]) ).

fof(f7006,plain,
    ( spl24_129
    | ~ spl24_5 ),
    inference(avatar_split_clause,[],[f7000,f6228,f7003]) ).

fof(f7000,plain,
    ( c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Nat_Onat)) = c_Polynomial_OpCons(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)))
    | ~ spl24_5 ),
    inference(resolution,[],[f4567,f6230]) ).

fof(f6995,plain,
    spl24_128,
    inference(avatar_split_clause,[],[f5301,f6992]) ).

fof(f5301,plain,
    c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,v_a,v_p),v_h),
    inference(cnf_transformation,[],[f1181]) ).

fof(f1181,axiom,
    c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,v_a,v_p),v_h),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).

fof(f6990,plain,
    spl24_127,
    inference(avatar_split_clause,[],[f5056,f6987]) ).

fof(f6987,plain,
    ( spl24_127
  <=> class_Rings_Olinordered__semiring__1(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_127])]) ).

fof(f5056,plain,
    class_Rings_Olinordered__semiring__1(tc_Int_Oint),
    inference(cnf_transformation,[],[f1031]) ).

fof(f1031,axiom,
    class_Rings_Olinordered__semiring__1(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1) ).

fof(f6984,plain,
    spl24_126,
    inference(avatar_split_clause,[],[f5149,f6981]) ).

fof(f6981,plain,
    ( spl24_126
  <=> class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_126])]) ).

fof(f5149,plain,
    class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1077]) ).

fof(f1077,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(f6969,plain,
    spl24_125,
    inference(avatar_split_clause,[],[f4674,f6966]) ).

fof(f6966,plain,
    ( spl24_125
  <=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_125])]) ).

fof(f4674,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
    inference(cnf_transformation,[],[f1018]) ).

fof(f1018,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(f6964,plain,
    spl24_124,
    inference(avatar_split_clause,[],[f5859,f6961]) ).

fof(f6961,plain,
    ( spl24_124
  <=> class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_124])]) ).

fof(f5859,plain,
    class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
    inference(cnf_transformation,[],[f1021]) ).

fof(f1021,axiom,
    class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__strict) ).

fof(f6959,plain,
    spl24_123,
    inference(avatar_split_clause,[],[f5340,f6956]) ).

fof(f6956,plain,
    ( spl24_123
  <=> class_Orderings_Opreorder(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_123])]) ).

fof(f5340,plain,
    class_Orderings_Opreorder(tc_Int_Oint),
    inference(cnf_transformation,[],[f1051]) ).

fof(f1051,axiom,
    class_Orderings_Opreorder(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Opreorder) ).

fof(f6953,plain,
    spl24_87,
    inference(avatar_split_clause,[],[f6195,f6730]) ).

fof(f6195,plain,
    ! [X1] : hBOOL(hAPP(hAPP(c_fequal,X1),X1)),
    inference(equality_resolution,[],[f5828]) ).

fof(f5828,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP(hAPP(c_fequal,X1),X0))
      | X0 != X1 ),
    inference(cnf_transformation,[],[f4368]) ).

fof(f4368,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP(hAPP(c_fequal,X1),X0))
      | X0 != X1 ),
    inference(rectify,[],[f1888]) ).

fof(f1888,plain,
    ! [X1,X0] :
      ( hBOOL(hAPP(hAPP(c_fequal,X0),X1))
      | X0 != X1 ),
    inference(rectify,[],[f1177]) ).

fof(f1177,axiom,
    ! [X13,X20] :
      ( hBOOL(hAPP(hAPP(c_fequal,X13),X20))
      | X13 != X20 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__2) ).

fof(f6950,plain,
    spl24_122,
    inference(avatar_split_clause,[],[f5682,f6947]) ).

fof(f6947,plain,
    ( spl24_122
  <=> class_Rings_Oordered__semiring(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_122])]) ).

fof(f5682,plain,
    class_Rings_Oordered__semiring(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1090]) ).

fof(f1090,axiom,
    class_Rings_Oordered__semiring(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__semiring) ).

fof(f6944,plain,
    spl24_121,
    inference(avatar_split_clause,[],[f5377,f6941]) ).

fof(f5377,plain,
    class_Rings_Ocomm__semiring__0(tc_Int_Oint),
    inference(cnf_transformation,[],[f1045]) ).

fof(f1045,axiom,
    class_Rings_Ocomm__semiring__0(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__0) ).

fof(f6939,plain,
    spl24_120,
    inference(avatar_split_clause,[],[f5845,f6936]) ).

fof(f5845,plain,
    class_Power_Opower(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1107]) ).

fof(f1107,axiom,
    class_Power_Opower(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Power_Opower) ).

fof(f6931,plain,
    spl24_119,
    inference(avatar_split_clause,[],[f5233,f6928]) ).

fof(f6928,plain,
    ( spl24_119
  <=> 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,[spl24_119])]) ).

fof(f5233,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,[],[f814]) ).

fof(f814,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(f6926,plain,
    spl24_118,
    inference(avatar_split_clause,[],[f5515,f6923]) ).

fof(f6923,plain,
    ( spl24_118
  <=> class_Rings_Oordered__semiring(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_118])]) ).

fof(f5515,plain,
    class_Rings_Oordered__semiring(tc_Int_Oint),
    inference(cnf_transformation,[],[f1039]) ).

fof(f1039,axiom,
    class_Rings_Oordered__semiring(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__semiring) ).

fof(f6921,plain,
    spl24_117,
    inference(avatar_split_clause,[],[f4455,f6918]) ).

fof(f6918,plain,
    ( spl24_117
  <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_117])]) ).

fof(f4455,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(cnf_transformation,[],[f840]) ).

fof(f840,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).

fof(f6911,plain,
    spl24_116,
    inference(avatar_split_clause,[],[f4452,f6908]) ).

fof(f6908,plain,
    ( spl24_116
  <=> class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_116])]) ).

fof(f4452,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1081]) ).

fof(f1081,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(f6906,plain,
    spl24_115,
    inference(avatar_split_clause,[],[f5559,f6903]) ).

fof(f6903,plain,
    ( spl24_115
  <=> class_Rings_Odvd(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_115])]) ).

fof(f5559,plain,
    class_Rings_Odvd(tc_Int_Oint),
    inference(cnf_transformation,[],[f1072]) ).

fof(f1072,axiom,
    class_Rings_Odvd(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Odvd) ).

fof(f6901,plain,
    spl24_114,
    inference(avatar_split_clause,[],[f5722,f6898]) ).

fof(f5722,plain,
    class_Rings_Osemiring__0(tc_Int_Oint),
    inference(cnf_transformation,[],[f1056]) ).

fof(f1056,axiom,
    class_Rings_Osemiring__0(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring__0) ).

fof(f6896,plain,
    spl24_113,
    inference(avatar_split_clause,[],[f4825,f6893]) ).

fof(f6893,plain,
    ( spl24_113
  <=> class_Rings_Ocomm__ring(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_113])]) ).

fof(f4825,plain,
    class_Rings_Ocomm__ring(tc_Int_Oint),
    inference(cnf_transformation,[],[f1060]) ).

fof(f1060,axiom,
    class_Rings_Ocomm__ring(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring) ).

fof(f6891,plain,
    spl24_112,
    inference(avatar_split_clause,[],[f4829,f6888]) ).

fof(f4829,plain,
    class_Power_Opower(tc_Int_Oint),
    inference(cnf_transformation,[],[f1067]) ).

fof(f1067,axiom,
    class_Power_Opower(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Power_Opower) ).

fof(f6886,plain,
    spl24_111,
    inference(avatar_split_clause,[],[f6881,f6883]) ).

fof(f6881,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(backward_demodulation,[],[f6094,f6880]) ).

fof(f6094,plain,
    ! [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),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(equality_resolution,[],[f5108]) ).

fof(f5108,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),X0),X1))
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
    inference(cnf_transformation,[],[f3912]) ).

fof(f3912,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),X0),X1))
        | ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
          & ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ) )
      & ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1)) ) ),
    inference(flattening,[],[f3911]) ).

fof(f3911,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),X0),X1))
        | ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
          & ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ) )
      & ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1)) ) ),
    inference(nnf_transformation,[],[f1729]) ).

fof(f1729,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),X0),X1))
    <=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ) ),
    inference(rectify,[],[f718]) ).

fof(f718,axiom,
    ! [X13,X18] :
      ( 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),X13),X18))
    <=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X18
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X13) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__power__nat__eq) ).

fof(f6877,plain,
    spl24_110,
    inference(avatar_split_clause,[],[f5725,f6874]) ).

fof(f6874,plain,
    ( spl24_110
  <=> class_Rings_Omult__zero(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_110])]) ).

fof(f5725,plain,
    class_Rings_Omult__zero(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1103]) ).

fof(f1103,axiom,
    class_Rings_Omult__zero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Omult__zero) ).

fof(f6871,plain,
    spl24_109,
    inference(avatar_split_clause,[],[f5742,f6868]) ).

fof(f6868,plain,
    ( spl24_109
  <=> class_Groups_Omonoid__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_109])]) ).

fof(f5742,plain,
    class_Groups_Omonoid__add(tc_Int_Oint),
    inference(cnf_transformation,[],[f1055]) ).

fof(f1055,axiom,
    class_Groups_Omonoid__add(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__add) ).

fof(f6866,plain,
    spl24_108,
    inference(avatar_split_clause,[],[f4980,f6863]) ).

fof(f6863,plain,
    ( spl24_108
  <=> class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_108])]) ).

fof(f4980,plain,
    class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
    inference(cnf_transformation,[],[f1019]) ).

fof(f1019,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(f6860,plain,
    spl24_107,
    inference(avatar_split_clause,[],[f4469,f6857]) ).

fof(f6857,plain,
    ( spl24_107
  <=> class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_107])]) ).

fof(f4469,plain,
    class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
    inference(cnf_transformation,[],[f1023]) ).

fof(f1023,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(f6853,plain,
    spl24_106,
    inference(avatar_split_clause,[],[f4471,f6850]) ).

fof(f6850,plain,
    ( spl24_106
  <=> class_Rings_Olinordered__semidom(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_106])]) ).

fof(f4471,plain,
    class_Rings_Olinordered__semidom(tc_Int_Oint),
    inference(cnf_transformation,[],[f1035]) ).

fof(f1035,axiom,
    class_Rings_Olinordered__semidom(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semidom) ).

fof(f6842,plain,
    spl24_105,
    inference(avatar_split_clause,[],[f5781,f6839]) ).

fof(f6839,plain,
    ( spl24_105
  <=> class_Rings_Olinordered__idom(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_105])]) ).

fof(f5781,plain,
    class_Rings_Olinordered__idom(tc_Int_Oint),
    inference(cnf_transformation,[],[f1043]) ).

fof(f1043,axiom,
    class_Rings_Olinordered__idom(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__idom) ).

fof(f6837,plain,
    spl24_104,
    inference(avatar_split_clause,[],[f4753,f6834]) ).

fof(f6834,plain,
    ( spl24_104
  <=> class_Orderings_Opreorder(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_104])]) ).

fof(f4753,plain,
    class_Orderings_Opreorder(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1098]) ).

fof(f1098,axiom,
    class_Orderings_Opreorder(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).

fof(f6831,plain,
    spl24_103,
    inference(avatar_split_clause,[],[f5277,f6828]) ).

fof(f5277,plain,
    class_Rings_Oidom(tc_Int_Oint),
    inference(cnf_transformation,[],[f1070]) ).

fof(f1070,axiom,
    class_Rings_Oidom(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oidom) ).

fof(f6826,plain,
    spl24_102,
    inference(avatar_split_clause,[],[f5302,f6823]) ).

fof(f6823,plain,
    ( spl24_102
  <=> class_Rings_Olinordered__semidom(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_102])]) ).

fof(f5302,plain,
    class_Rings_Olinordered__semidom(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1086]) ).

fof(f1086,axiom,
    class_Rings_Olinordered__semidom(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semidom) ).

fof(f6818,plain,
    spl24_101,
    inference(avatar_split_clause,[],[f4502,f6815]) ).

fof(f4502,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(cnf_transformation,[],[f289]) ).

fof(f289,axiom,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osize_I1_J) ).

fof(f6811,plain,
    spl24_100,
    inference(avatar_split_clause,[],[f4451,f6808]) ).

fof(f6808,plain,
    ( spl24_100
  <=> class_Orderings_Olinorder(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_100])]) ).

fof(f4451,plain,
    class_Orderings_Olinorder(tc_Int_Oint),
    inference(cnf_transformation,[],[f1052]) ).

fof(f1052,axiom,
    class_Orderings_Olinorder(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Olinorder) ).

fof(f6806,plain,
    spl24_99,
    inference(avatar_split_clause,[],[f5147,f6803]) ).

fof(f6803,plain,
    ( spl24_99
  <=> class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_99])]) ).

fof(f5147,plain,
    class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
    inference(cnf_transformation,[],[f1037]) ).

fof(f1037,axiom,
    class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__mult) ).

fof(f6800,plain,
    spl24_98,
    inference(avatar_split_clause,[],[f5568,f6797]) ).

fof(f6797,plain,
    ( spl24_98
  <=> class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_98])]) ).

fof(f5568,plain,
    class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1079]) ).

fof(f1079,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(f6795,plain,
    spl24_97,
    inference(avatar_split_clause,[],[f4426,f6792]) ).

fof(f6792,plain,
    ( spl24_97
  <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fTrue) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_97])]) ).

fof(f4426,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fTrue),
    inference(cnf_transformation,[],[f613]) ).

fof(f613,axiom,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fTrue),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bool_Osize_I1_J) ).

fof(f6787,plain,
    spl24_96,
    inference(avatar_split_clause,[],[f4441,f6784]) ).

fof(f6784,plain,
    ( spl24_96
  <=> class_Orderings_Oord(tc_HOL_Obool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_96])]) ).

fof(f4441,plain,
    class_Orderings_Oord(tc_HOL_Obool),
    inference(cnf_transformation,[],[f1115]) ).

fof(f1115,axiom,
    class_Orderings_Oord(tc_HOL_Obool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oord) ).

fof(f6782,plain,
    spl24_95,
    inference(avatar_split_clause,[],[f5066,f6779]) ).

fof(f6779,plain,
    ( spl24_95
  <=> class_Groups_Oone(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_95])]) ).

fof(f5066,plain,
    class_Groups_Oone(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1109]) ).

fof(f1109,axiom,
    class_Groups_Oone(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oone) ).

fof(f6777,plain,
    spl24_94,
    inference(avatar_split_clause,[],[f5713,f6774]) ).

fof(f5713,plain,
    class_HOL_Oequal(tc_HOL_Obool),
    inference(cnf_transformation,[],[f1117]) ).

fof(f1117,axiom,
    class_HOL_Oequal(tc_HOL_Obool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__HOL_Oequal) ).

fof(f6772,plain,
    spl24_93,
    inference(avatar_split_clause,[],[f5426,f6769]) ).

fof(f6769,plain,
    ( spl24_93
  <=> class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_93])]) ).

fof(f5426,plain,
    class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1080]) ).

fof(f1080,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(f6767,plain,
    spl24_92,
    inference(avatar_split_clause,[],[f5468,f6764]) ).

fof(f5468,plain,
    class_Rings_Ocomm__semiring__0(t_a),
    inference(cnf_transformation,[],[f1184]) ).

fof(f1184,axiom,
    class_Rings_Ocomm__semiring__0(t_a),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_0) ).

fof(f6756,plain,
    spl24_91,
    inference(avatar_split_clause,[],[f5113,f6753]) ).

fof(f6753,plain,
    ( spl24_91
  <=> class_Orderings_Oorder(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_91])]) ).

fof(f5113,plain,
    class_Orderings_Oorder(tc_Int_Oint),
    inference(cnf_transformation,[],[f1061]) ).

fof(f1061,axiom,
    class_Orderings_Oorder(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oorder) ).

fof(f6751,plain,
    spl24_90,
    inference(avatar_split_clause,[],[f4536,f6748]) ).

fof(f6748,plain,
    ( spl24_90
  <=> class_Enum_Oenum(tc_HOL_Obool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_90])]) ).

fof(f4536,plain,
    class_Enum_Oenum(tc_HOL_Obool),
    inference(cnf_transformation,[],[f1006]) ).

fof(f1006,axiom,
    class_Enum_Oenum(tc_HOL_Obool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Enum_Oenum) ).

fof(f6746,plain,
    ( spl24_86
    | spl24_87 ),
    inference(avatar_split_clause,[],[f6745,f6730,f6727]) ).

fof(f6745,plain,
    ! [X2,X1] :
      ( hBOOL(hAPP(hAPP(c_fequal,X1),X1))
      | ~ class_HOL_Oequal(X2) ),
    inference(forward_subsumption_demodulation,[],[f6012,f4657]) ).

fof(f6012,plain,
    ! [X2,X1] :
      ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(X2),X1),X1))
      | ~ class_HOL_Oequal(X2) ),
    inference(equality_resolution,[],[f4453]) ).

fof(f4453,plain,
    ! [X2,X0,X1] :
      ( ~ class_HOL_Oequal(X2)
      | hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(X2),X1),X0))
      | X0 != X1 ),
    inference(cnf_transformation,[],[f3489]) ).

fof(f3489,plain,
    ! [X0,X1,X2] :
      ( ~ class_HOL_Oequal(X2)
      | ( ( X0 = X1
          | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(X2),X1),X0)) )
        & ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(X2),X1),X0))
          | X0 != X1 ) ) ),
    inference(rectify,[],[f3488]) ).

fof(f3488,plain,
    ! [X2,X1,X0] :
      ( ~ class_HOL_Oequal(X0)
      | ( ( X1 = X2
          | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(X0),X1),X2)) )
        & ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(X0),X1),X2))
          | X1 != X2 ) ) ),
    inference(nnf_transformation,[],[f2503]) ).

fof(f2503,plain,
    ! [X2,X1,X0] :
      ( ~ class_HOL_Oequal(X0)
      | ( X1 = X2
      <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(X0),X1),X2)) ) ),
    inference(ennf_transformation,[],[f1649]) ).

fof(f1649,plain,
    ! [X1,X0,X2] :
      ( class_HOL_Oequal(X0)
     => ( X1 = X2
      <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(X0),X1),X2)) ) ),
    inference(rectify,[],[f23]) ).

fof(f23,axiom,
    ! [X8,X13,X20] :
      ( class_HOL_Oequal(X8)
     => ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(X8),X13),X20))
      <=> X13 = X20 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equal__eq) ).

fof(f6742,plain,
    spl24_89,
    inference(avatar_split_clause,[],[f5089,f6739]) ).

fof(f6739,plain,
    ( spl24_89
  <=> class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_89])]) ).

fof(f5089,plain,
    class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
    inference(cnf_transformation,[],[f1026]) ).

fof(f1026,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(f6737,plain,
    spl24_88,
    inference(avatar_split_clause,[],[f5019,f6734]) ).

fof(f6734,plain,
    ( spl24_88
  <=> class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_88])]) ).

fof(f5019,plain,
    class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
    inference(cnf_transformation,[],[f1022]) ).

fof(f1022,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(f6732,plain,
    ( spl24_86
    | spl24_87 ),
    inference(avatar_split_clause,[],[f6725,f6730,f6727]) ).

fof(f6725,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP(hAPP(c_fequal,X0),X0))
      | ~ class_HOL_Oequal(X1) ),
    inference(forward_subsumption_demodulation,[],[f4888,f4657]) ).

fof(f4888,plain,
    ! [X0,X1] :
      ( ~ class_HOL_Oequal(X1)
      | hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(X1),X0),X0)) ),
    inference(cnf_transformation,[],[f3773]) ).

fof(f3773,plain,
    ! [X0,X1] :
      ( ~ class_HOL_Oequal(X1)
      | hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(X1),X0),X0)) ),
    inference(rectify,[],[f3096]) ).

fof(f3096,plain,
    ! [X1,X0] :
      ( ~ class_HOL_Oequal(X0)
      | hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(X0),X1),X1)) ),
    inference(ennf_transformation,[],[f1983]) ).

fof(f1983,plain,
    ! [X1,X0] :
      ( class_HOL_Oequal(X0)
     => hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(X0),X1),X1)) ),
    inference(rectify,[],[f22]) ).

fof(f22,axiom,
    ! [X4,X19] :
      ( class_HOL_Oequal(X4)
     => hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(X4),X19),X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equal__refl) ).

fof(f6724,plain,
    ~ spl24_85,
    inference(avatar_split_clause,[],[f4472,f6721]) ).

fof(f4472,plain,
    c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) != c_Polynomial_OpCons(t_a,v_a,v_p),
    inference(cnf_transformation,[],[f2064]) ).

fof(f2064,plain,
    c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) != c_Polynomial_OpCons(t_a,v_a,v_p),
    inference(flattening,[],[f1183]) ).

fof(f1183,negated_conjecture,
    c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) != c_Polynomial_OpCons(t_a,v_a,v_p),
    inference(negated_conjecture,[],[f1182]) ).

fof(f1182,conjecture,
    c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = c_Polynomial_OpCons(t_a,v_a,v_p),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).

fof(f6718,plain,
    spl24_84,
    inference(avatar_split_clause,[],[f5508,f6715]) ).

fof(f6715,plain,
    ( spl24_84
  <=> class_Groups_Oab__semigroup__mult(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_84])]) ).

fof(f5508,plain,
    class_Groups_Oab__semigroup__mult(tc_Int_Oint),
    inference(cnf_transformation,[],[f1036]) ).

fof(f1036,axiom,
    class_Groups_Oab__semigroup__mult(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__mult) ).

fof(f6713,plain,
    spl24_83,
    inference(avatar_split_clause,[],[f5084,f6710]) ).

fof(f6710,plain,
    ( spl24_83
  <=> class_Int_Oring__char__0(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_83])]) ).

fof(f5084,plain,
    class_Int_Oring__char__0(tc_Int_Oint),
    inference(cnf_transformation,[],[f1062]) ).

fof(f1062,axiom,
    class_Int_Oring__char__0(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Int_Oring__char__0) ).

fof(f6708,plain,
    spl24_82,
    inference(avatar_split_clause,[],[f5275,f6705]) ).

fof(f6705,plain,
    ( spl24_82
  <=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_82])]) ).

fof(f5275,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
    inference(cnf_transformation,[],[f1017]) ).

fof(f1017,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(f6699,plain,
    spl24_81,
    inference(avatar_split_clause,[],[f4614,f6696]) ).

fof(f6696,plain,
    ( spl24_81
  <=> class_Groups_Oordered__ab__group__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_81])]) ).

fof(f4614,plain,
    class_Groups_Oordered__ab__group__add(tc_Int_Oint),
    inference(cnf_transformation,[],[f1032]) ).

fof(f1032,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(f6694,plain,
    spl24_80,
    inference(avatar_split_clause,[],[f5025,f6691]) ).

fof(f6691,plain,
    ( spl24_80
  <=> class_Orderings_Oord(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_80])]) ).

fof(f5025,plain,
    class_Orderings_Oord(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1106]) ).

fof(f1106,axiom,
    class_Orderings_Oord(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).

fof(f6689,plain,
    spl24_79,
    inference(avatar_split_clause,[],[f5078,f6686]) ).

fof(f6686,plain,
    ( spl24_79
  <=> class_Rings_Olinordered__ring__strict(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_79])]) ).

fof(f5078,plain,
    class_Rings_Olinordered__ring__strict(tc_Int_Oint),
    inference(cnf_transformation,[],[f1028]) ).

fof(f1028,axiom,
    class_Rings_Olinordered__ring__strict(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring__strict) ).

fof(f6684,plain,
    spl24_78,
    inference(avatar_split_clause,[],[f5443,f6681]) ).

fof(f6681,plain,
    ( spl24_78
  <=> class_Groups_Ouminus(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_78])]) ).

fof(f5443,plain,
    class_Groups_Ouminus(tc_Int_Oint),
    inference(cnf_transformation,[],[f1065]) ).

fof(f1065,axiom,
    class_Groups_Ouminus(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ouminus) ).

fof(f6679,plain,
    spl24_77,
    inference(avatar_split_clause,[],[f5254,f6676]) ).

fof(f6676,plain,
    ( spl24_77
  <=> class_Rings_Ocomm__semiring(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_77])]) ).

fof(f5254,plain,
    class_Rings_Ocomm__semiring(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1096]) ).

fof(f1096,axiom,
    class_Rings_Ocomm__semiring(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring) ).

fof(f6673,plain,
    spl24_76,
    inference(avatar_split_clause,[],[f5662,f6670]) ).

fof(f6670,plain,
    ( spl24_76
  <=> class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_76])]) ).

fof(f5662,plain,
    class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1007]) ).

fof(f1007,axiom,
    class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__comm__monoid__add) ).

fof(f6667,plain,
    spl24_75,
    inference(avatar_split_clause,[],[f5633,f6664]) ).

fof(f6664,plain,
    ( spl24_75
  <=> class_Rings_Ono__zero__divisors(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_75])]) ).

fof(f5633,plain,
    class_Rings_Ono__zero__divisors(tc_Int_Oint),
    inference(cnf_transformation,[],[f1040]) ).

fof(f1040,axiom,
    class_Rings_Ono__zero__divisors(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ono__zero__divisors) ).

fof(f6662,plain,
    ~ spl24_74,
    inference(avatar_split_clause,[],[f4881,f6659]) ).

fof(f4881,plain,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
    inference(cnf_transformation,[],[f803]) ).

fof(f803,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(f6655,plain,
    spl24_73,
    inference(avatar_split_clause,[],[f5220,f6652]) ).

fof(f6652,plain,
    ( spl24_73
  <=> class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_73])]) ).

fof(f5220,plain,
    class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
    inference(cnf_transformation,[],[f1027]) ).

fof(f1027,axiom,
    class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__cancel__semiring) ).

fof(f6650,plain,
    spl24_72,
    inference(avatar_split_clause,[],[f5572,f6647]) ).

fof(f6647,plain,
    ( spl24_72
  <=> class_Groups_Omonoid__mult(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_72])]) ).

fof(f5572,plain,
    class_Groups_Omonoid__mult(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1100]) ).

fof(f1100,axiom,
    class_Groups_Omonoid__mult(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__mult) ).

fof(f6639,plain,
    spl24_71,
    inference(avatar_split_clause,[],[f5734,f6636]) ).

fof(f6636,plain,
    ( spl24_71
  <=> class_Rings_Osemiring(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_71])]) ).

fof(f5734,plain,
    class_Rings_Osemiring(tc_Int_Oint),
    inference(cnf_transformation,[],[f1063]) ).

fof(f1063,axiom,
    class_Rings_Osemiring(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring) ).

fof(f6623,plain,
    spl24_70,
    inference(avatar_split_clause,[],[f5549,f6620]) ).

fof(f6620,plain,
    ( spl24_70
  <=> class_Rings_Oring__1(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_70])]) ).

fof(f5549,plain,
    class_Rings_Oring__1(tc_Int_Oint),
    inference(cnf_transformation,[],[f1066]) ).

fof(f1066,axiom,
    class_Rings_Oring__1(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1) ).

fof(f6597,plain,
    spl24_69,
    inference(avatar_split_clause,[],[f5355,f6594]) ).

fof(f6594,plain,
    ( spl24_69
  <=> class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_69])]) ).

fof(f5355,plain,
    class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1082]) ).

fof(f1082,axiom,
    class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__cancel__semiring) ).

fof(f6588,plain,
    spl24_68,
    inference(avatar_split_clause,[],[f4515,f6585]) ).

fof(f6585,plain,
    ( spl24_68
  <=> class_Rings_Osemiring(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_68])]) ).

fof(f4515,plain,
    class_Rings_Osemiring(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1105]) ).

fof(f1105,axiom,
    class_Rings_Osemiring(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring) ).

fof(f6582,plain,
    spl24_67,
    inference(avatar_split_clause,[],[f5393,f6579]) ).

fof(f6579,plain,
    ( spl24_67
  <=> class_Rings_Ocomm__ring__1(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_67])]) ).

fof(f5393,plain,
    class_Rings_Ocomm__ring__1(tc_Int_Oint),
    inference(cnf_transformation,[],[f1054]) ).

fof(f1054,axiom,
    class_Rings_Ocomm__ring__1(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring__1) ).

fof(f6574,plain,
    spl24_66,
    inference(avatar_split_clause,[],[f5556,f6571]) ).

fof(f6571,plain,
    ( spl24_66
  <=> class_Rings_Odvd(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_66])]) ).

fof(f5556,plain,
    class_Rings_Odvd(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1110]) ).

fof(f1110,axiom,
    class_Rings_Odvd(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Odvd) ).

fof(f6569,plain,
    spl24_65,
    inference(avatar_split_clause,[],[f5391,f6566]) ).

fof(f6566,plain,
    ( spl24_65
  <=> class_Rings_Oordered__comm__semiring(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_65])]) ).

fof(f5391,plain,
    class_Rings_Oordered__comm__semiring(tc_Int_Oint),
    inference(cnf_transformation,[],[f1030]) ).

fof(f1030,axiom,
    class_Rings_Oordered__comm__semiring(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__comm__semiring) ).

fof(f6564,plain,
    spl24_64,
    inference(avatar_split_clause,[],[f5624,f6561]) ).

fof(f6561,plain,
    ( spl24_64
  <=> class_Rings_Olinordered__semiring(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_64])]) ).

fof(f5624,plain,
    class_Rings_Olinordered__semiring(tc_Int_Oint),
    inference(cnf_transformation,[],[f1034]) ).

fof(f1034,axiom,
    class_Rings_Olinordered__semiring(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring) ).

fof(f6559,plain,
    spl24_63,
    inference(avatar_split_clause,[],[f5642,f6556]) ).

fof(f6556,plain,
    ( spl24_63
  <=> class_Divides_Oring__div(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_63])]) ).

fof(f5642,plain,
    class_Divides_Oring__div(tc_Int_Oint),
    inference(cnf_transformation,[],[f1058]) ).

fof(f1058,axiom,
    class_Divides_Oring__div(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Divides_Oring__div) ).

fof(f6552,plain,
    spl24_62,
    inference(avatar_split_clause,[],[f5432,f6549]) ).

fof(f6549,plain,
    ( spl24_62
  <=> class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_62])]) ).

fof(f5432,plain,
    class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint),
    inference(cnf_transformation,[],[f1008]) ).

fof(f1008,axiom,
    class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__comm__monoid__add) ).

fof(f6545,plain,
    spl24_61,
    inference(avatar_split_clause,[],[f5540,f6542]) ).

fof(f6542,plain,
    ( spl24_61
  <=> class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_61])]) ).

fof(f5540,plain,
    class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1087]) ).

fof(f1087,axiom,
    class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__mult) ).

fof(f6537,plain,
    ~ spl24_60,
    inference(avatar_split_clause,[],[f5276,f6534]) ).

fof(f6534,plain,
    ( spl24_60
  <=> hBOOL(c_fFalse) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_60])]) ).

fof(f5276,plain,
    ~ hBOOL(c_fFalse),
    inference(cnf_transformation,[],[f1178]) ).

fof(f1178,axiom,
    ~ hBOOL(c_fFalse),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fFalse__1) ).

fof(f6530,plain,
    spl24_59,
    inference(avatar_split_clause,[],[f5764,f6527]) ).

fof(f6527,plain,
    ( spl24_59
  <=> class_Groups_Oab__semigroup__add(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_59])]) ).

fof(f5764,plain,
    class_Groups_Oab__semigroup__add(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1089]) ).

fof(f1089,axiom,
    class_Groups_Oab__semigroup__add(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__add) ).

fof(f6524,plain,
    spl24_58,
    inference(avatar_split_clause,[],[f4601,f6521]) ).

fof(f4601,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,[],[f822]) ).

fof(f822,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(f6519,plain,
    spl24_57,
    inference(avatar_split_clause,[],[f5790,f6516]) ).

fof(f6516,plain,
    ( spl24_57
  <=> class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_57])]) ).

fof(f5790,plain,
    class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
    inference(cnf_transformation,[],[f1033]) ).

fof(f1033,axiom,
    class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__semigroup__add) ).

fof(f6509,plain,
    spl24_56,
    inference(avatar_split_clause,[],[f5501,f6506]) ).

fof(f6506,plain,
    ( spl24_56
  <=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_56])]) ).

fof(f5501,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1075]) ).

fof(f1075,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(f6503,plain,
    spl24_55,
    inference(avatar_split_clause,[],[f4702,f6500]) ).

fof(f6500,plain,
    ( spl24_55
  <=> class_Rings_Oring(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_55])]) ).

fof(f4702,plain,
    class_Rings_Oring(tc_Int_Oint),
    inference(cnf_transformation,[],[f1069]) ).

fof(f1069,axiom,
    class_Rings_Oring(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring) ).

fof(f6498,plain,
    spl24_54,
    inference(avatar_split_clause,[],[f4781,f6495]) ).

fof(f6495,plain,
    ( spl24_54
  <=> class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_54])]) ).

fof(f4781,plain,
    class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
    inference(cnf_transformation,[],[f1020]) ).

fof(f1020,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(f6493,plain,
    spl24_53,
    inference(avatar_split_clause,[],[f4654,f6490]) ).

fof(f6490,plain,
    ( spl24_53
  <=> class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_53])]) ).

fof(f4654,plain,
    class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
    inference(cnf_transformation,[],[f1029]) ).

fof(f1029,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(f6488,plain,
    spl24_52,
    inference(avatar_split_clause,[],[f5829,f6485]) ).

fof(f6485,plain,
    ( spl24_52
  <=> class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_52])]) ).

fof(f5829,plain,
    class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
    inference(cnf_transformation,[],[f1024]) ).

fof(f1024,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(f6483,plain,
    spl24_51,
    inference(avatar_split_clause,[],[f5576,f6480]) ).

fof(f6480,plain,
    ( spl24_51
  <=> class_Rings_Ono__zero__divisors(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_51])]) ).

fof(f5576,plain,
    class_Rings_Ono__zero__divisors(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1091]) ).

fof(f1091,axiom,
    class_Rings_Ono__zero__divisors(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ono__zero__divisors) ).

fof(f6478,plain,
    spl24_50,
    inference(avatar_split_clause,[],[f4917,f6475]) ).

fof(f4917,plain,
    class_HOL_Oequal(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1111]) ).

fof(f1111,axiom,
    class_HOL_Oequal(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__HOL_Oequal) ).

fof(f6473,plain,
    spl24_49,
    inference(avatar_split_clause,[],[f5290,f6470]) ).

fof(f6470,plain,
    ( spl24_49
  <=> class_Groups_Omonoid__mult(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_49])]) ).

fof(f5290,plain,
    class_Groups_Omonoid__mult(tc_Int_Oint),
    inference(cnf_transformation,[],[f1053]) ).

fof(f1053,axiom,
    class_Groups_Omonoid__mult(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__mult) ).

fof(f6468,plain,
    spl24_48,
    inference(avatar_split_clause,[],[f5852,f6465]) ).

fof(f6465,plain,
    ( spl24_48
  <=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_48])]) ).

fof(f5852,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1074]) ).

fof(f1074,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(f6463,plain,
    spl24_47,
    inference(avatar_split_clause,[],[f4528,f6460]) ).

fof(f6460,plain,
    ( spl24_47
  <=> class_Rings_Omult__zero(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_47])]) ).

fof(f4528,plain,
    class_Rings_Omult__zero(tc_Int_Oint),
    inference(cnf_transformation,[],[f1059]) ).

fof(f1059,axiom,
    class_Rings_Omult__zero(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Omult__zero) ).

fof(f6458,plain,
    spl24_46,
    inference(avatar_split_clause,[],[f4475,f6455]) ).

fof(f6455,plain,
    ( spl24_46
  <=> class_Groups_Omonoid__add(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_46])]) ).

fof(f4475,plain,
    class_Groups_Omonoid__add(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1101]) ).

fof(f1101,axiom,
    class_Groups_Omonoid__add(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__add) ).

fof(f6453,plain,
    spl24_45,
    inference(avatar_split_clause,[],[f4656,f6450]) ).

fof(f6450,plain,
    ( spl24_45
  <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_45])]) ).

fof(f4656,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(cnf_transformation,[],[f257]) ).

fof(f257,axiom,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osize_I3_J) ).

fof(f6448,plain,
    spl24_44,
    inference(avatar_split_clause,[],[f4697,f6445]) ).

fof(f6445,plain,
    ( spl24_44
  <=> hBOOL(c_fTrue) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_44])]) ).

fof(f4697,plain,
    hBOOL(c_fTrue),
    inference(cnf_transformation,[],[f1179]) ).

fof(f1179,axiom,
    hBOOL(c_fTrue),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fTrue__1) ).

fof(f6443,plain,
    spl24_43,
    inference(avatar_split_clause,[],[f4510,f6440]) ).

fof(f6440,plain,
    ( spl24_43
  <=> class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_43])]) ).

fof(f4510,plain,
    class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1078]) ).

fof(f1078,axiom,
    class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring__strict) ).

fof(f6438,plain,
    spl24_42,
    inference(avatar_split_clause,[],[f6433,f6435]) ).

fof(f6435,plain,
    ( spl24_42
  <=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_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)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_42])]) ).

fof(f6433,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_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(forward_demodulation,[],[f6182,f4806]) ).

fof(f6182,plain,
    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_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(equality_resolution,[],[f6181]) ).

fof(f6181,plain,
    ! [X0] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,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))
      | 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(equality_resolution,[],[f5997]) ).

fof(f5997,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)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != 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 ),
    inference(definition_unfolding,[],[f5801,f4877,f4877]) ).

fof(f5801,plain,
    ! [X0,X1] :
      ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
      | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0 ),
    inference(cnf_transformation,[],[f4350]) ).

fof(f4350,plain,
    ! [X0,X1] :
      ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)
        | ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != 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
            | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) ) )
      & ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = 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
          & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
        | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) ) ),
    inference(rectify,[],[f4349]) ).

fof(f4349,plain,
    ! [X1,X0] :
      ( ( c_Nat_OSuc(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_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 )
        | ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
          & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
        | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) ) ),
    inference(flattening,[],[f4348]) ).

fof(f4348,plain,
    ! [X1,X0] :
      ( ( c_Nat_OSuc(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_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 )
        | ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
          & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = 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,[],[f1891]) ).

fof(f1891,plain,
    ! [X1,X0] :
      ( c_Nat_OSuc(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_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 ) ) ),
    inference(rectify,[],[f138]) ).

fof(f138,axiom,
    ! [X18,X43] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X43,X18) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    <=> ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X43
          & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X18 )
        | ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X43
          & c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X18 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__is__add) ).

fof(f6432,plain,
    spl24_41,
    inference(avatar_split_clause,[],[f5330,f6429]) ).

fof(f6429,plain,
    ( spl24_41
  <=> class_Groups_Ogroup__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_41])]) ).

fof(f5330,plain,
    class_Groups_Ogroup__add(tc_Int_Oint),
    inference(cnf_transformation,[],[f1057]) ).

fof(f1057,axiom,
    class_Groups_Ogroup__add(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ogroup__add) ).

fof(f6427,plain,
    spl24_40,
    inference(avatar_split_clause,[],[f5441,f6424]) ).

fof(f6424,plain,
    ( spl24_40
  <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fFalse) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_40])]) ).

fof(f5441,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fFalse),
    inference(cnf_transformation,[],[f381]) ).

fof(f381,axiom,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fFalse),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bool_Osize_I2_J) ).

fof(f6422,plain,
    spl24_39,
    inference(avatar_split_clause,[],[f4872,f6419]) ).

fof(f6419,plain,
    ( spl24_39
  <=> class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_39])]) ).

fof(f4872,plain,
    class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1092]) ).

fof(f1092,axiom,
    class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__add) ).

fof(f6417,plain,
    spl24_38,
    inference(avatar_split_clause,[],[f5415,f6414]) ).

fof(f5415,plain,
    class_Divides_Osemiring__div(tc_Int_Oint),
    inference(cnf_transformation,[],[f1046]) ).

fof(f1046,axiom,
    class_Divides_Osemiring__div(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Divides_Osemiring__div) ).

fof(f6412,plain,
    spl24_37,
    inference(avatar_split_clause,[],[f5573,f6409]) ).

fof(f6409,plain,
    ( spl24_37
  <=> class_Rings_Ozero__neq__one(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_37])]) ).

fof(f5573,plain,
    class_Rings_Ozero__neq__one(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1097]) ).

fof(f1097,axiom,
    class_Rings_Ozero__neq__one(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ozero__neq__one) ).

fof(f6407,plain,
    spl24_36,
    inference(avatar_split_clause,[],[f5348,f6404]) ).

fof(f6404,plain,
    ( spl24_36
  <=> class_Groups_Oab__semigroup__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_36])]) ).

fof(f5348,plain,
    class_Groups_Oab__semigroup__add(tc_Int_Oint),
    inference(cnf_transformation,[],[f1038]) ).

fof(f1038,axiom,
    class_Groups_Oab__semigroup__add(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__add) ).

fof(f6402,plain,
    spl24_35,
    inference(avatar_split_clause,[],[f5832,f6399]) ).

fof(f6399,plain,
    ( spl24_35
  <=> class_Groups_Oab__group__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_35])]) ).

fof(f5832,plain,
    class_Groups_Oab__group__add(tc_Int_Oint),
    inference(cnf_transformation,[],[f1048]) ).

fof(f1048,axiom,
    class_Groups_Oab__group__add(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__group__add) ).

fof(f6396,plain,
    spl24_34,
    inference(avatar_split_clause,[],[f6391,f6393]) ).

fof(f6393,plain,
    ( spl24_34
  <=> 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_Oplus__class_Oplus(tc_Nat_Onat,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))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_34])]) ).

fof(f6391,plain,
    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_Oplus__class_Oplus(tc_Nat_Onat,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(forward_demodulation,[],[f6184,f4806]) ).

fof(f6184,plain,
    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_Oplus__class_Oplus(tc_Nat_Onat,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(equality_resolution,[],[f6183]) ).

fof(f6183,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)) = c_Groups_Oplus__class_Oplus(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(equality_resolution,[],[f5998]) ).

fof(f5998,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)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ),
    inference(definition_unfolding,[],[f5800,f4877,f4877]) ).

fof(f5800,plain,
    ! [X0,X1] :
      ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)
      | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ),
    inference(cnf_transformation,[],[f4350]) ).

fof(f6390,plain,
    spl24_33,
    inference(avatar_split_clause,[],[f5352,f6387]) ).

fof(f6387,plain,
    ( spl24_33
  <=> class_Groups_Ocomm__monoid__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_33])]) ).

fof(f5352,plain,
    class_Groups_Ocomm__monoid__add(tc_Int_Oint),
    inference(cnf_transformation,[],[f1041]) ).

fof(f1041,axiom,
    class_Groups_Ocomm__monoid__add(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__add) ).

fof(f6385,plain,
    spl24_32,
    inference(avatar_split_clause,[],[f4559,f6382]) ).

fof(f6382,plain,
    ( spl24_32
  <=> class_Orderings_Olinorder(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_32])]) ).

fof(f4559,plain,
    class_Orderings_Olinorder(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1099]) ).

fof(f1099,axiom,
    class_Orderings_Olinorder(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).

fof(f6380,plain,
    spl24_31,
    inference(avatar_split_clause,[],[f5643,f6377]) ).

fof(f6377,plain,
    ( spl24_31
  <=> class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_31])]) ).

fof(f5643,plain,
    class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1084]) ).

fof(f1084,axiom,
    class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).

fof(f6375,plain,
    spl24_30,
    inference(avatar_split_clause,[],[f5296,f6372]) ).

fof(f6372,plain,
    ( spl24_30
  <=> class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_30])]) ).

fof(f5296,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
    inference(cnf_transformation,[],[f1025]) ).

fof(f1025,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(f6369,plain,
    spl24_29,
    inference(avatar_split_clause,[],[f4989,f6366]) ).

fof(f6366,plain,
    ( spl24_29
  <=> class_Rings_Ozero__neq__one(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_29])]) ).

fof(f4989,plain,
    class_Rings_Ozero__neq__one(tc_Int_Oint),
    inference(cnf_transformation,[],[f1049]) ).

fof(f1049,axiom,
    class_Rings_Ozero__neq__one(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ozero__neq__one) ).

fof(f6364,plain,
    spl24_28,
    inference(avatar_split_clause,[],[f5543,f6361]) ).

fof(f5543,plain,
    class_Divides_Osemiring__div(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1095]) ).

fof(f1095,axiom,
    class_Divides_Osemiring__div(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Divides_Osemiring__div) ).

fof(f6359,plain,
    spl24_27,
    inference(avatar_split_clause,[],[f5427,f6356]) ).

fof(f6356,plain,
    ( spl24_27
  <=> class_Orderings_Oorder(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_27])]) ).

fof(f5427,plain,
    class_Orderings_Oorder(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1104]) ).

fof(f1104,axiom,
    class_Orderings_Oorder(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).

fof(f6354,plain,
    spl24_26,
    inference(avatar_split_clause,[],[f4776,f6351]) ).

fof(f6351,plain,
    ( spl24_26
  <=> class_Rings_Oordered__ring(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_26])]) ).

fof(f4776,plain,
    class_Rings_Oordered__ring(tc_Int_Oint),
    inference(cnf_transformation,[],[f1050]) ).

fof(f1050,axiom,
    class_Rings_Oordered__ring(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring) ).

fof(f6343,plain,
    spl24_25,
    inference(avatar_split_clause,[],[f4576,f6340]) ).

fof(f4576,plain,
    class_Rings_Osemiring__0(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1102]) ).

fof(f1102,axiom,
    class_Rings_Osemiring__0(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__0) ).

fof(f6338,plain,
    spl24_24,
    inference(avatar_split_clause,[],[f4798,f6335]) ).

fof(f4798,plain,
    class_Groups_Ozero(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1108]) ).

fof(f1108,axiom,
    class_Groups_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ozero) ).

fof(f6333,plain,
    spl24_23,
    inference(avatar_split_clause,[],[f4716,f6330]) ).

fof(f4716,plain,
    class_Groups_Ozero(tc_Int_Oint),
    inference(cnf_transformation,[],[f1068]) ).

fof(f1068,axiom,
    class_Groups_Ozero(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ozero) ).

fof(f6328,plain,
    spl24_22,
    inference(avatar_split_clause,[],[f4613,f6325]) ).

fof(f6325,plain,
    ( spl24_22
  <=> class_Rings_Ocomm__semiring(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_22])]) ).

fof(f4613,plain,
    class_Rings_Ocomm__semiring(tc_Int_Oint),
    inference(cnf_transformation,[],[f1047]) ).

fof(f1047,axiom,
    class_Rings_Ocomm__semiring(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring) ).

fof(f6323,plain,
    spl24_21,
    inference(avatar_split_clause,[],[f6318,f6320]) ).

fof(f6320,plain,
    ( spl24_21
  <=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(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,[spl24_21])]) ).

fof(f6318,plain,
    c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
    inference(forward_demodulation,[],[f6127,f4806]) ).

fof(f6127,plain,
    c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(equality_resolution,[],[f5964]) ).

fof(f5964,plain,
    ! [X0] :
      ( c_Rings_Odvd__class_Odvd(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_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0 ),
    inference(definition_unfolding,[],[f5396,f4877,f4877]) ).

fof(f5396,plain,
    ! [X0] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
      | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0 ),
    inference(cnf_transformation,[],[f4066]) ).

fof(f4066,plain,
    ! [X0] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0 )
      & ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
    inference(nnf_transformation,[],[f1856]) ).

fof(f1856,plain,
    ! [X0] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    <=> c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0 ),
    inference(rectify,[],[f623]) ).

fof(f623,axiom,
    ! [X43] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X43,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    <=> c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X43 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__1__iff__1) ).

fof(f6316,plain,
    spl24_20,
    inference(avatar_split_clause,[],[f5809,f6313]) ).

fof(f6313,plain,
    ( spl24_20
  <=> class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_20])]) ).

fof(f5809,plain,
    class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1083]) ).

fof(f1083,axiom,
    class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__comm__semiring) ).

fof(f6311,plain,
    spl24_19,
    inference(avatar_split_clause,[],[f5774,f6308]) ).

fof(f6308,plain,
    ( spl24_19
  <=> class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_19])]) ).

fof(f5774,plain,
    class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1088]) ).

fof(f1088,axiom,
    class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__mult) ).

fof(f6304,plain,
    spl24_18,
    inference(avatar_split_clause,[],[f5242,f6301]) ).

fof(f6301,plain,
    ( spl24_18
  <=> class_Rings_Olinordered__semiring(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_18])]) ).

fof(f5242,plain,
    class_Rings_Olinordered__semiring(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1085]) ).

fof(f1085,axiom,
    class_Rings_Olinordered__semiring(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring) ).

fof(f6296,plain,
    spl24_17,
    inference(avatar_split_clause,[],[f5372,f6293]) ).

fof(f6293,plain,
    ( spl24_17
  <=> class_Orderings_Oord(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_17])]) ).

fof(f5372,plain,
    class_Orderings_Oord(tc_Int_Oint),
    inference(cnf_transformation,[],[f1064]) ).

fof(f1064,axiom,
    class_Orderings_Oord(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oord) ).

fof(f6291,plain,
    spl24_16,
    inference(avatar_split_clause,[],[f5283,f6288]) ).

fof(f6288,plain,
    ( spl24_16
  <=> class_Groups_Ouminus(tc_HOL_Obool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_16])]) ).

fof(f5283,plain,
    class_Groups_Ouminus(tc_HOL_Obool),
    inference(cnf_transformation,[],[f1116]) ).

fof(f1116,axiom,
    class_Groups_Ouminus(tc_HOL_Obool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Groups_Ouminus) ).

fof(f6280,plain,
    spl24_15,
    inference(avatar_split_clause,[],[f4906,f6277]) ).

fof(f4906,plain,
    class_Rings_Ocomm__semiring__0(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1094]) ).

fof(f1094,axiom,
    class_Rings_Ocomm__semiring__0(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__0) ).

fof(f6275,plain,
    ( spl24_13
    | ~ spl24_14 ),
    inference(avatar_split_clause,[],[f4579,f6272,f6268]) ).

fof(f4579,plain,
    ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
    | v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
    inference(cnf_transformation,[],[f2686]) ).

fof(f2686,plain,
    ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
    | v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
    inference(ennf_transformation,[],[f1180]) ).

fof(f1180,axiom,
    ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
   => v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

fof(f6266,plain,
    spl24_12,
    inference(avatar_split_clause,[],[f4396,f6263]) ).

fof(f6263,plain,
    ( spl24_12
  <=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_12])]) ).

fof(f4396,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
    inference(cnf_transformation,[],[f1016]) ).

fof(f1016,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(f6261,plain,
    spl24_11,
    inference(avatar_split_clause,[],[f4465,f6258]) ).

fof(f6258,plain,
    ( spl24_11
  <=> class_Orderings_Opreorder(tc_HOL_Obool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_11])]) ).

fof(f4465,plain,
    class_Orderings_Opreorder(tc_HOL_Obool),
    inference(cnf_transformation,[],[f1113]) ).

fof(f1113,axiom,
    class_Orderings_Opreorder(tc_HOL_Obool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Opreorder) ).

fof(f6256,plain,
    spl24_10,
    inference(avatar_split_clause,[],[f4852,f6253]) ).

fof(f6253,plain,
    ( spl24_10
  <=> class_Rings_Olinordered__ring(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_10])]) ).

fof(f4852,plain,
    class_Rings_Olinordered__ring(tc_Int_Oint),
    inference(cnf_transformation,[],[f1042]) ).

fof(f1042,axiom,
    class_Rings_Olinordered__ring(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring) ).

fof(f6251,plain,
    spl24_9,
    inference(avatar_split_clause,[],[f5621,f6248]) ).

fof(f5621,plain,
    class_Rings_Ocomm__semiring__1(tc_Int_Oint),
    inference(cnf_transformation,[],[f1044]) ).

fof(f1044,axiom,
    class_Rings_Ocomm__semiring__1(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__1) ).

fof(f6246,plain,
    spl24_8,
    inference(avatar_split_clause,[],[f5864,f6243]) ).

fof(f6243,plain,
    ( spl24_8
  <=> class_Groups_Oone(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_8])]) ).

fof(f5864,plain,
    class_Groups_Oone(tc_Int_Oint),
    inference(cnf_transformation,[],[f1071]) ).

fof(f1071,axiom,
    class_Groups_Oone(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oone) ).

fof(f6241,plain,
    spl24_7,
    inference(avatar_split_clause,[],[f5291,f6238]) ).

fof(f6238,plain,
    ( spl24_7
  <=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_7])]) ).

fof(f5291,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1076]) ).

fof(f1076,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(f6236,plain,
    spl24_6,
    inference(avatar_split_clause,[],[f4731,f6233]) ).

fof(f4731,plain,
    class_HOL_Oequal(tc_Int_Oint),
    inference(cnf_transformation,[],[f1073]) ).

fof(f1073,axiom,
    class_HOL_Oequal(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__HOL_Oequal) ).

fof(f6231,plain,
    spl24_5,
    inference(avatar_split_clause,[],[f4511,f6228]) ).

fof(f4511,plain,
    class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
    inference(cnf_transformation,[],[f1093]) ).

fof(f1093,axiom,
    class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).

fof(f6226,plain,
    spl24_4,
    inference(avatar_split_clause,[],[f5565,f6223]) ).

fof(f6223,plain,
    ( spl24_4
  <=> class_Orderings_Oorder(tc_HOL_Obool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_4])]) ).

fof(f5565,plain,
    class_Orderings_Oorder(tc_HOL_Obool),
    inference(cnf_transformation,[],[f1114]) ).

fof(f1114,axiom,
    class_Orderings_Oorder(tc_HOL_Obool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oorder) ).

fof(f6221,plain,
    spl24_3,
    inference(avatar_split_clause,[],[f6086,f6218]) ).

fof(f6218,plain,
    ( spl24_3
  <=> 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_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_3])]) ).

fof(f6086,plain,
    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_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(equality_resolution,[],[f6085]) ).

fof(f6085,plain,
    ! [X0] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,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))
      | 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(equality_resolution,[],[f5927]) ).

fof(f5927,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)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != 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 ),
    inference(definition_unfolding,[],[f5076,f4877,f4877]) ).

fof(f5076,plain,
    ! [X0,X1] :
      ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)
      | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
      | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0 ),
    inference(cnf_transformation,[],[f3892]) ).

fof(f3892,plain,
    ! [X0,X1] :
      ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)
        | ( ( 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) != X0
            | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ) ) )
      & ( ( 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) = X0
          & c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 )
        | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) ) ),
    inference(rectify,[],[f3891]) ).

fof(f3891,plain,
    ! [X1,X0] :
      ( ( c_Nat_OSuc(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_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 )
          & ( 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) = X0
          & c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 )
        | ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
          & c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0 )
        | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) ) ),
    inference(flattening,[],[f3890]) ).

fof(f3890,plain,
    ! [X1,X0] :
      ( ( c_Nat_OSuc(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_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 )
          & ( 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) = X0
          & c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 )
        | ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
          & c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0 )
        | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) ) ),
    inference(nnf_transformation,[],[f1656]) ).

fof(f1656,plain,
    ! [X1,X0] :
      ( c_Nat_OSuc(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_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 )
        | ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
          & c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0 ) ) ),
    inference(rectify,[],[f139]) ).

fof(f139,axiom,
    ! [X18,X43] :
      ( ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X18
          & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X43 )
        | ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X43
          & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X18 ) )
    <=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X43,X18) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__is__1) ).

fof(f6216,plain,
    spl24_2,
    inference(avatar_split_clause,[],[f5081,f6213]) ).

fof(f6213,plain,
    ( spl24_2
  <=> class_Lattices_Oboolean__algebra(tc_HOL_Obool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl24_2])]) ).

fof(f5081,plain,
    class_Lattices_Oboolean__algebra(tc_HOL_Obool),
    inference(cnf_transformation,[],[f1112]) ).

fof(f1112,axiom,
    class_Lattices_Oboolean__algebra(tc_HOL_Obool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Oboolean__algebra) ).

fof(f6211,plain,
    spl24_1,
    inference(avatar_split_clause,[],[f5295,f6208]) ).

fof(f5295,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(cnf_transformation,[],[f841]) ).

fof(f841,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SWW185+1 : TPTP v8.1.0. Released v5.2.0.
% 0.03/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.12/0.33  % Computer : n011.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Tue Aug 30 20:18:55 EDT 2022
% 0.12/0.34  % CPUTime    : 
% 0.19/0.53  % (21947)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.19/0.53  % (21939)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.19/0.54  % (21931)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.27/0.57  % (21930)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 1.27/0.58  % (21932)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 1.27/0.58  % (21940)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 1.27/0.58  % (21925)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 1.27/0.58  % (21929)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.27/0.58  % (21938)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 1.27/0.58  % (21928)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.27/0.58  % (21954)ott+10_7:2_awrs=decay:awrsf=8:bd=preordered:drc=off:fd=preordered:fde=unused:fsr=off:slsq=on:slsqc=2:slsqr=5,8:sp=const_min:spb=units:to=lpo:i=355:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/355Mi)
% 1.27/0.59  % (21926)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 1.27/0.59  % (21952)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/177Mi)
% 1.27/0.59  % (21953)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 1.27/0.59  % (21946)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 1.27/0.59  % (21932)Instruction limit reached!
% 1.27/0.59  % (21932)------------------------------
% 1.27/0.59  % (21932)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.27/0.59  % (21948)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 1.27/0.59  % (21932)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.27/0.59  % (21932)Termination reason: Unknown
% 1.27/0.59  % (21932)Termination phase: Preprocessing 1
% 1.27/0.59  
% 1.27/0.59  % (21932)Memory used [KB]: 2558
% 1.27/0.59  % (21932)Time elapsed: 0.008 s
% 1.27/0.59  % (21932)Instructions burned: 8 (million)
% 1.27/0.59  % (21932)------------------------------
% 1.27/0.59  % (21932)------------------------------
% 1.27/0.60  % (21944)ott+4_1:1_av=off:bd=off:nwc=5.0:rp=on:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 1.27/0.60  % (21945)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 1.27/0.60  % (21933)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 1.27/0.60  % (21933)Instruction limit reached!
% 1.27/0.60  % (21933)------------------------------
% 1.27/0.60  % (21933)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.27/0.60  % (21933)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.27/0.60  % (21933)Termination reason: Unknown
% 1.27/0.60  % (21933)Termination phase: shuffling
% 1.27/0.60  
% 1.27/0.60  % (21933)Memory used [KB]: 2046
% 1.27/0.60  % (21933)Time elapsed: 0.003 s
% 1.27/0.60  % (21933)Instructions burned: 2 (million)
% 1.27/0.60  % (21933)------------------------------
% 1.27/0.60  % (21933)------------------------------
% 1.27/0.60  % (21942)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 1.27/0.60  % (21936)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 1.27/0.60  % (21927)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 1.27/0.60  % (21937)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 1.27/0.60  % (21934)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.27/0.60  % (21941)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 1.27/0.61  % (21950)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 1.27/0.61  % (21951)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 1.27/0.61  % (21931)Instruction limit reached!
% 1.27/0.61  % (21931)------------------------------
% 1.27/0.61  % (21931)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.27/0.61  % (21931)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.27/0.61  % (21931)Termination reason: Unknown
% 1.27/0.61  % (21931)Termination phase: Function definition elimination
% 1.27/0.61  
% 1.27/0.61  % (21931)Memory used [KB]: 4605
% 1.27/0.61  % (21931)Time elapsed: 0.045 s
% 1.27/0.61  % (21931)Instructions burned: 54 (million)
% 1.27/0.61  % (21931)------------------------------
% 1.27/0.61  % (21931)------------------------------
% 1.27/0.62  % (21943)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 1.27/0.62  % (21935)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 1.27/0.63  % (21939)Instruction limit reached!
% 1.27/0.63  % (21939)------------------------------
% 1.27/0.63  % (21939)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.27/0.63  % (21939)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.27/0.63  % (21939)Termination reason: Unknown
% 1.27/0.63  % (21939)Termination phase: Property scanning
% 1.27/0.63  
% 1.27/0.63  % (21939)Memory used [KB]: 4989
% 1.27/0.63  % (21939)Time elapsed: 0.053 s
% 1.27/0.63  % (21939)Instructions burned: 69 (million)
% 1.27/0.63  % (21939)------------------------------
% 1.27/0.63  % (21939)------------------------------
% 1.27/0.64  % (21949)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 1.81/0.65  % (21930)Instruction limit reached!
% 1.81/0.65  % (21930)------------------------------
% 1.81/0.65  % (21930)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.81/0.65  % (21930)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.81/0.65  % (21930)Termination reason: Unknown
% 1.81/0.65  % (21930)Termination phase: Property scanning
% 1.81/0.65  
% 1.81/0.65  % (21930)Memory used [KB]: 4605
% 1.81/0.65  % (21930)Time elapsed: 0.025 s
% 1.81/0.65  % (21930)Instructions burned: 49 (million)
% 1.81/0.65  % (21930)------------------------------
% 1.81/0.65  % (21930)------------------------------
% 1.81/0.67  % (21929)Instruction limit reached!
% 1.81/0.67  % (21929)------------------------------
% 1.81/0.67  % (21929)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.81/0.67  % (21929)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.81/0.67  % (21929)Termination reason: Unknown
% 1.81/0.67  % (21929)Termination phase: Property scanning
% 1.81/0.67  
% 1.81/0.67  % (21929)Memory used [KB]: 4477
% 1.81/0.67  % (21929)Time elapsed: 0.029 s
% 1.81/0.67  % (21929)Instructions burned: 52 (million)
% 1.81/0.67  % (21929)------------------------------
% 1.81/0.67  % (21929)------------------------------
% 1.81/0.67  % (21940)Instruction limit reached!
% 1.81/0.67  % (21940)------------------------------
% 1.81/0.67  % (21940)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.81/0.67  % (21940)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.81/0.67  % (21940)Termination reason: Unknown
% 1.81/0.67  % (21940)Termination phase: Saturation
% 1.81/0.67  
% 1.81/0.67  % (21940)Memory used [KB]: 4733
% 1.81/0.67  % (21940)Time elapsed: 0.078 s
% 1.81/0.67  % (21940)Instructions burned: 75 (million)
% 1.81/0.67  % (21940)------------------------------
% 1.81/0.67  % (21940)------------------------------
% 1.81/0.67  % (21928)Instruction limit reached!
% 1.81/0.67  % (21928)------------------------------
% 1.81/0.67  % (21928)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.81/0.67  % (21928)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.81/0.67  % (21928)Termination reason: Unknown
% 1.81/0.67  % (21928)Termination phase: Equality resolution with deletion
% 1.81/0.67  
% 1.81/0.67  % (21928)Memory used [KB]: 4349
% 1.81/0.67  % (21928)Time elapsed: 0.027 s
% 1.81/0.67  % (21928)Instructions burned: 52 (million)
% 1.81/0.67  % (21928)------------------------------
% 1.81/0.67  % (21928)------------------------------
% 1.81/0.67  % (21926)Instruction limit reached!
% 1.81/0.67  % (21926)------------------------------
% 1.81/0.67  % (21926)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.81/0.67  % (21926)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.81/0.67  % (21926)Termination reason: Unknown
% 1.81/0.67  % (21926)Termination phase: Property scanning
% 1.81/0.67  
% 1.81/0.67  % (21926)Memory used [KB]: 4477
% 1.81/0.67  % (21926)Time elapsed: 0.026 s
% 1.81/0.67  % (21926)Instructions burned: 53 (million)
% 1.81/0.67  % (21926)------------------------------
% 1.81/0.67  % (21926)------------------------------
% 2.08/0.68  % (21927)Instruction limit reached!
% 2.08/0.68  % (21927)------------------------------
% 2.08/0.68  % (21927)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.08/0.68  % (21927)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.08/0.68  % (21927)Termination reason: Unknown
% 2.08/0.68  % (21927)Termination phase: Preprocessing 3
% 2.08/0.68  
% 2.08/0.68  % (21927)Memory used [KB]: 3965
% 2.08/0.68  % (21927)Time elapsed: 0.024 s
% 2.08/0.68  % (21927)Instructions burned: 37 (million)
% 2.08/0.68  % (21927)------------------------------
% 2.08/0.68  % (21927)------------------------------
% 2.08/0.68  % (21934)Instruction limit reached!
% 2.08/0.68  % (21934)------------------------------
% 2.08/0.68  % (21934)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.08/0.68  % (21934)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.08/0.68  % (21934)Termination reason: Unknown
% 2.08/0.68  % (21934)Termination phase: Property scanning
% 2.08/0.68  
% 2.08/0.68  % (21934)Memory used [KB]: 4605
% 2.08/0.68  % (21934)Time elapsed: 0.026 s
% 2.08/0.68  % (21934)Instructions burned: 53 (million)
% 2.08/0.68  % (21934)------------------------------
% 2.08/0.68  % (21934)------------------------------
% 2.08/0.71  % (21942)Instruction limit reached!
% 2.08/0.71  % (21942)------------------------------
% 2.08/0.71  % (21942)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.08/0.71  % (21942)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.08/0.71  % (21942)Termination reason: Unknown
% 2.08/0.71  % (21942)Termination phase: Property scanning
% 2.08/0.71  
% 2.08/0.71  % (21942)Memory used [KB]: 4605
% 2.08/0.71  % (21942)Time elapsed: 0.031 s
% 2.08/0.71  % (21942)Instructions burned: 61 (million)
% 2.08/0.71  % (21942)------------------------------
% 2.08/0.71  % (21942)------------------------------
% 2.08/0.72  % (21956)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=211:si=on:rawr=on:rtra=on_0 on theBenchmark for (2997ds/211Mi)
% 2.08/0.72  % (21935)Instruction limit reached!
% 2.08/0.72  % (21935)------------------------------
% 2.08/0.72  % (21935)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.08/0.72  % (21935)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.08/0.72  % (21935)Termination reason: Unknown
% 2.08/0.72  % (21935)Termination phase: Property scanning
% 2.08/0.72  
% 2.08/0.72  % (21935)Memory used [KB]: 4605
% 2.08/0.72  % (21935)Time elapsed: 0.028 s
% 2.08/0.72  % (21935)Instructions burned: 52 (million)
% 2.08/0.72  % (21935)------------------------------
% 2.08/0.72  % (21935)------------------------------
% 2.43/0.74  % (21951)Instruction limit reached!
% 2.43/0.74  % (21951)------------------------------
% 2.43/0.74  % (21951)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.43/0.74  % (21951)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.43/0.74  % (21951)Termination reason: Unknown
% 2.43/0.74  % (21951)Termination phase: Property scanning
% 2.43/0.74  
% 2.43/0.74  % (21951)Memory used [KB]: 4989
% 2.43/0.74  % (21951)Time elapsed: 0.034 s
% 2.43/0.74  % (21951)Instructions burned: 68 (million)
% 2.43/0.74  % (21951)------------------------------
% 2.43/0.74  % (21951)------------------------------
% 2.43/0.74  % (21941)Instruction limit reached!
% 2.43/0.74  % (21941)------------------------------
% 2.43/0.74  % (21941)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.43/0.74  % (21941)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.43/0.74  % (21941)Termination reason: Unknown
% 2.43/0.74  % (21941)Termination phase: Saturation
% 2.43/0.74  
% 2.43/0.74  % (21941)Memory used [KB]: 9338
% 2.43/0.74  % (21941)Time elapsed: 0.278 s
% 2.43/0.74  % (21941)Instructions burned: 100 (million)
% 2.43/0.74  % (21941)------------------------------
% 2.43/0.74  % (21941)------------------------------
% 2.43/0.74  % (21938)Instruction limit reached!
% 2.43/0.74  % (21938)------------------------------
% 2.43/0.74  % (21938)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.43/0.74  % (21938)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.43/0.74  % (21938)Termination reason: Unknown
% 2.43/0.74  % (21938)Termination phase: Saturation
% 2.43/0.74  
% 2.43/0.74  % (21938)Memory used [KB]: 9466
% 2.43/0.74  % (21938)Time elapsed: 0.049 s
% 2.43/0.74  % (21938)Instructions burned: 99 (million)
% 2.43/0.74  % (21938)------------------------------
% 2.43/0.74  % (21938)------------------------------
% 2.43/0.74  % (21955)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=388:si=on:rawr=on:rtra=on_0 on theBenchmark for (2997ds/388Mi)
% 2.43/0.75  % (21936)Instruction limit reached!
% 2.43/0.75  % (21936)------------------------------
% 2.43/0.75  % (21936)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.43/0.75  % (21936)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.43/0.75  % (21936)Termination reason: Unknown
% 2.43/0.75  % (21936)Termination phase: Saturation
% 2.43/0.75  
% 2.43/0.75  % (21936)Memory used [KB]: 9338
% 2.43/0.75  % (21936)Time elapsed: 0.050 s
% 2.43/0.75  % (21936)Instructions burned: 100 (million)
% 2.43/0.75  % (21936)------------------------------
% 2.43/0.75  % (21936)------------------------------
% 2.57/0.76  % (21944)Instruction limit reached!
% 2.57/0.76  % (21944)------------------------------
% 2.57/0.76  % (21944)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.57/0.76  % (21944)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.57/0.76  % (21944)Termination reason: Unknown
% 2.57/0.76  % (21944)Termination phase: Saturation
% 2.57/0.76  
% 2.57/0.76  % (21944)Memory used [KB]: 4989
% 2.57/0.76  % (21944)Time elapsed: 0.050 s
% 2.57/0.76  % (21944)Instructions burned: 101 (million)
% 2.57/0.76  % (21944)------------------------------
% 2.57/0.76  % (21944)------------------------------
% 2.57/0.76  % (21958)ott+1_1:2_i=920:si=on:rawr=on:rtra=on_0 on theBenchmark for (2997ds/920Mi)
% 2.57/0.77  % (21957)dis+22_1:128_bsd=on:rp=on:slsq=on:slsqc=1:slsqr=1,6:sp=frequency:spb=goal:thsq=on:thsqc=16:thsqd=1:thsql=off:i=90:si=on:rawr=on:rtra=on_0 on theBenchmark for (2997ds/90Mi)
% 2.57/0.77  % (21937)Instruction limit reached!
% 2.57/0.77  % (21937)------------------------------
% 2.57/0.77  % (21937)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.57/0.77  % (21937)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.57/0.77  % (21937)Termination reason: Unknown
% 2.57/0.77  % (21937)Termination phase: Saturation
% 2.57/0.77  
% 2.57/0.77  % (21937)Memory used [KB]: 9594
% 2.57/0.77  % (21937)Time elapsed: 0.050 s
% 2.57/0.77  % (21937)Instructions burned: 102 (million)
% 2.57/0.77  % (21937)------------------------------
% 2.57/0.77  % (21937)------------------------------
% 2.57/0.77  % (21943)Instruction limit reached!
% 2.57/0.77  % (21943)------------------------------
% 2.57/0.77  % (21943)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.57/0.77  % (21943)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.57/0.77  % (21943)Termination reason: Unknown
% 2.57/0.77  % (21943)Termination phase: Saturation
% 2.57/0.77  
% 2.57/0.77  % (21943)Memory used [KB]: 9466
% 2.57/0.77  % (21943)Time elapsed: 0.056 s
% 2.57/0.77  % (21943)Instructions burned: 100 (million)
% 2.57/0.77  % (21943)------------------------------
% 2.57/0.77  % (21943)------------------------------
% 2.57/0.79  % (21959)ott+1_1:7_bd=off:i=934:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/934Mi)
% 2.57/0.80  % (21962)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/68Mi)
% 2.57/0.80  % (21965)dis+22_1:128_bsd=on:rp=on:slsq=on:slsqc=1:slsqr=1,6:sp=frequency:spb=goal:thsq=on:thsqc=16:thsqd=1:thsql=off:i=90:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/90Mi)
% 2.57/0.81  % (21960)ott+10_1:50_bsr=unit_only:drc=off:fd=preordered:sp=frequency:i=747:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/747Mi)
% 2.57/0.82  WARNING Broken Constraint: if sine_depth(2) has been set then sine_selection(off) is not equal to off
% 2.57/0.82  % (21946)Instruction limit reached!
% 2.57/0.82  % (21946)------------------------------
% 2.57/0.82  % (21946)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.75/0.83  % (21946)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.75/0.83  % (21946)Termination reason: Unknown
% 2.75/0.83  % (21946)Termination phase: Saturation
% 2.75/0.83  
% 2.75/0.83  % (21946)Memory used [KB]: 9850
% 2.75/0.83  % (21946)Time elapsed: 0.072 s
% 2.75/0.83  % (21946)Instructions burned: 139 (million)
% 2.75/0.83  % (21946)------------------------------
% 2.75/0.83  % (21946)------------------------------
% 2.75/0.83  % (21964)ott+11_4:1_br=off:fde=none:s2a=on:sd=2:sp=frequency:urr=on:i=981:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/981Mi)
% 2.75/0.84  % (21961)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=655:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/655Mi)
% 2.75/0.84  % (21966)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=2016:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/2016Mi)
% 2.75/0.86  % (21963)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=940:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/940Mi)
% 2.86/0.86  % (21967)dis+10_1:2_atotf=0.3:i=3735:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/3735Mi)
% 2.86/0.88  % (21971)ott+3_1:1_atotf=0.2:fsr=off:kws=precedence:sp=weighted_frequency:spb=intro:tgt=ground:i=4931:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/4931Mi)
% 2.86/0.88  % (21968)ott+11_9:8_add=large:afp=10:amm=off:fsd=on:fsr=off:lma=on:nm=0:nwc=2.4:s2a=on:s2agt=10:sas=z3:sp=reverse_arity:tha=some:thi=overlap:i=4958:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/4958Mi)
% 2.86/0.89  % (21970)ott+10_1:1_kws=precedence:tgt=ground:i=4756:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/4756Mi)
% 2.86/0.89  % (21969)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=4959:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/4959Mi)
% 2.86/0.90  % (21957)Instruction limit reached!
% 2.86/0.90  % (21957)------------------------------
% 2.86/0.90  % (21957)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.86/0.90  % (21957)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.86/0.90  % (21957)Termination reason: Unknown
% 2.86/0.90  % (21957)Termination phase: Saturation
% 2.86/0.90  
% 2.86/0.90  % (21957)Memory used [KB]: 9466
% 2.86/0.90  % (21957)Time elapsed: 0.057 s
% 2.86/0.90  % (21957)Instructions burned: 91 (million)
% 2.86/0.90  % (21957)------------------------------
% 2.86/0.90  % (21957)------------------------------
% 2.86/0.90  % (21972)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2995ds/68Mi)
% 2.86/0.90  % (21973)ott+11_9:8_amm=off:bsd=on:etr=on:fsd=on:fsr=off:lma=on:newcnf=on:nm=0:nwc=3.0:s2a=on:s2agt=10:sas=z3:tha=some:i=1824:si=on:rawr=on:rtra=on_0 on theBenchmark for (2995ds/1824Mi)
% 2.86/0.91  % (21962)Instruction limit reached!
% 2.86/0.91  % (21962)------------------------------
% 2.86/0.91  % (21962)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.86/0.91  % (21962)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.86/0.91  % (21962)Termination reason: Unknown
% 2.86/0.91  % (21962)Termination phase: Property scanning
% 2.86/0.91  
% 2.86/0.91  % (21962)Memory used [KB]: 4989
% 2.86/0.91  % (21962)Time elapsed: 0.033 s
% 2.86/0.91  % (21962)Instructions burned: 68 (million)
% 2.86/0.91  % (21962)------------------------------
% 2.86/0.91  % (21962)------------------------------
% 2.86/0.91  % (21945)Instruction limit reached!
% 2.86/0.91  % (21945)------------------------------
% 2.86/0.91  % (21945)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.86/0.91  % (21945)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.86/0.91  % (21945)Termination reason: Unknown
% 2.86/0.91  % (21945)Termination phase: Saturation
% 2.86/0.91  
% 2.86/0.91  % (21945)Memory used [KB]: 10106
% 2.86/0.91  % (21945)Time elapsed: 0.107 s
% 2.86/0.91  % (21945)Instructions burned: 178 (million)
% 2.86/0.91  % (21945)------------------------------
% 2.86/0.91  % (21945)------------------------------
% 2.86/0.91  % (21974)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=2134:si=on:rawr=on:rtra=on_0 on theBenchmark for (2995ds/2134Mi)
% 2.86/0.91  % (21952)Instruction limit reached!
% 2.86/0.91  % (21952)------------------------------
% 2.86/0.91  % (21952)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.86/0.91  % (21952)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.86/0.91  % (21952)Termination reason: Unknown
% 2.86/0.91  % (21952)Termination phase: Saturation
% 2.86/0.91  
% 2.86/0.91  % (21952)Memory used [KB]: 5884
% 2.86/0.91  % (21952)Time elapsed: 0.455 s
% 2.86/0.91  % (21952)Instructions burned: 178 (million)
% 2.86/0.91  % (21952)------------------------------
% 2.86/0.91  % (21952)------------------------------
% 3.21/0.94  % (21965)Instruction limit reached!
% 3.21/0.94  % (21965)------------------------------
% 3.21/0.94  % (21965)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 3.21/0.94  % (21965)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 3.21/0.94  % (21965)Termination reason: Unknown
% 3.21/0.94  % (21965)Termination phase: Saturation
% 3.21/0.94  
% 3.21/0.94  % (21965)Memory used [KB]: 9338
% 3.21/0.94  % (21965)Time elapsed: 0.042 s
% 3.21/0.94  % (21965)Instructions burned: 90 (million)
% 3.21/0.94  % (21965)------------------------------
% 3.21/0.94  % (21965)------------------------------
% 3.21/0.97  % (21975)ott-1_1:1_sp=const_frequency:i=2891:si=on:rawr=on:rtra=on_0 on theBenchmark for (2995ds/2891Mi)
% 3.33/1.00  % (21972)Instruction limit reached!
% 3.33/1.00  % (21972)------------------------------
% 3.33/1.00  % (21972)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 3.33/1.00  % (21972)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 3.33/1.00  % (21972)Termination reason: Unknown
% 3.33/1.00  % (21972)Termination phase: Property scanning
% 3.33/1.00  
% 3.33/1.00  % (21972)Memory used [KB]: 4989
% 3.33/1.00  % (21972)Time elapsed: 0.032 s
% 3.33/1.00  % (21972)Instructions burned: 70 (million)
% 3.33/1.00  % (21972)------------------------------
% 3.33/1.00  % (21972)------------------------------
% 3.50/1.04  % (21977)dis+22_1:128_bsd=on:rp=on:slsq=on:slsqc=1:slsqr=1,6:sp=frequency:spb=goal:thsq=on:thsqc=16:thsqd=1:thsql=off:i=90:si=on:rawr=on:rtra=on_0 on theBenchmark for (2994ds/90Mi)
% 3.50/1.04  % (21979)dis+10_1:2_atotf=0.3:i=8004:si=on:rawr=on:rtra=on_0 on theBenchmark for (2994ds/8004Mi)
% 3.50/1.05  % (21976)dis+2_1:64_add=large:bce=on:bd=off:i=4585:si=on:rawr=on:rtra=on_0 on theBenchmark for (2994ds/4585Mi)
% 3.50/1.05  % (21978)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=2016:si=on:rawr=on:rtra=on_0 on theBenchmark for (2994ds/2016Mi)
% 5.21/1.08  % (21980)ott+11_9:8_add=large:afp=10:amm=off:fsd=on:fsr=off:lma=on:nm=0:nwc=2.4:s2a=on:s2agt=10:sas=z3:sp=reverse_arity:tha=some:thi=overlap:i=9965:si=on:rawr=on:rtra=on_0 on theBenchmark for (2994ds/9965Mi)
% 5.21/1.10  % (21956)Instruction limit reached!
% 5.21/1.10  % (21956)------------------------------
% 5.21/1.10  % (21956)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 5.21/1.10  % (21956)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 5.21/1.10  % (21956)Termination reason: Unknown
% 5.21/1.10  % (21956)Termination phase: Saturation
% 5.21/1.10  
% 5.21/1.10  % (21956)Memory used [KB]: 6396
% 5.21/1.10  % (21956)Time elapsed: 0.446 s
% 5.21/1.10  % (21956)Instructions burned: 212 (million)
% 5.21/1.10  % (21956)------------------------------
% 5.21/1.10  % (21956)------------------------------
% 5.73/1.14  % (21981)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=9877:si=on:rawr=on:rtra=on_0 on theBenchmark for (2993ds/9877Mi)
% 6.05/1.20  % (21977)Instruction limit reached!
% 6.05/1.20  % (21977)------------------------------
% 6.05/1.20  % (21977)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 6.05/1.20  % (21977)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 6.05/1.20  % (21977)Termination reason: Unknown
% 6.05/1.20  % (21977)Termination phase: Saturation
% 6.05/1.20  
% 6.05/1.20  % (21977)Memory used [KB]: 9338
% 6.05/1.20  % (21977)Time elapsed: 0.055 s
% 6.05/1.20  % (21977)Instructions burned: 90 (million)
% 6.05/1.20  % (21977)------------------------------
% 6.05/1.20  % (21977)------------------------------
% 6.05/1.24  % (21982)ins+10_1:16_bce=on:fde=unused:igpr=on:igs=35:igwr=on:sp=const_frequency:tgt=full:to=lpo:i=9902:si=on:rawr=on:rtra=on_0 on theBenchmark for (2992ds/9902Mi)
% 6.52/1.24  % (21954)Instruction limit reached!
% 6.52/1.24  % (21954)------------------------------
% 6.52/1.24  % (21954)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 6.52/1.24  % (21954)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 6.52/1.24  % (21954)Termination reason: Unknown
% 6.52/1.24  % (21954)Termination phase: Saturation
% 6.52/1.24  
% 6.52/1.24  % (21954)Memory used [KB]: 12792
% 6.52/1.24  % (21954)Time elapsed: 0.767 s
% 6.52/1.24  % (21954)Instructions burned: 356 (million)
% 6.52/1.24  % (21954)------------------------------
% 6.52/1.24  % (21954)------------------------------
% 6.69/1.28  % (21947)Instruction limit reached!
% 6.69/1.28  % (21947)------------------------------
% 6.69/1.28  % (21947)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 6.69/1.28  % (21947)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 6.69/1.28  % (21947)Termination reason: Unknown
% 6.69/1.28  % (21947)Termination phase: Saturation
% 6.69/1.28  
% 6.69/1.29  % (21947)Memory used [KB]: 6780
% 6.69/1.29  % (21947)Time elapsed: 0.588 s
% 6.69/1.29  % (21947)Instructions burned: 500 (million)
% 6.69/1.29  % (21947)------------------------------
% 6.69/1.29  % (21947)------------------------------
% 6.69/1.30  TRYING [1]
% 7.11/1.32  % (21983)ott+11_9:8_amm=off:bsd=on:etr=on:fsd=on:fsr=off:lma=on:newcnf=on:nm=0:nwc=3.0:s2a=on:s2agt=10:sas=z3:tha=some:i=1824:si=on:rawr=on:rtra=on_0 on theBenchmark for (2991ds/1824Mi)
% 7.40/1.36  % (21953)Instruction limit reached!
% 7.40/1.36  % (21953)------------------------------
% 7.40/1.36  % (21953)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 7.40/1.36  % (21953)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 7.40/1.36  % (21953)Termination reason: Unknown
% 7.40/1.36  % (21953)Termination phase: Saturation
% 7.40/1.36  
% 7.40/1.36  % (21953)Memory used [KB]: 14711
% 7.40/1.36  % (21953)Time elapsed: 0.908 s
% 7.40/1.36  % (21953)Instructions burned: 440 (million)
% 7.40/1.36  % (21953)------------------------------
% 7.40/1.36  % (21953)------------------------------
% 7.40/1.37  % (21955)Instruction limit reached!
% 7.40/1.37  % (21955)------------------------------
% 7.40/1.37  % (21955)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 7.40/1.38  % (21984)dis+2_1:64_add=large:bce=on:bd=off:i=9989:si=on:rawr=on:rtra=on_0 on theBenchmark for (2991ds/9989Mi)
% 7.40/1.38  % (21955)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 7.40/1.38  % (21955)Termination reason: Unknown
% 7.40/1.38  % (21955)Termination phase: Saturation
% 7.40/1.38  
% 7.40/1.38  % (21955)Memory used [KB]: 12665
% 7.40/1.38  % (21955)Time elapsed: 0.647 s
% 7.40/1.38  % (21955)Instructions burned: 390 (million)
% 7.40/1.38  % (21955)------------------------------
% 7.40/1.38  % (21955)------------------------------
% 7.40/1.40  % (21948)Instruction limit reached!
% 7.40/1.40  % (21948)------------------------------
% 7.40/1.40  % (21948)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 7.40/1.40  % (21948)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 7.40/1.40  % (21948)Termination reason: Unknown
% 7.40/1.40  % (21948)Termination phase: Saturation
% 7.40/1.40  
% 7.40/1.40  % (21948)Memory used [KB]: 14328
% 7.40/1.40  % (21948)Time elapsed: 0.905 s
% 7.40/1.40  % (21948)Instructions burned: 467 (million)
% 7.40/1.40  % (21948)------------------------------
% 7.40/1.40  % (21948)------------------------------
% 7.40/1.40  TRYING [2]
% 7.40/1.42  % (21985)ott-11_1:32_i=9707:si=on:rawr=on:rtra=on_0 on theBenchmark for (2990ds/9707Mi)
% 8.17/1.49  % (21950)Instruction limit reached!
% 8.17/1.49  % (21950)------------------------------
% 8.17/1.49  % (21950)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 8.17/1.49  % (21950)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 8.17/1.49  % (21950)Termination reason: Unknown
% 8.17/1.49  % (21950)Termination phase: Saturation
% 8.17/1.49  
% 8.17/1.49  % (21950)Memory used [KB]: 12665
% 8.17/1.49  % (21950)Time elapsed: 1.026 s
% 8.17/1.49  % (21950)Instructions burned: 500 (million)
% 8.17/1.49  % (21950)------------------------------
% 8.17/1.49  % (21950)------------------------------
% 8.17/1.51  % (21986)dis+22_1:128_bsd=on:rp=on:slsq=on:slsqc=1:slsqr=1,6:sp=frequency:spb=goal:thsq=on:thsqc=16:thsqd=1:thsql=off:i=90:si=on:rawr=on:rtra=on_0 on theBenchmark for (2989ds/90Mi)
% 8.17/1.51  % (21987)ott+3_1:1_abs=on:anc=none:bs=on:fsr=off:spb=goal_then_units:i=44001:si=on:rawr=on:rtra=on_0 on theBenchmark for (2989ds/44001Mi)
% 8.17/1.52  % (21949)Instruction limit reached!
% 8.17/1.52  % (21949)------------------------------
% 8.17/1.52  % (21949)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 8.17/1.52  % (21949)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 8.17/1.52  % (21949)Termination reason: Unknown
% 8.17/1.52  % (21949)Termination phase: Saturation
% 8.17/1.52  
% 8.17/1.52  % (21949)Memory used [KB]: 13432
% 8.17/1.52  % (21949)Time elapsed: 1.065 s
% 8.17/1.52  % (21949)Instructions burned: 484 (million)
% 8.17/1.52  % (21949)------------------------------
% 8.17/1.52  % (21949)------------------------------
% 8.17/1.53  % (21988)ott+11_9:8_add=large:afp=10:amm=off:fsd=on:fsr=off:lma=on:nm=0:nwc=2.4:s2a=on:s2agt=10:sas=z3:sp=reverse_arity:tha=some:thi=overlap:i=4958:si=on:rawr=on:rtra=on_0 on theBenchmark for (2989ds/4958Mi)
% 8.67/1.63  % (21989)ott+1_27:428_av=off:awrs=converge:awrsf=8:bsr=unit_only:drc=off:fd=preordered:newcnf=on:nwc=1.5:skr=on:slsq=on:slsqc=2:slsql=off:slsqr=1,4:sp=reverse_frequency:uwa=one_side_constant:i=35256:si=on:rawr=on:rtra=on_0 on theBenchmark for (2988ds/35256Mi)
% 9.65/1.65  % (21986)Instruction limit reached!
% 9.65/1.65  % (21986)------------------------------
% 9.65/1.65  % (21986)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 9.65/1.65  % (21986)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 9.65/1.65  % (21986)Termination reason: Unknown
% 9.65/1.65  % (21986)Termination phase: Saturation
% 9.65/1.65  
% 9.65/1.65  % (21986)Memory used [KB]: 9338
% 9.65/1.65  % (21986)Time elapsed: 0.041 s
% 9.65/1.65  % (21986)Instructions burned: 91 (million)
% 9.65/1.65  % (21986)------------------------------
% 9.65/1.65  % (21986)------------------------------
% 9.65/1.66  % (21990)dis+1002_1:1_fde=unused:nwc=10.0:s2a=on:s2at=3.0:sac=on:i=32293:si=on:rawr=on:rtra=on_0 on theBenchmark for (2988ds/32293Mi)
% 10.84/1.80  % (21961)Instruction limit reached!
% 10.84/1.80  % (21961)------------------------------
% 10.84/1.80  % (21961)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 10.84/1.80  % (21961)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 10.84/1.80  % (21961)Termination reason: Unknown
% 10.84/1.80  % (21961)Termination phase: Saturation
% 10.84/1.80  
% 10.84/1.80  % (21961)Memory used [KB]: 7419
% 10.84/1.80  % (21961)Time elapsed: 1.050 s
% 10.84/1.80  % (21961)Instructions burned: 655 (million)
% 10.84/1.80  % (21961)------------------------------
% 10.84/1.80  % (21961)------------------------------
% 10.84/1.81  % (21991)ott+21_1:28_afr=on:anc=all_dependent:bs=on:bsr=unit_only:nicw=on:sp=const_frequency:uhcvi=on:i=37001:si=on:rawr=on:rtra=on_0 on theBenchmark for (2986ds/37001Mi)
% 11.83/1.95  % (21992)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=10187:si=on:rawr=on:rtra=on_0 on theBenchmark for (2985ds/10187Mi)
% 13.00/2.09  % (21960)Instruction limit reached!
% 13.00/2.09  % (21960)------------------------------
% 13.00/2.09  % (21960)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 13.00/2.09  % (21960)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 13.00/2.09  % (21960)Termination reason: Unknown
% 13.00/2.09  % (21960)Termination phase: Saturation
% 13.00/2.09  
% 13.00/2.09  % (21960)Memory used [KB]: 14583
% 13.00/2.09  % (21960)Time elapsed: 1.387 s
% 13.00/2.09  % (21960)Instructions burned: 747 (million)
% 13.00/2.09  % (21960)------------------------------
% 13.00/2.09  % (21960)------------------------------
% 13.84/2.19  % (21963)Instruction limit reached!
% 13.84/2.19  % (21963)------------------------------
% 13.84/2.19  % (21963)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 13.84/2.19  % (21963)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 13.84/2.19  % (21963)Termination reason: Unknown
% 13.84/2.19  % (21963)Termination phase: Saturation
% 13.84/2.19  
% 13.84/2.19  % (21963)Memory used [KB]: 14456
% 13.84/2.19  % (21963)Time elapsed: 1.427 s
% 13.84/2.19  % (21963)Instructions burned: 940 (million)
% 13.84/2.19  % (21963)------------------------------
% 13.84/2.19  % (21963)------------------------------
% 14.42/2.23  % (21993)ott+3_1:1_atotf=0.2:fsr=off:kws=precedence:sp=weighted_frequency:spb=intro:tgt=ground:i=29337:si=on:rawr=on:rtra=on_0 on theBenchmark for (2982ds/29337Mi)
% 15.47/2.40  % (21994)ins+10_1:16_bce=on:fde=unused:igpr=on:igs=35:igwr=on:sp=const_frequency:tgt=full:to=lpo:i=10147:si=on:rawr=on:rtra=on_0 on theBenchmark for (2981ds/10147Mi)
% 15.47/2.41  % (21959)Instruction limit reached!
% 15.47/2.41  % (21959)------------------------------
% 15.47/2.41  % (21959)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 15.47/2.41  % (21959)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 15.47/2.41  % (21959)Termination reason: Unknown
% 15.47/2.41  % (21959)Termination phase: Saturation
% 15.47/2.41  
% 15.47/2.41  % (21959)Memory used [KB]: 18933
% 15.47/2.41  % (21959)Time elapsed: 1.722 s
% 15.47/2.41  % (21959)Instructions burned: 934 (million)
% 15.47/2.41  % (21959)------------------------------
% 15.47/2.41  % (21959)------------------------------
% 16.14/2.49  % (21958)Instruction limit reached!
% 16.14/2.49  % (21958)------------------------------
% 16.14/2.49  % (21958)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 16.14/2.49  % (21958)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 16.14/2.49  % (21958)Termination reason: Unknown
% 16.14/2.49  % (21958)Termination phase: Saturation
% 16.14/2.49  
% 16.14/2.49  % (21958)Memory used [KB]: 19189
% 16.14/2.49  % (21958)Time elapsed: 1.805 s
% 16.14/2.49  % (21958)Instructions burned: 920 (million)
% 16.14/2.49  % (21958)------------------------------
% 16.14/2.49  % (21958)------------------------------
% 16.14/2.50  % (21964)Instruction limit reached!
% 16.14/2.50  % (21964)------------------------------
% 16.14/2.50  % (21964)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 16.14/2.50  % (21964)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 16.14/2.50  % (21964)Termination reason: Unknown
% 16.14/2.50  % (21964)Termination phase: Saturation
% 16.14/2.50  
% 16.14/2.50  % (21964)Memory used [KB]: 18805
% 16.14/2.50  % (21964)Time elapsed: 1.790 s
% 16.14/2.50  % (21964)Instructions burned: 982 (million)
% 16.14/2.50  % (21964)------------------------------
% 16.14/2.50  % (21964)------------------------------
% 16.80/2.57  % (21995)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=38056:si=on:rawr=on:rtra=on_0 on theBenchmark for (2979ds/38056Mi)
% 17.11/2.63  % (21996)fmb+10_1:1_dr=on:fmbsr=2.0:newcnf=on:nm=2:i=33239:si=on:rawr=on:rtra=on_0 on theBenchmark for (2978ds/33239Mi)
% 17.11/2.64  % (21997)fmb+10_1:1_fmbas=predicate:gsp=on:nm=2:i=20987:si=on:rawr=on:rtra=on_0 on theBenchmark for (2978ds/20987Mi)
% 22.46/3.25  TRYING [1]
% 22.67/3.30  TRYING [3]
% 23.18/3.34  TRYING [2]
% 23.53/3.39  TRYING [1]
% 24.07/3.46  TRYING [1]
% 24.25/3.51  TRYING [2]
% 24.97/3.57  TRYING [2]
% 26.67/3.80  % (21973)Instruction limit reached!
% 26.67/3.80  % (21973)------------------------------
% 26.67/3.80  % (21973)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 26.67/3.80  % (21973)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 26.67/3.80  % (21973)Termination reason: Unknown
% 26.67/3.80  % (21973)Termination phase: Saturation
% 26.67/3.80  
% 26.67/3.80  % (21973)Memory used [KB]: 13176
% 26.67/3.80  % (21973)Time elapsed: 3.015 s
% 26.67/3.80  % (21973)Instructions burned: 1825 (million)
% 26.67/3.80  % (21973)------------------------------
% 26.67/3.80  % (21973)------------------------------
% 28.08/3.95  % (21966)Instruction limit reached!
% 28.08/3.95  % (21966)------------------------------
% 28.08/3.95  % (21966)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 28.08/3.95  % (21966)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 28.08/3.95  % (21966)Termination reason: Unknown
% 28.08/3.95  % (21966)Termination phase: Saturation
% 28.08/3.95  
% 28.08/3.95  % (21966)Memory used [KB]: 11129
% 28.08/3.95  % (21966)Time elapsed: 2.512 s
% 28.08/3.95  % (21966)Instructions burned: 2018 (million)
% 28.08/3.95  % (21966)------------------------------
% 28.08/3.95  % (21966)------------------------------
% 28.08/3.97  % (21998)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=49917:si=on:rawr=on:rtra=on_0 on theBenchmark for (2965ds/49917Mi)
% 28.95/4.09  % (21978)Instruction limit reached!
% 28.95/4.09  % (21978)------------------------------
% 28.95/4.09  % (21978)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 28.95/4.09  % (21978)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 28.95/4.09  % (21978)Termination reason: Unknown
% 28.95/4.09  % (21978)Termination phase: Saturation
% 28.95/4.09  
% 28.95/4.09  % (21978)Memory used [KB]: 11385
% 28.95/4.09  % (21978)Time elapsed: 3.104 s
% 28.95/4.09  % (21978)Instructions burned: 2016 (million)
% 28.95/4.09  % (21978)------------------------------
% 28.95/4.09  % (21978)------------------------------
% 28.95/4.10  % (21999)dis+2_1:64_add=large:bce=on:bd=off:i=19144:si=on:rawr=on:rtra=on_0 on theBenchmark for (2963ds/19144Mi)
% 29.47/4.14  % (21983)Instruction limit reached!
% 29.47/4.14  % (21983)------------------------------
% 29.47/4.14  % (21983)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 29.47/4.14  % (21983)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 29.47/4.14  % (21983)Termination reason: Unknown
% 29.47/4.14  % (21983)Termination phase: Saturation
% 29.47/4.14  
% 29.47/4.14  % (21983)Memory used [KB]: 17014
% 29.47/4.14  % (21983)Time elapsed: 2.880 s
% 29.47/4.14  % (21983)Instructions burned: 1825 (million)
% 29.47/4.14  % (21983)------------------------------
% 29.47/4.14  % (21983)------------------------------
% 29.83/4.23  % (22000)dis+10_1:128_bd=off:lcm=predicate:sac=on:sp=reverse_arity:urr=on:i=27492:si=on:rawr=on:rtra=on_0 on theBenchmark for (2962ds/27492Mi)
% 30.57/4.28  % (22001)ott-11_1:32_i=6101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2962ds/6101Mi)
% 31.38/4.43  % (21974)Instruction limit reached!
% 31.38/4.43  % (21974)------------------------------
% 31.38/4.43  % (21974)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 31.38/4.43  % (21974)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 31.38/4.43  % (21974)Termination reason: Unknown
% 31.38/4.43  % (21974)Termination phase: Saturation
% 31.38/4.43  
% 31.38/4.43  % (21974)Memory used [KB]: 21620
% 31.38/4.43  % (21974)Time elapsed: 3.520 s
% 31.38/4.43  % (21974)Instructions burned: 2134 (million)
% 31.38/4.43  % (21974)------------------------------
% 31.38/4.43  % (21974)------------------------------
% 32.96/4.59  % (22002)dis+22_1:128_bsd=on:rp=on:slsq=on:slsqc=1:slsqr=1,6:sp=frequency:spb=goal:thsq=on:thsqc=16:thsqd=1:thsql=off:i=90:si=on:rawr=on:rtra=on_0 on theBenchmark for (2959ds/90Mi)
% 33.66/4.71  % (22002)Instruction limit reached!
% 33.66/4.71  % (22002)------------------------------
% 33.66/4.71  % (22002)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 33.66/4.71  % (22002)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 33.66/4.71  % (22002)Termination reason: Unknown
% 33.66/4.71  % (22002)Termination phase: Saturation
% 33.66/4.71  
% 33.66/4.71  % (22002)Memory used [KB]: 9338
% 33.66/4.71  % (22002)Time elapsed: 0.041 s
% 33.66/4.71  % (22002)Instructions burned: 90 (million)
% 33.66/4.71  % (22002)------------------------------
% 33.66/4.71  % (22002)------------------------------
% 34.74/4.79  TRYING [1]
% 35.40/4.86  % (22003)ott+11_1:128_av=off:bd=off:bsr=unit_only:fd=preordered:to=lpo:updr=off:i=91600:si=on:rawr=on:rtra=on_0 on theBenchmark for (2956ds/91600Mi)
% 35.40/4.90  TRYING [2]
% 39.26/5.36  TRYING [3]
% 41.10/5.64  TRYING [3]
% 42.20/5.74  TRYING [3]
% 43.08/5.83  % (21975)Instruction limit reached!
% 43.08/5.83  % (21975)------------------------------
% 43.08/5.83  % (21975)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 43.08/5.83  % (21975)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 43.08/5.83  % (21975)Termination reason: Unknown
% 43.08/5.83  % (21975)Termination phase: Saturation
% 43.08/5.83  
% 43.08/5.83  % (21975)Memory used [KB]: 27121
% 43.08/5.83  % (21975)Time elapsed: 4.964 s
% 43.08/5.83  % (21975)Instructions burned: 2892 (million)
% 43.08/5.83  % (21975)------------------------------
% 43.08/5.83  % (21975)------------------------------
% 44.69/6.04  % (22004)ott+11_9:8_add=large:afp=10:amm=off:fsd=on:fsr=off:lma=on:nm=0:nwc=2.4:s2a=on:s2agt=10:sas=z3:sp=reverse_arity:tha=some:thi=overlap:i=7127:si=on:rawr=on:rtra=on_0 on theBenchmark for (2945ds/7127Mi)
% 49.75/6.74  % (21968)First to succeed.
% 51.23/6.91  % (21968)Refutation found. Thanks to Tanya!
% 51.23/6.91  % SZS status Theorem for theBenchmark
% 51.23/6.91  % SZS output start Proof for theBenchmark
% See solution above
% 51.90/6.95  % (21968)------------------------------
% 51.90/6.95  % (21968)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 51.90/6.95  % (21968)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 51.90/6.95  % (21968)Termination reason: Refutation
% 51.90/6.95  
% 51.90/6.95  % (21968)Memory used [KB]: 23155
% 51.90/6.95  % (21968)Time elapsed: 5.974 s
% 51.90/6.95  % (21968)Instructions burned: 3853 (million)
% 51.90/6.95  % (21968)------------------------------
% 51.90/6.95  % (21968)------------------------------
% 51.90/6.95  % (21924)Success in time 6.586 s
%------------------------------------------------------------------------------