%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SWV712-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n009.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Apr 30 17:05:42 EDT 2024

% Result   : Unsatisfiable 2.49s 0.76s
% Output   : Refutation 2.49s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      : 1229
% Syntax   : Number of formulae    : 2186 ( 700 unt;   0 def)
%            Number of atoms       : 5127 (1088 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives : 5144 (2203   ~;2264   |;   0   &)
%                                         ( 677 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   4 avg)
%            Maximal term depth    :   15 (   2 avg)
%            Number of predicates  :  732 ( 730 usr; 678 prp; 0-6 aty)
%            Number of functors    :   26 (  26 usr;   9 con; 0-5 aty)
%            Number of variables   : 3175 (3175   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f12772,plain,
    $false,
    inference(avatar_sat_refutation,[],[f851,f856,f861,f866,f871,f876,f881,f886,f891,f896,f901,f906,f911,f916,f921,f926,f931,f936,f941,f946,f951,f956,f961,f966,f971,f976,f981,f986,f991,f996,f1001,f1006,f1011,f1016,f1021,f1026,f1031,f1036,f1041,f1046,f1051,f1056,f1061,f1066,f1071,f1076,f1081,f1086,f1091,f1096,f1101,f1106,f1111,f1116,f1121,f1126,f1131,f1136,f1141,f1146,f1151,f1156,f1161,f1166,f1171,f1176,f1181,f1186,f1191,f1196,f1201,f1206,f1211,f1216,f1221,f1226,f1231,f1236,f1241,f1246,f1251,f1256,f1261,f1266,f1271,f1276,f1281,f1286,f1291,f1296,f1301,f1306,f1311,f1316,f1321,f1326,f1331,f1336,f1341,f1346,f1351,f1356,f1361,f1366,f1371,f1376,f1380,f1384,f1388,f1393,f1397,f1403,f1407,f1411,f1416,f1421,f1426,f1431,f1435,f1439,f1443,f1447,f1451,f1455,f1459,f1463,f1467,f1471,f1475,f1479,f1483,f1490,f1494,f1498,f1502,f1506,f1510,f1514,f1518,f1531,f1541,f1545,f1549,f1553,f1557,f1561,f1565,f1570,f1575,f1580,f1584,f1588,f1592,f1622,f1626,f1630,f1634,f1638,f1642,f1646,f1650,f1654,f1658,f1662,f1666,f1670,f1674,f1679,f1716,f1741,f1746,f1750,f1754,f1758,f1762,f1766,f1770,f1774,f1778,f1782,f1786,f1790,f1794,f1798,f1802,f1806,f1813,f1817,f1821,f1825,f1842,f1893,f1907,f1911,f1915,f1919,f1923,f1927,f1931,f1935,f1939,f1943,f1947,f1951,f1955,f1959,f1963,f1967,f1971,f1975,f1979,f1983,f1987,f1991,f1995,f1999,f2003,f2007,f2011,f2016,f2024,f2043,f2072,f2118,f2122,f2126,f2130,f2134,f2138,f2142,f2146,f2150,f2154,f2158,f2162,f2166,f2170,f2174,f2178,f2183,f2188,f2192,f2196,f2200,f2204,f2208,f2213,f2229,f2390,f2402,f2406,f2410,f2414,f2418,f2422,f2426,f2430,f2434,f2438,f2444,f2448,f2452,f2456,f2460,f2464,f2468,f2472,f2476,f2480,f2486,f2490,f2494,f2498,f2502,f2506,f2510,f2514,f2518,f2573,f2762,f2767,f2771,f2775,f2779,f2783,f2787,f2791,f2795,f2799,f2803,f2807,f2811,f2815,f2819,f2823,f2827,f2831,f2836,f2840,f2844,f2981,f3005,f3009,f3013,f3017,f3021,f3025,f3029,f3033,f3037,f3041,f3045,f3049,f3087,f3091,f3095,f3099,f3103,f3109,f3113,f3117,f3121,f3125,f3129,f3133,f3137,f3141,f3145,f3151,f3155,f3159,f3163,f3167,f3172,f3176,f3180,f3205,f3279,f3327,f3336,f3340,f3344,f3348,f3352,f3356,f3360,f3364,f3368,f3372,f3376,f3425,f3439,f3443,f3447,f3451,f3455,f3459,f3463,f3467,f3471,f3475,f3479,f3483,f3487,f3491,f3495,f3499,f3503,f3507,f3511,f3515,f3520,f3524,f3528,f3532,f3536,f3540,f3597,f3674,f3683,f3687,f3691,f3695,f3699,f3703,f3707,f3711,f3715,f3719,f3724,f3728,f3732,f3736,f3740,f3744,f3748,f3752,f3756,f3760,f3764,f3865,f3977,f3981,f3985,f3989,f3993,f3997,f4048,f4052,f4056,f4060,f4064,f4068,f4072,f4095,f4099,f4103,f4107,f4111,f4115,f4119,f4123,f4127,f4131,f4139,f4143,f4147,f4151,f4155,f4159,f4163,f4453,f4457,f4461,f4465,f4469,f4473,f4477,f4481,f4485,f4489,f4493,f4497,f4501,f4601,f4735,f4739,f4743,f4748,f4752,f4756,f4760,f4764,f4768,f4772,f4776,f4815,f4891,f4895,f4899,f4918,f4922,f4926,f4930,f4934,f4938,f4942,f4946,f4950,f4954,f4979,f4983,f4987,f4991,f4995,f4999,f5003,f5007,f5011,f5015,f5040,f5044,f5048,f5052,f5056,f5060,f5064,f5068,f5072,f5076,f5080,f5084,f5088,f5244,f5551,f5616,f5699,f5703,f5707,f5711,f5715,f5719,f5723,f5727,f5731,f5735,f5739,f5743,f5747,f5751,f5755,f5759,f5763,f5767,f5771,f5775,f5779,f5877,f5931,f5979,f5983,f5987,f5991,f5996,f6006,f6010,f6014,f6018,f6049,f6054,f6068,f6072,f6076,f6080,f6084,f6088,f6092,f6096,f6100,f6104,f6108,f6112,f6116,f6120,f6124,f6128,f6134,f6242,f6257,f6261,f6265,f6288,f6292,f6296,f6300,f6304,f6308,f6312,f6366,f6389,f6393,f6397,f6414,f6418,f6422,f6441,f6445,f6449,f6453,f6457,f6536,f6540,f6544,f6548,f6625,f6633,f6637,f6641,f6665,f6750,f6769,f6773,f6777,f6831,f6931,f6935,f6939,f6943,f6947,f6951,f6955,f6959,f7367,f7375,f7491,f7496,f7502,f7512,f7811,f8627,f8631,f8635,f8639,f8647,f8651,f8655,f8659,f8663,f8672,f8676,f8680,f8685,f8689,f8693,f9880,f9967,f9973,f9985,f9989,f9993,f10000,f10004,f10008,f10012,f10016,f10020,f10024,f10029,f10035,f10039,f10044,f10048,f10687,f10691,f10971,f10976,f11036,f11041,f11099,f11104,f11113,f11117,f11122,f11126,f11132,f11136,f11150,f11156,f11168,f11172,f11176,f11180,f12069,f12073,f12116,f12120,f12124,f12128,f12132,f12136,f12140,f12144,f12148,f12152,f12156,f12161,f12165,f12169,f12173,f12177,f12185,f12700]) ).

fof(f12700,plain,
    ( spl0_587
    | ~ spl0_666 ),
    inference(avatar_contradiction_clause,[],[f12699]) ).

fof(f12699,plain,
    ( $false
    | spl0_587
    | ~ spl0_666 ),
    inference(trivial_inequality_removal,[],[f12627]) ).

fof(f12627,plain,
    ( c_HOL_Ominus__class_Ominus(hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_Complex_Ocomplex,tc_nat)),v_i____),c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat)),v_i____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(c_Suc,v_ka____))),tc_Complex_Ocomplex)),v_i____)),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ominus__class_Ominus(hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_Complex_Ocomplex,tc_nat)),v_i____),c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat)),v_i____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(c_Suc,v_ka____))),tc_Complex_Ocomplex)),v_i____)),tc_Complex_Ocomplex),tc_Complex_Ocomplex)
    | spl0_587
    | ~ spl0_666 ),
    inference(superposition,[],[f6930,f12139]) ).

fof(f12139,plain,
    ( ! [X0,X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),X0),X1) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
    | ~ spl0_666 ),
    inference(avatar_component_clause,[],[f12138]) ).

fof(f12138,plain,
    ( spl0_666
  <=> ! [X0,X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),X0),X1) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_666])]) ).

fof(f6930,plain,
    ( c_HOL_Ominus__class_Ominus(hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_Complex_Ocomplex,tc_nat)),v_i____),c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat)),v_i____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(c_Suc,v_ka____))),tc_Complex_Ocomplex)),v_i____)),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_Complex_Ocomplex,tc_nat)),v_i____)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat)),v_i____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(c_Suc,v_ka____))),tc_Complex_Ocomplex)),v_i____)))
    | spl0_587 ),
    inference(avatar_component_clause,[],[f6928]) ).

fof(f6928,plain,
    ( spl0_587
  <=> c_HOL_Ominus__class_Ominus(hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_Complex_Ocomplex,tc_nat)),v_i____),c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat)),v_i____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(c_Suc,v_ka____))),tc_Complex_Ocomplex)),v_i____)),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_Complex_Ocomplex,tc_nat)),v_i____)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat)),v_i____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(c_Suc,v_ka____))),tc_Complex_Ocomplex)),v_i____))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_587])]) ).

fof(f12185,plain,
    ( ~ spl0_9
    | ~ spl0_676
    | spl0_677
    | ~ spl0_278
    | ~ spl0_442 ),
    inference(avatar_split_clause,[],[f4618,f4483,f2516,f12183,f12179,f888]) ).

fof(f888,plain,
    ( spl0_9
  <=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

fof(f12179,plain,
    ( spl0_676
  <=> c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_676])]) ).

fof(f12183,plain,
    ( spl0_677
  <=> ! [X0,X1] : X0 = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_677])]) ).

fof(f2516,plain,
    ( spl0_278
  <=> ! [X19] : c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat)),X19) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).

fof(f4483,plain,
    ( spl0_442
  <=> ! [X19,X0,X3,X1] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | X3 = X19
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3) != hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X19) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).

fof(f4618,plain,
    ( ! [X0,X1] :
        ( X0 = X1
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat),tc_nat)
        | ~ class_Ring__and__Field_Oordered__semidom(tc_nat) )
    | ~ spl0_278
    | ~ spl0_442 ),
    inference(trivial_inequality_removal,[],[f4617]) ).

fof(f4617,plain,
    ( ! [X0,X1] :
        ( c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat) != c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat)
        | X0 = X1
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat),tc_nat)
        | ~ class_Ring__and__Field_Oordered__semidom(tc_nat) )
    | ~ spl0_278
    | ~ spl0_442 ),
    inference(forward_demodulation,[],[f4611,f2517]) ).

fof(f2517,plain,
    ( ! [X19] : c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat)),X19)
    | ~ spl0_278 ),
    inference(avatar_component_clause,[],[f2516]) ).

fof(f4611,plain,
    ( ! [X0,X1] :
        ( c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat)),X1)
        | X0 = X1
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat),tc_nat)
        | ~ class_Ring__and__Field_Oordered__semidom(tc_nat) )
    | ~ spl0_278
    | ~ spl0_442 ),
    inference(superposition,[],[f4484,f2517]) ).

fof(f4484,plain,
    ( ! [X3,X0,X1,X19] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3) != hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X19)
        | X3 = X19
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
        | ~ class_Ring__and__Field_Oordered__semidom(X0) )
    | ~ spl0_442 ),
    inference(avatar_component_clause,[],[f4483]) ).

fof(f12177,plain,
    ( spl0_675
    | ~ spl0_89
    | ~ spl0_231
    | ~ spl0_323 ),
    inference(avatar_split_clause,[],[f3260,f3119,f2144,f1288,f12175]) ).

fof(f12175,plain,
    ( spl0_675
  <=> ! [X0,X1] : c_HOL_Ominus__class_Ominus(X1,X0,tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_675])]) ).

fof(f1288,plain,
    ( spl0_89
  <=> class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).

fof(f2144,plain,
    ( spl0_231
  <=> ! [X2,X0,X1] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_HOL_Ominus__class_Ominus(X2,X1,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X1,X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).

fof(f3119,plain,
    ( spl0_323
  <=> ! [X2,X0,X1] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X1,X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).

fof(f3260,plain,
    ( ! [X0,X1] : c_HOL_Ominus__class_Ominus(X1,X0,tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
    | ~ spl0_89
    | ~ spl0_231
    | ~ spl0_323 ),
    inference(forward_demodulation,[],[f3258,f2237]) ).

fof(f2237,plain,
    ( ! [X0,X1] : c_HOL_Ominus__class_Ominus(X0,X1,tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X1,X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
    | ~ spl0_89
    | ~ spl0_231 ),
    inference(resolution,[],[f2145,f1290]) ).

fof(f1290,plain,
    ( class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex)
    | ~ spl0_89 ),
    inference(avatar_component_clause,[],[f1288]) ).

fof(f2145,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_HOL_Ominus__class_Ominus(X2,X1,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X1,X2,X0),X0) )
    | ~ spl0_231 ),
    inference(avatar_component_clause,[],[f2144]) ).

fof(f3258,plain,
    ( ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
    | ~ spl0_89
    | ~ spl0_323 ),
    inference(resolution,[],[f3120,f1290]) ).

fof(f3120,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X1,X2,X0),X0) )
    | ~ spl0_323 ),
    inference(avatar_component_clause,[],[f3119]) ).

fof(f12173,plain,
    ( spl0_674
    | ~ spl0_55
    | ~ spl0_231
    | ~ spl0_323 ),
    inference(avatar_split_clause,[],[f3259,f3119,f2144,f1118,f12171]) ).

fof(f12171,plain,
    ( spl0_674
  <=> ! [X0,X1] : c_HOL_Ominus__class_Ominus(X1,X0,tc_Int_Oint) = c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X0,tc_Int_Oint),c_HOL_Ouminus__class_Ouminus(X1,tc_Int_Oint),tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_674])]) ).

fof(f1118,plain,
    ( spl0_55
  <=> class_OrderedGroup_Oab__group__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).

fof(f3259,plain,
    ( ! [X0,X1] : c_HOL_Ominus__class_Ominus(X1,X0,tc_Int_Oint) = c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X0,tc_Int_Oint),c_HOL_Ouminus__class_Ouminus(X1,tc_Int_Oint),tc_Int_Oint)
    | ~ spl0_55
    | ~ spl0_231
    | ~ spl0_323 ),
    inference(forward_demodulation,[],[f3257,f2236]) ).

fof(f2236,plain,
    ( ! [X0,X1] : c_HOL_Ominus__class_Ominus(X0,X1,tc_Int_Oint) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X1,X0,tc_Int_Oint),tc_Int_Oint)
    | ~ spl0_55
    | ~ spl0_231 ),
    inference(resolution,[],[f2145,f1120]) ).

fof(f1120,plain,
    ( class_OrderedGroup_Oab__group__add(tc_Int_Oint)
    | ~ spl0_55 ),
    inference(avatar_component_clause,[],[f1118]) ).

fof(f3257,plain,
    ( ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X0,tc_Int_Oint),c_HOL_Ouminus__class_Ouminus(X1,tc_Int_Oint),tc_Int_Oint) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X0,X1,tc_Int_Oint),tc_Int_Oint)
    | ~ spl0_55
    | ~ spl0_323 ),
    inference(resolution,[],[f3120,f1120]) ).

fof(f12169,plain,
    ( spl0_673
    | ~ spl0_77
    | ~ spl0_300 ),
    inference(avatar_split_clause,[],[f2955,f2838,f1228,f12167]) ).

fof(f12167,plain,
    ( spl0_673
  <=> ! [X0,X1] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_673])]) ).

fof(f1228,plain,
    ( spl0_77
  <=> class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).

fof(f2838,plain,
    ( spl0_300
  <=> ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).

fof(f2955,plain,
    ( ! [X0,X1] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X0)
    | ~ spl0_77
    | ~ spl0_300 ),
    inference(resolution,[],[f2839,f1230]) ).

fof(f1230,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
    | ~ spl0_77 ),
    inference(avatar_component_clause,[],[f1228]) ).

fof(f2839,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1) )
    | ~ spl0_300 ),
    inference(avatar_component_clause,[],[f2838]) ).

fof(f12165,plain,
    ( spl0_672
    | ~ spl0_43
    | ~ spl0_300 ),
    inference(avatar_split_clause,[],[f2954,f2838,f1058,f12163]) ).

fof(f12163,plain,
    ( spl0_672
  <=> ! [X0,X1] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),X0),X1) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),X1),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_672])]) ).

fof(f1058,plain,
    ( spl0_43
  <=> class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).

fof(f2954,plain,
    ( ! [X0,X1] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),X0),X1) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),X1),X0)
    | ~ spl0_43
    | ~ spl0_300 ),
    inference(resolution,[],[f2839,f1060]) ).

fof(f1060,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint)
    | ~ spl0_43 ),
    inference(avatar_component_clause,[],[f1058]) ).

fof(f12161,plain,
    ( spl0_671
    | ~ spl0_549
    | ~ spl0_649 ),
    inference(avatar_split_clause,[],[f11142,f11134,f6132,f12158]) ).

fof(f12158,plain,
    ( spl0_671
  <=> c_Parity_Oeven__odd__class_Oeven(hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_671])]) ).

fof(f6132,plain,
    ( spl0_549
  <=> ! [X0] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_549])]) ).

fof(f11134,plain,
    ( spl0_649
  <=> ! [X0] : c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_649])]) ).

fof(f11142,plain,
    ( c_Parity_Oeven__odd__class_Oeven(hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
    | ~ spl0_549
    | ~ spl0_649 ),
    inference(superposition,[],[f11135,f6133]) ).

fof(f6133,plain,
    ( ! [X0] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X0) = X0
    | ~ spl0_549 ),
    inference(avatar_component_clause,[],[f6132]) ).

fof(f11135,plain,
    ( ! [X0] : c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),tc_nat)
    | ~ spl0_649 ),
    inference(avatar_component_clause,[],[f11134]) ).

fof(f12156,plain,
    ( spl0_670
    | ~ spl0_77
    | ~ spl0_94
    | ~ spl0_290
    | ~ spl0_297 ),
    inference(avatar_split_clause,[],[f2941,f2825,f2797,f1313,f1228,f12154]) ).

fof(f12154,plain,
    ( spl0_670
  <=> ! [X0,X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),X0),X1) = c_HOL_Ominus__class_Ominus(X1,c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_670])]) ).

fof(f1313,plain,
    ( spl0_94
  <=> class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).

fof(f2797,plain,
    ( spl0_290
  <=> ! [X2,X0,X1] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2) = c_HOL_Ominus__class_Ominus(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).

fof(f2825,plain,
    ( spl0_297
  <=> ! [X4,X0,X9] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X4),X9) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X9),X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).

fof(f2941,plain,
    ( ! [X0,X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),X0),X1) = c_HOL_Ominus__class_Ominus(X1,c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
    | ~ spl0_77
    | ~ spl0_94
    | ~ spl0_290
    | ~ spl0_297 ),
    inference(forward_demodulation,[],[f2939,f2897]) ).

fof(f2897,plain,
    ( ! [X0,X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),X0),X1) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
    | ~ spl0_94
    | ~ spl0_290 ),
    inference(resolution,[],[f2798,f1315]) ).

fof(f1315,plain,
    ( class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex)
    | ~ spl0_94 ),
    inference(avatar_component_clause,[],[f1313]) ).

fof(f2798,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2) = c_HOL_Ominus__class_Ominus(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) )
    | ~ spl0_290 ),
    inference(avatar_component_clause,[],[f2797]) ).

fof(f2939,plain,
    ( ! [X0,X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),X0),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),X1),X0)
    | ~ spl0_77
    | ~ spl0_297 ),
    inference(resolution,[],[f2826,f1230]) ).

fof(f2826,plain,
    ( ! [X0,X9,X4] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X4),X9) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X9),X4) )
    | ~ spl0_297 ),
    inference(avatar_component_clause,[],[f2825]) ).

fof(f12152,plain,
    ( spl0_669
    | ~ spl0_43
    | ~ spl0_60
    | ~ spl0_290
    | ~ spl0_297 ),
    inference(avatar_split_clause,[],[f2940,f2825,f2797,f1143,f1058,f12150]) ).

fof(f12150,plain,
    ( spl0_669
  <=> ! [X0,X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),X0),X1) = c_HOL_Ominus__class_Ominus(X1,c_HOL_Ouminus__class_Ouminus(X0,tc_Int_Oint),tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_669])]) ).

fof(f1143,plain,
    ( spl0_60
  <=> class_OrderedGroup_Ogroup__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).

fof(f2940,plain,
    ( ! [X0,X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),X0),X1) = c_HOL_Ominus__class_Ominus(X1,c_HOL_Ouminus__class_Ouminus(X0,tc_Int_Oint),tc_Int_Oint)
    | ~ spl0_43
    | ~ spl0_60
    | ~ spl0_290
    | ~ spl0_297 ),
    inference(forward_demodulation,[],[f2938,f2896]) ).

fof(f2896,plain,
    ( ! [X0,X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),X0),X1) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_Int_Oint),tc_Int_Oint)
    | ~ spl0_60
    | ~ spl0_290 ),
    inference(resolution,[],[f2798,f1145]) ).

fof(f1145,plain,
    ( class_OrderedGroup_Ogroup__add(tc_Int_Oint)
    | ~ spl0_60 ),
    inference(avatar_component_clause,[],[f1143]) ).

fof(f2938,plain,
    ( ! [X0,X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),X0),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),X1),X0)
    | ~ spl0_43
    | ~ spl0_297 ),
    inference(resolution,[],[f2826,f1060]) ).

fof(f12148,plain,
    ( spl0_668
    | ~ spl0_10
    | ~ spl0_297 ),
    inference(avatar_split_clause,[],[f2937,f2825,f893,f12146]) ).

fof(f12146,plain,
    ( spl0_668
  <=> ! [X0,X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_668])]) ).

fof(f893,plain,
    ( spl0_10
  <=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

fof(f2937,plain,
    ( ! [X0,X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0)
    | ~ spl0_10
    | ~ spl0_297 ),
    inference(resolution,[],[f2826,f895]) ).

fof(f895,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
    | ~ spl0_10 ),
    inference(avatar_component_clause,[],[f893]) ).

fof(f12144,plain,
    ( spl0_667
    | ~ spl0_97
    | ~ spl0_295 ),
    inference(avatar_split_clause,[],[f2935,f2817,f1328,f12142]) ).

fof(f12142,plain,
    ( spl0_667
  <=> ! [X0,X1] : c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_667])]) ).

fof(f1328,plain,
    ( spl0_97
  <=> class_Ring__and__Field_Ofield(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).

fof(f2817,plain,
    ( spl0_295
  <=> ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).

fof(f2935,plain,
    ( ! [X0,X1] : c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex)
    | ~ spl0_97
    | ~ spl0_295 ),
    inference(resolution,[],[f2818,f1330]) ).

fof(f1330,plain,
    ( class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
    | ~ spl0_97 ),
    inference(avatar_component_clause,[],[f1328]) ).

fof(f2818,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) )
    | ~ spl0_295 ),
    inference(avatar_component_clause,[],[f2817]) ).

fof(f12140,plain,
    ( spl0_666
    | ~ spl0_94
    | ~ spl0_290 ),
    inference(avatar_split_clause,[],[f2897,f2797,f1313,f12138]) ).

fof(f12136,plain,
    ( spl0_665
    | ~ spl0_60
    | ~ spl0_290 ),
    inference(avatar_split_clause,[],[f2896,f2797,f1143,f12134]) ).

fof(f12134,plain,
    ( spl0_665
  <=> ! [X0,X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),X0),X1) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_Int_Oint),tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_665])]) ).

fof(f12132,plain,
    ( spl0_664
    | ~ spl0_94
    | ~ spl0_286 ),
    inference(avatar_split_clause,[],[f2890,f2781,f1313,f12130]) ).

fof(f12130,plain,
    ( spl0_664
  <=> ! [X0,X1] : c_HOL_Ominus__class_Ominus(X0,X1,tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),X0),c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_664])]) ).

fof(f2781,plain,
    ( spl0_286
  <=> ! [X2,X0,X1] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ominus__class_Ominus(X1,X2,X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),c_HOL_Ouminus__class_Ouminus(X2,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).

fof(f2890,plain,
    ( ! [X0,X1] : c_HOL_Ominus__class_Ominus(X0,X1,tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),X0),c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex))
    | ~ spl0_94
    | ~ spl0_286 ),
    inference(resolution,[],[f2782,f1315]) ).

fof(f2782,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ominus__class_Ominus(X1,X2,X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),c_HOL_Ouminus__class_Ouminus(X2,X0)) )
    | ~ spl0_286 ),
    inference(avatar_component_clause,[],[f2781]) ).

fof(f12128,plain,
    ( spl0_663
    | ~ spl0_60
    | ~ spl0_286 ),
    inference(avatar_split_clause,[],[f2889,f2781,f1143,f12126]) ).

fof(f12126,plain,
    ( spl0_663
  <=> ! [X0,X1] : c_HOL_Ominus__class_Ominus(X0,X1,tc_Int_Oint) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),X0),c_HOL_Ouminus__class_Ouminus(X1,tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_663])]) ).

fof(f2889,plain,
    ( ! [X0,X1] : c_HOL_Ominus__class_Ominus(X0,X1,tc_Int_Oint) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),X0),c_HOL_Ouminus__class_Ouminus(X1,tc_Int_Oint))
    | ~ spl0_60
    | ~ spl0_286 ),
    inference(resolution,[],[f2782,f1145]) ).

fof(f12124,plain,
    ( spl0_662
    | ~ spl0_135
    | ~ spl0_284 ),
    inference(avatar_split_clause,[],[f2870,f2773,f1500,f12122]) ).

fof(f12122,plain,
    ( spl0_662
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_662])]) ).

fof(f1500,plain,
    ( spl0_135
  <=> ! [X3] :
        ( c_Parity_Oeven__odd__class_Oeven(X3,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).

fof(f2773,plain,
    ( spl0_284
  <=> ! [X3,X19] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X19,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X19),X3),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).

fof(f2870,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1),tc_nat) )
    | ~ spl0_135
    | ~ spl0_284 ),
    inference(resolution,[],[f2774,f1501]) ).

fof(f1501,plain,
    ( ! [X3] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(X3,tc_nat) )
    | ~ spl0_135 ),
    inference(avatar_component_clause,[],[f1500]) ).

fof(f2774,plain,
    ( ! [X3,X19] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X19),X3),tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X19,tc_nat) )
    | ~ spl0_284 ),
    inference(avatar_component_clause,[],[f2773]) ).

fof(f12120,plain,
    ( spl0_661
    | ~ spl0_135
    | ~ spl0_283 ),
    inference(avatar_split_clause,[],[f2858,f2769,f1500,f12118]) ).

fof(f12118,plain,
    ( spl0_661
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X0),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_661])]) ).

fof(f2769,plain,
    ( spl0_283
  <=> ! [X19,X3] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X19),X3),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).

fof(f2858,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X0),tc_nat) )
    | ~ spl0_135
    | ~ spl0_283 ),
    inference(resolution,[],[f2770,f1501]) ).

fof(f2770,plain,
    ( ! [X3,X19] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X19),X3),tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) )
    | ~ spl0_283 ),
    inference(avatar_component_clause,[],[f2769]) ).

fof(f12116,plain,
    ( ~ spl0_658
    | ~ spl0_659
    | spl0_660
    | ~ spl0_116
    | ~ spl0_276 ),
    inference(avatar_split_clause,[],[f2747,f2508,f1418,f12114,f12110,f12106]) ).

fof(f12106,plain,
    ( spl0_658
  <=> class_Int_Oring__char__0(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_658])]) ).

fof(f12110,plain,
    ( spl0_659
  <=> class_Int_Onumber__ring(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_659])]) ).

fof(f12114,plain,
    ( spl0_660
  <=> ! [X0] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) != c_Int_Onumber__class_Onumber__of(X0,tc_nat)
        | c_Int_OMin = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_660])]) ).

fof(f1418,plain,
    ( spl0_116
  <=> c_HOL_Ozero__class_Ozero(tc_nat) = c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).

fof(f2508,plain,
    ( spl0_276
  <=> ! [X9,X0,X4] :
        ( ~ class_Int_Oring__char__0(X0)
        | ~ class_Int_Onumber__ring(X0)
        | X4 = X9
        | c_Int_Onumber__class_Onumber__of(X4,X0) != c_Int_Onumber__class_Onumber__of(X9,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).

fof(f2747,plain,
    ( ! [X0] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) != c_Int_Onumber__class_Onumber__of(X0,tc_nat)
        | ~ class_Int_Onumber__ring(tc_nat)
        | c_Int_OMin = X0
        | ~ class_Int_Oring__char__0(tc_nat) )
    | ~ spl0_116
    | ~ spl0_276 ),
    inference(superposition,[],[f2509,f1420]) ).

fof(f1420,plain,
    ( c_HOL_Ozero__class_Ozero(tc_nat) = c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)
    | ~ spl0_116 ),
    inference(avatar_component_clause,[],[f1418]) ).

fof(f2509,plain,
    ( ! [X0,X9,X4] :
        ( c_Int_Onumber__class_Onumber__of(X4,X0) != c_Int_Onumber__class_Onumber__of(X9,X0)
        | ~ class_Int_Onumber__ring(X0)
        | X4 = X9
        | ~ class_Int_Oring__char__0(X0) )
    | ~ spl0_276 ),
    inference(avatar_component_clause,[],[f2508]) ).

fof(f12073,plain,
    ( ~ spl0_25
    | spl0_657
    | ~ spl0_127
    | ~ spl0_274 ),
    inference(avatar_split_clause,[],[f2711,f2500,f1465,f12071,f968]) ).

fof(f968,plain,
    ( spl0_25
  <=> class_Orderings_Oorder(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).

fof(f12071,plain,
    ( spl0_657
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(hAPP(c_Suc,X0),X1,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_657])]) ).

fof(f1465,plain,
    ( spl0_127
  <=> ! [X3] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,X3),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).

fof(f2500,plain,
    ( spl0_274
  <=> ! [X18,X4,X0,X9] :
        ( ~ class_Orderings_Oorder(X0)
        | ~ c_HOL_Oord__class_Oless(X9,X4,X0)
        | ~ c_HOL_Oord__class_Oless(X18,X9,X0)
        | c_HOL_Oord__class_Oless(X18,X4,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).

fof(f2711,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(hAPP(c_Suc,X0),X1,tc_nat)
        | ~ class_Orderings_Oorder(tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) )
    | ~ spl0_127
    | ~ spl0_274 ),
    inference(resolution,[],[f2501,f1466]) ).

fof(f1466,plain,
    ( ! [X3] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,X3),tc_nat)
    | ~ spl0_127 ),
    inference(avatar_component_clause,[],[f1465]) ).

fof(f2501,plain,
    ( ! [X0,X18,X9,X4] :
        ( ~ c_HOL_Oord__class_Oless(X18,X9,X0)
        | ~ c_HOL_Oord__class_Oless(X9,X4,X0)
        | ~ class_Orderings_Oorder(X0)
        | c_HOL_Oord__class_Oless(X18,X4,X0) )
    | ~ spl0_274 ),
    inference(avatar_component_clause,[],[f2500]) ).

fof(f12069,plain,
    ( spl0_656
    | ~ spl0_124
    | ~ spl0_147 ),
    inference(avatar_split_clause,[],[f1604,f1563,f1453,f12067]) ).

fof(f12067,plain,
    ( spl0_656
  <=> ! [X2,X0,X1] :
        ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_fun(X1,X2)),tc_fun(X1,X2)) = X0
        | ~ class_Lattices_Oboolean__algebra(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_656])]) ).

fof(f1453,plain,
    ( spl0_124
  <=> ! [X46,X47] :
        ( ~ class_Lattices_Oboolean__algebra(X47)
        | class_Lattices_Oboolean__algebra(tc_fun(X46,X47)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).

fof(f1563,plain,
    ( spl0_147
  <=> ! [X4,X0] :
        ( ~ class_Lattices_Oboolean__algebra(X0)
        | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X4,X0),X0) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).

fof(f1604,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_fun(X1,X2)),tc_fun(X1,X2)) = X0
        | ~ class_Lattices_Oboolean__algebra(X2) )
    | ~ spl0_124
    | ~ spl0_147 ),
    inference(resolution,[],[f1564,f1454]) ).

fof(f1454,plain,
    ( ! [X46,X47] :
        ( class_Lattices_Oboolean__algebra(tc_fun(X46,X47))
        | ~ class_Lattices_Oboolean__algebra(X47) )
    | ~ spl0_124 ),
    inference(avatar_component_clause,[],[f1453]) ).

fof(f1564,plain,
    ( ! [X0,X4] :
        ( ~ class_Lattices_Oboolean__algebra(X0)
        | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X4,X0),X0) = X4 )
    | ~ spl0_147 ),
    inference(avatar_component_clause,[],[f1563]) ).

fof(f11180,plain,
    ( spl0_655
    | ~ spl0_101
    | ~ spl0_270 ),
    inference(avatar_split_clause,[],[f2662,f2484,f1348,f11178]) ).

fof(f11178,plain,
    ( spl0_655
  <=> ! [X0] : c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_655])]) ).

fof(f1348,plain,
    ( spl0_101
  <=> class_Int_Onumber__ring(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).

fof(f2484,plain,
    ( spl0_270
  <=> ! [X18,X0] :
        ( ~ class_Int_Onumber__ring(X0)
        | c_HOL_Ouminus__class_Ouminus(X18,X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X18),c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).

fof(f2662,plain,
    ( ! [X0] : c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_Complex_Ocomplex))
    | ~ spl0_101
    | ~ spl0_270 ),
    inference(resolution,[],[f2485,f1350]) ).

fof(f1350,plain,
    ( class_Int_Onumber__ring(tc_Complex_Ocomplex)
    | ~ spl0_101 ),
    inference(avatar_component_clause,[],[f1348]) ).

fof(f2485,plain,
    ( ! [X0,X18] :
        ( ~ class_Int_Onumber__ring(X0)
        | c_HOL_Ouminus__class_Ouminus(X18,X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X18),c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0)) )
    | ~ spl0_270 ),
    inference(avatar_component_clause,[],[f2484]) ).

fof(f11176,plain,
    ( spl0_654
    | ~ spl0_68
    | ~ spl0_270 ),
    inference(avatar_split_clause,[],[f2661,f2484,f1183,f11174]) ).

fof(f11174,plain,
    ( spl0_654
  <=> ! [X0] : c_HOL_Ouminus__class_Ouminus(X0,tc_Int_Oint) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),X0),c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_654])]) ).

fof(f1183,plain,
    ( spl0_68
  <=> class_Int_Onumber__ring(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).

fof(f2661,plain,
    ( ! [X0] : c_HOL_Ouminus__class_Ouminus(X0,tc_Int_Oint) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),X0),c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_Int_Oint))
    | ~ spl0_68
    | ~ spl0_270 ),
    inference(resolution,[],[f2485,f1185]) ).

fof(f1185,plain,
    ( class_Int_Onumber__ring(tc_Int_Oint)
    | ~ spl0_68 ),
    inference(avatar_component_clause,[],[f1183]) ).

fof(f11172,plain,
    ( spl0_653
    | ~ spl0_101
    | ~ spl0_269 ),
    inference(avatar_split_clause,[],[f2660,f2478,f1348,f11170]) ).

fof(f11170,plain,
    ( spl0_653
  <=> ! [X0] : c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_Complex_Ocomplex)),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_653])]) ).

fof(f2478,plain,
    ( spl0_269
  <=> ! [X18,X0] :
        ( ~ class_Int_Onumber__ring(X0)
        | c_HOL_Ouminus__class_Ouminus(X18,X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0)),X18) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).

fof(f2660,plain,
    ( ! [X0] : c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_Complex_Ocomplex)),X0)
    | ~ spl0_101
    | ~ spl0_269 ),
    inference(resolution,[],[f2479,f1350]) ).

fof(f2479,plain,
    ( ! [X0,X18] :
        ( ~ class_Int_Onumber__ring(X0)
        | c_HOL_Ouminus__class_Ouminus(X18,X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0)),X18) )
    | ~ spl0_269 ),
    inference(avatar_component_clause,[],[f2478]) ).

fof(f11168,plain,
    ( spl0_652
    | ~ spl0_68
    | ~ spl0_269 ),
    inference(avatar_split_clause,[],[f2659,f2478,f1183,f11166]) ).

fof(f11166,plain,
    ( spl0_652
  <=> ! [X0] : c_HOL_Ouminus__class_Ouminus(X0,tc_Int_Oint) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_Int_Oint)),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_652])]) ).

fof(f2659,plain,
    ( ! [X0] : c_HOL_Ouminus__class_Ouminus(X0,tc_Int_Oint) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_Int_Oint)),X0)
    | ~ spl0_68
    | ~ spl0_269 ),
    inference(resolution,[],[f2479,f1185]) ).

fof(f11156,plain,
    ( spl0_651
    | ~ spl0_220
    | ~ spl0_634
    | ~ spl0_650 ),
    inference(avatar_split_clause,[],[f11151,f11147,f10041,f2013,f11153]) ).

fof(f11153,plain,
    ( spl0_651
  <=> c_HOL_Oord__class_Oless(hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_651])]) ).

fof(f2013,plain,
    ( spl0_220
  <=> c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat) = hAPP(c_Suc,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).

fof(f10041,plain,
    ( spl0_634
  <=> c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat) = c_HOL_Oone__class_Oone(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_634])]) ).

fof(f11147,plain,
    ( spl0_650
  <=> c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_650])]) ).

fof(f11151,plain,
    ( c_HOL_Oord__class_Oless(hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)
    | ~ spl0_220
    | ~ spl0_634
    | ~ spl0_650 ),
    inference(forward_demodulation,[],[f11149,f11022]) ).

fof(f11022,plain,
    ( c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat) = hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))
    | ~ spl0_220
    | ~ spl0_634 ),
    inference(superposition,[],[f2015,f10043]) ).

fof(f10043,plain,
    ( c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat) = c_HOL_Oone__class_Oone(tc_nat)
    | ~ spl0_634 ),
    inference(avatar_component_clause,[],[f10041]) ).

fof(f2015,plain,
    ( c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat) = hAPP(c_Suc,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat))
    | ~ spl0_220 ),
    inference(avatar_component_clause,[],[f2013]) ).

fof(f11149,plain,
    ( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)
    | ~ spl0_650 ),
    inference(avatar_component_clause,[],[f11147]) ).

fof(f11150,plain,
    ( spl0_650
    | ~ spl0_123
    | ~ spl0_247 ),
    inference(avatar_split_clause,[],[f2371,f2210,f1449,f11147]) ).

fof(f1449,plain,
    ( spl0_123
  <=> ! [X4] : c_HOL_Oord__class_Oless(X4,hAPP(c_Suc,X4),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).

fof(f2210,plain,
    ( spl0_247
  <=> c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat) = hAPP(c_Suc,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).

fof(f2371,plain,
    ( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)
    | ~ spl0_123
    | ~ spl0_247 ),
    inference(superposition,[],[f1450,f2212]) ).

fof(f2212,plain,
    ( c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat) = hAPP(c_Suc,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))
    | ~ spl0_247 ),
    inference(avatar_component_clause,[],[f2210]) ).

fof(f1450,plain,
    ( ! [X4] : c_HOL_Oord__class_Oless(X4,hAPP(c_Suc,X4),tc_nat)
    | ~ spl0_123 ),
    inference(avatar_component_clause,[],[f1449]) ).

fof(f11136,plain,
    ( spl0_649
    | ~ spl0_220
    | ~ spl0_634
    | ~ spl0_647 ),
    inference(avatar_split_clause,[],[f11127,f11124,f10041,f2013,f11134]) ).

fof(f11124,plain,
    ( spl0_647
  <=> ! [X0] : c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_647])]) ).

fof(f11127,plain,
    ( ! [X0] : c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),tc_nat)
    | ~ spl0_220
    | ~ spl0_634
    | ~ spl0_647 ),
    inference(forward_demodulation,[],[f11125,f11022]) ).

fof(f11125,plain,
    ( ! [X0] : c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat)
    | ~ spl0_647 ),
    inference(avatar_component_clause,[],[f11124]) ).

fof(f11132,plain,
    ( ~ spl0_648
    | spl0_223
    | ~ spl0_634 ),
    inference(avatar_split_clause,[],[f11023,f10041,f2069,f11129]) ).

fof(f11129,plain,
    ( spl0_648
  <=> c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Oone__class_Oone(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_648])]) ).

fof(f2069,plain,
    ( spl0_223
  <=> c_HOL_Ozero__class_Ozero(tc_nat) = c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).

fof(f11023,plain,
    ( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
    | spl0_223
    | ~ spl0_634 ),
    inference(superposition,[],[f2071,f10043]) ).

fof(f2071,plain,
    ( c_HOL_Ozero__class_Ozero(tc_nat) != c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat)
    | spl0_223 ),
    inference(avatar_component_clause,[],[f2069]) ).

fof(f11126,plain,
    ( spl0_647
    | ~ spl0_210
    | ~ spl0_246 ),
    inference(avatar_split_clause,[],[f2360,f2206,f1973,f11124]) ).

fof(f1973,plain,
    ( spl0_210
  <=> ! [X4] : c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X4),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).

fof(f2206,plain,
    ( spl0_246
  <=> ! [X3,X19] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X19),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X3),X19) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).

fof(f2360,plain,
    ( ! [X0] : c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat)
    | ~ spl0_210
    | ~ spl0_246 ),
    inference(superposition,[],[f1974,f2207]) ).

fof(f2207,plain,
    ( ! [X3,X19] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X19),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X3),X19)
    | ~ spl0_246 ),
    inference(avatar_component_clause,[],[f2206]) ).

fof(f1974,plain,
    ( ! [X4] : c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X4),tc_nat)
    | ~ spl0_210 ),
    inference(avatar_component_clause,[],[f1973]) ).

fof(f11122,plain,
    ( spl0_646
    | ~ spl0_165
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1735,f1668,f1664,f11120]) ).

fof(f11120,plain,
    ( spl0_646
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(hAPP(c_Suc,X0),X1,tc_nat)
        | c_HOL_Oord__class_Oless(X0,hAPP(c_Suc,X1),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_646])]) ).

fof(f1664,plain,
    ( spl0_165
  <=> ! [X19,X3] :
        ( c_HOL_Oord__class_Oless(X19,X3,tc_nat)
        | ~ c_HOL_Oord__class_Oless(hAPP(c_Suc,X19),X3,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).

fof(f1668,plain,
    ( spl0_166
  <=> ! [X19,X3] :
        ( ~ c_HOL_Oord__class_Oless(X19,X3,tc_nat)
        | c_HOL_Oord__class_Oless(X19,hAPP(c_Suc,X3),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).

fof(f1735,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(hAPP(c_Suc,X0),X1,tc_nat)
        | c_HOL_Oord__class_Oless(X0,hAPP(c_Suc,X1),tc_nat) )
    | ~ spl0_165
    | ~ spl0_166 ),
    inference(resolution,[],[f1669,f1665]) ).

fof(f1665,plain,
    ( ! [X3,X19] :
        ( ~ c_HOL_Oord__class_Oless(hAPP(c_Suc,X19),X3,tc_nat)
        | c_HOL_Oord__class_Oless(X19,X3,tc_nat) )
    | ~ spl0_165 ),
    inference(avatar_component_clause,[],[f1664]) ).

fof(f1669,plain,
    ( ! [X3,X19] :
        ( c_HOL_Oord__class_Oless(X19,hAPP(c_Suc,X3),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X19,X3,tc_nat) )
    | ~ spl0_166 ),
    inference(avatar_component_clause,[],[f1668]) ).

fof(f11117,plain,
    ( spl0_645
    | ~ spl0_148
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1726,f1664,f1567,f11115]) ).

fof(f11115,plain,
    ( spl0_645
  <=> ! [X0] :
        ( ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat),X0,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_645])]) ).

fof(f1567,plain,
    ( spl0_148
  <=> hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).

fof(f1726,plain,
    ( ! [X0] :
        ( ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat),X0,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) )
    | ~ spl0_148
    | ~ spl0_165 ),
    inference(superposition,[],[f1665,f1569]) ).

fof(f1569,plain,
    ( hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat)
    | ~ spl0_148 ),
    inference(avatar_component_clause,[],[f1567]) ).

fof(f11113,plain,
    ( spl0_644
    | ~ spl0_160
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1725,f1664,f1644,f11111]) ).

fof(f11111,plain,
    ( spl0_644
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,hAPP(c_Suc,X1),tc_nat)
        | c_HOL_Oord__class_Oless(X1,hAPP(c_Suc,X0),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_644])]) ).

fof(f1644,plain,
    ( spl0_160
  <=> ! [X19,X3] :
        ( c_HOL_Oord__class_Oless(X19,X3,tc_nat)
        | c_HOL_Oord__class_Oless(X3,hAPP(c_Suc,X19),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).

fof(f1725,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,hAPP(c_Suc,X1),tc_nat)
        | c_HOL_Oord__class_Oless(X1,hAPP(c_Suc,X0),tc_nat) )
    | ~ spl0_160
    | ~ spl0_165 ),
    inference(resolution,[],[f1665,f1645]) ).

fof(f1645,plain,
    ( ! [X3,X19] :
        ( c_HOL_Oord__class_Oless(X3,hAPP(c_Suc,X19),tc_nat)
        | c_HOL_Oord__class_Oless(X19,X3,tc_nat) )
    | ~ spl0_160 ),
    inference(avatar_component_clause,[],[f1644]) ).

fof(f11104,plain,
    ( spl0_643
    | ~ spl0_634
    | ~ spl0_642 ),
    inference(avatar_split_clause,[],[f11100,f11097,f10041,f11102]) ).

fof(f11102,plain,
    ( spl0_643
  <=> ! [X0] :
        ( hAPP(c_Suc,X0) != c_HOL_Oone__class_Oone(tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_643])]) ).

fof(f11097,plain,
    ( spl0_642
  <=> ! [X0] :
        ( c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat) != hAPP(c_Suc,X0)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_642])]) ).

fof(f11100,plain,
    ( ! [X0] :
        ( hAPP(c_Suc,X0) != c_HOL_Oone__class_Oone(tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
    | ~ spl0_634
    | ~ spl0_642 ),
    inference(forward_demodulation,[],[f11098,f10043]) ).

fof(f11098,plain,
    ( ! [X0] :
        ( c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat) != hAPP(c_Suc,X0)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
    | ~ spl0_642 ),
    inference(avatar_component_clause,[],[f11097]) ).

fof(f11099,plain,
    ( spl0_642
    | ~ spl0_148
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f1695,f1648,f1567,f11097]) ).

fof(f1648,plain,
    ( spl0_161
  <=> ! [X37,X40] :
        ( X37 = X40
        | hAPP(c_Suc,X37) != hAPP(c_Suc,X40) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).

fof(f1695,plain,
    ( ! [X0] :
        ( c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat) != hAPP(c_Suc,X0)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
    | ~ spl0_148
    | ~ spl0_161 ),
    inference(superposition,[],[f1649,f1569]) ).

fof(f1649,plain,
    ( ! [X40,X37] :
        ( hAPP(c_Suc,X37) != hAPP(c_Suc,X40)
        | X37 = X40 )
    | ~ spl0_161 ),
    inference(avatar_component_clause,[],[f1648]) ).

fof(f11041,plain,
    ( spl0_641
    | ~ spl0_634
    | ~ spl0_640 ),
    inference(avatar_split_clause,[],[f11037,f11034,f10041,f11039]) ).

fof(f11039,plain,
    ( spl0_641
  <=> ! [X0] :
        ( c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_641])]) ).

fof(f11034,plain,
    ( spl0_640
  <=> ! [X0] :
        ( c_HOL_Oord__class_Oless(X0,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_640])]) ).

fof(f11037,plain,
    ( ! [X0] :
        ( c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) )
    | ~ spl0_634
    | ~ spl0_640 ),
    inference(forward_demodulation,[],[f11035,f10043]) ).

fof(f11035,plain,
    ( ! [X0] :
        ( c_HOL_Oord__class_Oless(X0,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) )
    | ~ spl0_640 ),
    inference(avatar_component_clause,[],[f11034]) ).

fof(f11036,plain,
    ( spl0_640
    | ~ spl0_148
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f1694,f1644,f1567,f11034]) ).

fof(f1694,plain,
    ( ! [X0] :
        ( c_HOL_Oord__class_Oless(X0,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) )
    | ~ spl0_148
    | ~ spl0_160 ),
    inference(superposition,[],[f1645,f1569]) ).

fof(f10976,plain,
    ( spl0_639
    | ~ spl0_634
    | ~ spl0_638 ),
    inference(avatar_split_clause,[],[f10972,f10969,f10041,f10974]) ).

fof(f10974,plain,
    ( spl0_639
  <=> ! [X0] :
        ( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_639])]) ).

fof(f10969,plain,
    ( spl0_638
  <=> ! [X0] :
        ( ~ c_HOL_Oord__class_Oless(X0,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_638])]) ).

fof(f10972,plain,
    ( ! [X0] :
        ( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) )
    | ~ spl0_634
    | ~ spl0_638 ),
    inference(forward_demodulation,[],[f10970,f10043]) ).

fof(f10970,plain,
    ( ! [X0] :
        ( ~ c_HOL_Oord__class_Oless(X0,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) )
    | ~ spl0_638 ),
    inference(avatar_component_clause,[],[f10969]) ).

fof(f10971,plain,
    ( spl0_638
    | ~ spl0_148
    | ~ spl0_159 ),
    inference(avatar_split_clause,[],[f1688,f1640,f1567,f10969]) ).

fof(f1640,plain,
    ( spl0_159
  <=> ! [X19,X3] :
        ( ~ c_HOL_Oord__class_Oless(X19,X3,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X3,hAPP(c_Suc,X19),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).

fof(f1688,plain,
    ( ! [X0] :
        ( ~ c_HOL_Oord__class_Oless(X0,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) )
    | ~ spl0_148
    | ~ spl0_159 ),
    inference(superposition,[],[f1641,f1569]) ).

fof(f1641,plain,
    ( ! [X3,X19] :
        ( ~ c_HOL_Oord__class_Oless(X3,hAPP(c_Suc,X19),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X19,X3,tc_nat) )
    | ~ spl0_159 ),
    inference(avatar_component_clause,[],[f1640]) ).

fof(f10691,plain,
    ( spl0_637
    | ~ spl0_94
    | ~ spl0_290
    | ~ spl0_631 ),
    inference(avatar_split_clause,[],[f10030,f10027,f2797,f1313,f10689]) ).

fof(f10689,plain,
    ( spl0_637
  <=> ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_637])]) ).

fof(f10027,plain,
    ( spl0_631
  <=> ! [X0,X1] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),X0),X1),X1,tc_Complex_Ocomplex) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_631])]) ).

fof(f10030,plain,
    ( ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) = X0
    | ~ spl0_94
    | ~ spl0_290
    | ~ spl0_631 ),
    inference(forward_demodulation,[],[f10028,f2897]) ).

fof(f10028,plain,
    ( ! [X0,X1] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),X0),X1),X1,tc_Complex_Ocomplex) = X0
    | ~ spl0_631 ),
    inference(avatar_component_clause,[],[f10027]) ).

fof(f10687,plain,
    ( spl0_636
    | ~ spl0_60
    | ~ spl0_290
    | ~ spl0_630 ),
    inference(avatar_split_clause,[],[f10025,f10022,f2797,f1143,f10685]) ).

fof(f10685,plain,
    ( spl0_636
  <=> ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_Int_Oint),tc_Int_Oint),X1,tc_Int_Oint) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_636])]) ).

fof(f10022,plain,
    ( spl0_630
  <=> ! [X0,X1] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),X0),X1),X1,tc_Int_Oint) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_630])]) ).

fof(f10025,plain,
    ( ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_Int_Oint),tc_Int_Oint),X1,tc_Int_Oint) = X0
    | ~ spl0_60
    | ~ spl0_290
    | ~ spl0_630 ),
    inference(forward_demodulation,[],[f10023,f2896]) ).

fof(f10023,plain,
    ( ! [X0,X1] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),X0),X1),X1,tc_Int_Oint) = X0
    | ~ spl0_630 ),
    inference(avatar_component_clause,[],[f10022]) ).

fof(f10048,plain,
    ( spl0_635
    | ~ spl0_89
    | ~ spl0_94
    | ~ spl0_231
    | ~ spl0_290
    | ~ spl0_323
    | ~ spl0_329 ),
    inference(avatar_split_clause,[],[f3293,f3143,f3119,f2797,f2144,f1313,f1288,f10046]) ).

fof(f10046,plain,
    ( spl0_635
  <=> ! [X0,X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),X0),c_HOL_Ominus__class_Ominus(X1,X0,tc_Complex_Ocomplex)) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_635])]) ).

fof(f3143,plain,
    ( spl0_329
  <=> ! [X2,X0,X1] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ouminus__class_Ouminus(X1,X0)),X2)) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).

fof(f3293,plain,
    ( ! [X0,X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),X0),c_HOL_Ominus__class_Ominus(X1,X0,tc_Complex_Ocomplex)) = X1
    | ~ spl0_89
    | ~ spl0_94
    | ~ spl0_231
    | ~ spl0_290
    | ~ spl0_323
    | ~ spl0_329 ),
    inference(forward_demodulation,[],[f3292,f3260]) ).

fof(f3292,plain,
    ( ! [X0,X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),X0),c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex)) = X1
    | ~ spl0_94
    | ~ spl0_290
    | ~ spl0_329 ),
    inference(forward_demodulation,[],[f3289,f2897]) ).

fof(f3289,plain,
    ( ! [X0,X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex)),X1)) = X1
    | ~ spl0_94
    | ~ spl0_329 ),
    inference(resolution,[],[f3144,f1315]) ).

fof(f3144,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ouminus__class_Ouminus(X1,X0)),X2)) = X2 )
    | ~ spl0_329 ),
    inference(avatar_component_clause,[],[f3143]) ).

fof(f10044,plain,
    ( spl0_634
    | ~ spl0_219
    | ~ spl0_602 ),
    inference(avatar_split_clause,[],[f8694,f8625,f2009,f10041]) ).

fof(f2009,plain,
    ( spl0_219
  <=> ! [X4] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X4),c_HOL_Ozero__class_Ozero(tc_nat)) = c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).

fof(f8625,plain,
    ( spl0_602
  <=> ! [X0] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X0),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_602])]) ).

fof(f8694,plain,
    ( c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat) = c_HOL_Oone__class_Oone(tc_nat)
    | ~ spl0_219
    | ~ spl0_602 ),
    inference(superposition,[],[f8626,f2010]) ).

fof(f2010,plain,
    ( ! [X4] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X4),c_HOL_Ozero__class_Ozero(tc_nat)) = c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat)
    | ~ spl0_219 ),
    inference(avatar_component_clause,[],[f2009]) ).

fof(f8626,plain,
    ( ! [X0] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X0),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_nat)
    | ~ spl0_602 ),
    inference(avatar_component_clause,[],[f8625]) ).

fof(f10039,plain,
    ( spl0_633
    | ~ spl0_55
    | ~ spl0_60
    | ~ spl0_231
    | ~ spl0_290
    | ~ spl0_323
    | ~ spl0_329 ),
    inference(avatar_split_clause,[],[f3291,f3143,f3119,f2797,f2144,f1143,f1118,f10037]) ).

fof(f10037,plain,
    ( spl0_633
  <=> ! [X0,X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),X0),c_HOL_Ominus__class_Ominus(X1,X0,tc_Int_Oint)) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_633])]) ).

fof(f3291,plain,
    ( ! [X0,X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),X0),c_HOL_Ominus__class_Ominus(X1,X0,tc_Int_Oint)) = X1
    | ~ spl0_55
    | ~ spl0_60
    | ~ spl0_231
    | ~ spl0_290
    | ~ spl0_323
    | ~ spl0_329 ),
    inference(forward_demodulation,[],[f3290,f3259]) ).

fof(f3290,plain,
    ( ! [X0,X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),X0),c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X0,tc_Int_Oint),c_HOL_Ouminus__class_Ouminus(X1,tc_Int_Oint),tc_Int_Oint)) = X1
    | ~ spl0_60
    | ~ spl0_290
    | ~ spl0_329 ),
    inference(forward_demodulation,[],[f3288,f2896]) ).

fof(f3288,plain,
    ( ! [X0,X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_HOL_Ouminus__class_Ouminus(X0,tc_Int_Oint)),X1)) = X1
    | ~ spl0_60
    | ~ spl0_329 ),
    inference(resolution,[],[f3144,f1145]) ).

fof(f10035,plain,
    ( ~ spl0_632
    | ~ spl0_113
    | ~ spl0_247 ),
    inference(avatar_split_clause,[],[f2369,f2210,f1405,f10032]) ).

fof(f10032,plain,
    ( spl0_632
  <=> c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat) = c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_632])]) ).

fof(f1405,plain,
    ( spl0_113
  <=> ! [X3] : hAPP(c_Suc,X3) != X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).

fof(f2369,plain,
    ( c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat) != c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)
    | ~ spl0_113
    | ~ spl0_247 ),
    inference(superposition,[],[f1406,f2212]) ).

fof(f1406,plain,
    ( ! [X3] : hAPP(c_Suc,X3) != X3
    | ~ spl0_113 ),
    inference(avatar_component_clause,[],[f1405]) ).

fof(f10029,plain,
    ( spl0_631
    | ~ spl0_94
    | ~ spl0_235 ),
    inference(avatar_split_clause,[],[f2244,f2160,f1313,f10027]) ).

fof(f2160,plain,
    ( spl0_235
  <=> ! [X2,X0,X1] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2),X2,X0) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).

fof(f2244,plain,
    ( ! [X0,X1] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),X0),X1),X1,tc_Complex_Ocomplex) = X0
    | ~ spl0_94
    | ~ spl0_235 ),
    inference(resolution,[],[f2161,f1315]) ).

fof(f2161,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2),X2,X0) = X1 )
    | ~ spl0_235 ),
    inference(avatar_component_clause,[],[f2160]) ).

fof(f10024,plain,
    ( spl0_630
    | ~ spl0_60
    | ~ spl0_235 ),
    inference(avatar_split_clause,[],[f2243,f2160,f1143,f10022]) ).

fof(f2243,plain,
    ( ! [X0,X1] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),X0),X1),X1,tc_Int_Oint) = X0
    | ~ spl0_60
    | ~ spl0_235 ),
    inference(resolution,[],[f2161,f1145]) ).

fof(f10020,plain,
    ( spl0_629
    | ~ spl0_94
    | ~ spl0_232 ),
    inference(avatar_split_clause,[],[f2239,f2148,f1313,f10018]) ).

fof(f10018,plain,
    ( spl0_629
  <=> ! [X0,X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(X0,X1,tc_Complex_Ocomplex)),X1) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_629])]) ).

fof(f2148,plain,
    ( spl0_232
  <=> ! [X2,X0,X1] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ominus__class_Ominus(X1,X2,X0)),X2) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).

fof(f2239,plain,
    ( ! [X0,X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(X0,X1,tc_Complex_Ocomplex)),X1) = X0
    | ~ spl0_94
    | ~ spl0_232 ),
    inference(resolution,[],[f2149,f1315]) ).

fof(f2149,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ominus__class_Ominus(X1,X2,X0)),X2) = X1 )
    | ~ spl0_232 ),
    inference(avatar_component_clause,[],[f2148]) ).

fof(f10016,plain,
    ( spl0_628
    | ~ spl0_60
    | ~ spl0_232 ),
    inference(avatar_split_clause,[],[f2238,f2148,f1143,f10014]) ).

fof(f10014,plain,
    ( spl0_628
  <=> ! [X0,X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_HOL_Ominus__class_Ominus(X0,X1,tc_Int_Oint)),X1) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_628])]) ).

fof(f2238,plain,
    ( ! [X0,X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_HOL_Ominus__class_Ominus(X0,X1,tc_Int_Oint)),X1) = X0
    | ~ spl0_60
    | ~ spl0_232 ),
    inference(resolution,[],[f2149,f1145]) ).

fof(f10012,plain,
    ( spl0_627
    | ~ spl0_89
    | ~ spl0_231 ),
    inference(avatar_split_clause,[],[f2237,f2144,f1288,f10010]) ).

fof(f10010,plain,
    ( spl0_627
  <=> ! [X0,X1] : c_HOL_Ominus__class_Ominus(X0,X1,tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X1,X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_627])]) ).

fof(f10008,plain,
    ( spl0_626
    | ~ spl0_55
    | ~ spl0_231 ),
    inference(avatar_split_clause,[],[f2236,f2144,f1118,f10006]) ).

fof(f10006,plain,
    ( spl0_626
  <=> ! [X0,X1] : c_HOL_Ominus__class_Ominus(X0,X1,tc_Int_Oint) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X1,X0,tc_Int_Oint),tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_626])]) ).

fof(f10004,plain,
    ( spl0_625
    | ~ spl0_94
    | ~ spl0_230 ),
    inference(avatar_split_clause,[],[f2235,f2140,f1313,f10002]) ).

fof(f10002,plain,
    ( spl0_625
  <=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),X0),c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_625])]) ).

fof(f2140,plain,
    ( spl0_230
  <=> ! [X0,X1] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),c_HOL_Ouminus__class_Ouminus(X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).

fof(f2235,plain,
    ( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),X0),c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex))
    | ~ spl0_94
    | ~ spl0_230 ),
    inference(resolution,[],[f2141,f1315]) ).

fof(f2141,plain,
    ( ! [X0,X1] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),c_HOL_Ouminus__class_Ouminus(X1,X0)) )
    | ~ spl0_230 ),
    inference(avatar_component_clause,[],[f2140]) ).

fof(f10000,plain,
    ( spl0_624
    | ~ spl0_60
    | ~ spl0_230 ),
    inference(avatar_split_clause,[],[f2234,f2140,f1143,f9998]) ).

fof(f9998,plain,
    ( spl0_624
  <=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),X0),c_HOL_Ouminus__class_Ouminus(X0,tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_624])]) ).

fof(f2234,plain,
    ( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),X0),c_HOL_Ouminus__class_Ouminus(X0,tc_Int_Oint))
    | ~ spl0_60
    | ~ spl0_230 ),
    inference(resolution,[],[f2141,f1145]) ).

fof(f9993,plain,
    ( spl0_623
    | ~ spl0_94
    | ~ spl0_227 ),
    inference(avatar_split_clause,[],[f2231,f2128,f1313,f9991]) ).

fof(f9991,plain,
    ( spl0_623
  <=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex)),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_623])]) ).

fof(f2128,plain,
    ( spl0_227
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ouminus__class_Ouminus(X2,X0)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).

fof(f2231,plain,
    ( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex)),X0)
    | ~ spl0_94
    | ~ spl0_227 ),
    inference(resolution,[],[f2129,f1315]) ).

fof(f2129,plain,
    ( ! [X2,X0] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ouminus__class_Ouminus(X2,X0)),X2) )
    | ~ spl0_227 ),
    inference(avatar_component_clause,[],[f2128]) ).

fof(f9989,plain,
    ( spl0_622
    | ~ spl0_60
    | ~ spl0_227 ),
    inference(avatar_split_clause,[],[f2230,f2128,f1143,f9987]) ).

fof(f9987,plain,
    ( spl0_622
  <=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_HOL_Ouminus__class_Ouminus(X0,tc_Int_Oint)),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_622])]) ).

fof(f2230,plain,
    ( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_HOL_Ouminus__class_Ouminus(X0,tc_Int_Oint)),X0)
    | ~ spl0_60
    | ~ spl0_227 ),
    inference(resolution,[],[f2129,f1145]) ).

fof(f9985,plain,
    ( spl0_621
    | ~ spl0_97
    | ~ spl0_226 ),
    inference(avatar_split_clause,[],[f2224,f2124,f1328,f9983]) ).

fof(f9983,plain,
    ( spl0_621
  <=> ! [X0] :
        ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0
        | c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(X0,X0,tc_Complex_Ocomplex) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_621])]) ).

fof(f2124,plain,
    ( spl0_226
  <=> ! [X4,X0] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X4
        | c_HOL_Oone__class_Oone(X0) = c_HOL_Oinverse__class_Odivide(X4,X4,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).

fof(f2224,plain,
    ( ! [X0] :
        ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0
        | c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(X0,X0,tc_Complex_Ocomplex) )
    | ~ spl0_97
    | ~ spl0_226 ),
    inference(resolution,[],[f2125,f1330]) ).

fof(f2125,plain,
    ( ! [X0,X4] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X4
        | c_HOL_Oone__class_Oone(X0) = c_HOL_Oinverse__class_Odivide(X4,X4,X0) )
    | ~ spl0_226 ),
    inference(avatar_component_clause,[],[f2124]) ).

fof(f9973,plain,
    ( spl0_620
    | ~ spl0_219
    | ~ spl0_602
    | ~ spl0_619 ),
    inference(avatar_split_clause,[],[f9968,f9964,f8625,f2009,f9970]) ).

fof(f9970,plain,
    ( spl0_620
  <=> c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_620])]) ).

fof(f9964,plain,
    ( spl0_619
  <=> c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_619])]) ).

fof(f9968,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)
    | ~ spl0_219
    | ~ spl0_602
    | ~ spl0_619 ),
    inference(forward_demodulation,[],[f9966,f8694]) ).

fof(f9966,plain,
    ( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)
    | ~ spl0_619 ),
    inference(avatar_component_clause,[],[f9964]) ).

fof(f9967,plain,
    ( spl0_619
    | ~ spl0_123
    | ~ spl0_220 ),
    inference(avatar_split_clause,[],[f2100,f2013,f1449,f9964]) ).

fof(f2100,plain,
    ( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)
    | ~ spl0_123
    | ~ spl0_220 ),
    inference(superposition,[],[f1450,f2015]) ).

fof(f9880,plain,
    ( ~ spl0_618
    | ~ spl0_247
    | ~ spl0_272
    | ~ spl0_526 ),
    inference(avatar_split_clause,[],[f7755,f5994,f2492,f2210,f9877]) ).

fof(f9877,plain,
    ( spl0_618
  <=> c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_618])]) ).

fof(f2492,plain,
    ( spl0_272
  <=> ! [X4] : ~ c_Parity_Oeven__odd__class_Oeven(hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X4)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).

fof(f5994,plain,
    ( spl0_526
  <=> ! [X0] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),c_HOL_Oone__class_Oone(tc_nat)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_526])]) ).

fof(f7755,plain,
    ( ~ c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)
    | ~ spl0_247
    | ~ spl0_272
    | ~ spl0_526 ),
    inference(forward_demodulation,[],[f7638,f2212]) ).

fof(f7638,plain,
    ( ~ c_Parity_Oeven__odd__class_Oeven(hAPP(c_Suc,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat)
    | ~ spl0_272
    | ~ spl0_526 ),
    inference(superposition,[],[f2493,f5995]) ).

fof(f5995,plain,
    ( ! [X0] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),c_HOL_Oone__class_Oone(tc_nat)) = X0
    | ~ spl0_526 ),
    inference(avatar_component_clause,[],[f5994]) ).

fof(f2493,plain,
    ( ! [X4] : ~ c_Parity_Oeven__odd__class_Oeven(hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X4)),tc_nat)
    | ~ spl0_272 ),
    inference(avatar_component_clause,[],[f2492]) ).

fof(f8693,plain,
    ( spl0_617
    | ~ spl0_397
    | ~ spl0_399 ),
    inference(avatar_split_clause,[],[f3930,f3750,f3742,f8691]) ).

fof(f8691,plain,
    ( spl0_617
  <=> ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,X0,X1)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
        | ~ c_HOL_Oord__class_Oless(X2,X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_617])]) ).

fof(f3742,plain,
    ( spl0_397
  <=> ! [X0,X6,X2,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
        | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X6),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X6),X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).

fof(f3750,plain,
    ( spl0_399
  <=> ! [X0,X6,X2,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
        | c_HOL_Oord__class_Oless(X1,X2,X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X6),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).

fof(f3930,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,X0,X1)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
        | ~ c_HOL_Oord__class_Oless(X2,X2,X1) )
    | ~ spl0_397
    | ~ spl0_399 ),
    inference(duplicate_literal_removal,[],[f3923]) ).

fof(f3923,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,X0,X1)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
        | ~ c_HOL_Oord__class_Oless(X2,X2,X1)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) )
    | ~ spl0_397
    | ~ spl0_399 ),
    inference(resolution,[],[f3751,f3743]) ).

fof(f3743,plain,
    ( ! [X2,X0,X1,X6] :
        ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X6),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X6),X2),X0)
        | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0) )
    | ~ spl0_397 ),
    inference(avatar_component_clause,[],[f3742]) ).

fof(f3751,plain,
    ( ! [X2,X0,X1,X6] :
        ( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X6),X0)
        | c_HOL_Oord__class_Oless(X1,X2,X0)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0) )
    | ~ spl0_399 ),
    inference(avatar_component_clause,[],[f3750]) ).

fof(f8689,plain,
    ( spl0_616
    | ~ spl0_315
    | ~ spl0_326 ),
    inference(avatar_split_clause,[],[f3265,f3131,f3085,f8687]) ).

fof(f8687,plain,
    ( spl0_616
  <=> ! [X0] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ class_Ring__and__Field_Oordered__semidom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_616])]) ).

fof(f3085,plain,
    ( spl0_315
  <=> ! [X0,X1,X3] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).

fof(f3131,plain,
    ( spl0_326
  <=> ! [X0] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ozero__class_Ozero(X0)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).

fof(f3265,plain,
    ( ! [X0] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ class_Ring__and__Field_Oordered__semidom(X0) )
    | ~ spl0_315
    | ~ spl0_326 ),
    inference(resolution,[],[f3132,f3086]) ).

fof(f3086,plain,
    ( ! [X3,X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3),X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | ~ class_Ring__and__Field_Oordered__semidom(X0) )
    | ~ spl0_315 ),
    inference(avatar_component_clause,[],[f3085]) ).

fof(f3132,plain,
    ( ! [X0] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ozero__class_Ozero(X0)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X0)
        | ~ class_Ring__and__Field_Oordered__idom(X0) )
    | ~ spl0_326 ),
    inference(avatar_component_clause,[],[f3131]) ).

fof(f8685,plain,
    ( ~ spl0_615
    | ~ spl0_113
    | ~ spl0_220 ),
    inference(avatar_split_clause,[],[f2098,f2013,f1405,f8682]) ).

fof(f8682,plain,
    ( spl0_615
  <=> c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat) = c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_615])]) ).

fof(f2098,plain,
    ( c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat) != c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)
    | ~ spl0_113
    | ~ spl0_220 ),
    inference(superposition,[],[f1406,f2015]) ).

fof(f8680,plain,
    ( spl0_614
    | ~ spl0_91
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f2059,f1985,f1298,f8678]) ).

fof(f8678,plain,
    ( spl0_614
  <=> ! [X0] : c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_614])]) ).

fof(f1298,plain,
    ( spl0_91
  <=> class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).

fof(f1985,plain,
    ( spl0_213
  <=> ! [X0,X3] :
        ( ~ class_OrderedGroup_Omonoid__mult(X0)
        | c_HOL_Oone__class_Oone(X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Oone__class_Oone(X0)),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).

fof(f2059,plain,
    ( ! [X0] : c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),X0)
    | ~ spl0_91
    | ~ spl0_213 ),
    inference(resolution,[],[f1986,f1300]) ).

fof(f1300,plain,
    ( class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex)
    | ~ spl0_91 ),
    inference(avatar_component_clause,[],[f1298]) ).

fof(f1986,plain,
    ( ! [X3,X0] :
        ( ~ class_OrderedGroup_Omonoid__mult(X0)
        | c_HOL_Oone__class_Oone(X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Oone__class_Oone(X0)),X3) )
    | ~ spl0_213 ),
    inference(avatar_component_clause,[],[f1985]) ).

fof(f8676,plain,
    ( spl0_613
    | ~ spl0_57
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f2058,f1985,f1128,f8674]) ).

fof(f8674,plain,
    ( spl0_613
  <=> ! [X0] : c_HOL_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint)),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_613])]) ).

fof(f1128,plain,
    ( spl0_57
  <=> class_OrderedGroup_Omonoid__mult(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).

fof(f2058,plain,
    ( ! [X0] : c_HOL_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint)),X0)
    | ~ spl0_57
    | ~ spl0_213 ),
    inference(resolution,[],[f1986,f1130]) ).

fof(f1130,plain,
    ( class_OrderedGroup_Omonoid__mult(tc_Int_Oint)
    | ~ spl0_57 ),
    inference(avatar_component_clause,[],[f1128]) ).

fof(f8672,plain,
    ( spl0_612
    | ~ spl0_20
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f2057,f1985,f943,f8670]) ).

fof(f8670,plain,
    ( spl0_612
  <=> ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_612])]) ).

fof(f943,plain,
    ( spl0_20
  <=> class_OrderedGroup_Omonoid__mult(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).

fof(f2057,plain,
    ( ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X0)
    | ~ spl0_20
    | ~ spl0_213 ),
    inference(resolution,[],[f1986,f945]) ).

fof(f945,plain,
    ( class_OrderedGroup_Omonoid__mult(tc_nat)
    | ~ spl0_20 ),
    inference(avatar_component_clause,[],[f943]) ).

fof(f8663,plain,
    ( spl0_611
    | ~ spl0_76
    | ~ spl0_97
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2056,f1981,f1328,f1223,f8661]) ).

fof(f8661,plain,
    ( spl0_611
  <=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_611])]) ).

fof(f1223,plain,
    ( spl0_76
  <=> class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).

fof(f1981,plain,
    ( spl0_212
  <=> ! [X2,X0] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | ~ class_Ring__and__Field_Odivision__by__zero(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(X2,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).

fof(f2056,plain,
    ( ! [X0] :
        ( ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
        | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) )
    | ~ spl0_97
    | ~ spl0_212 ),
    inference(resolution,[],[f1982,f1330]) ).

fof(f1982,plain,
    ( ! [X2,X0] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | ~ class_Ring__and__Field_Odivision__by__zero(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(X2,c_HOL_Ozero__class_Ozero(X0),X0) )
    | ~ spl0_212 ),
    inference(avatar_component_clause,[],[f1981]) ).

fof(f8659,plain,
    ( spl0_610
    | ~ spl0_72
    | ~ spl0_203 ),
    inference(avatar_split_clause,[],[f2036,f1945,f1203,f8657]) ).

fof(f8657,plain,
    ( spl0_610
  <=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_610])]) ).

fof(f1203,plain,
    ( spl0_72
  <=> class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).

fof(f1945,plain,
    ( spl0_203
  <=> ! [X2,X0] :
        ( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
        | c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ozero__class_Ozero(X0)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).

fof(f2036,plain,
    ( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),X0)
    | ~ spl0_72
    | ~ spl0_203 ),
    inference(resolution,[],[f1946,f1205]) ).

fof(f1205,plain,
    ( class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex)
    | ~ spl0_72 ),
    inference(avatar_component_clause,[],[f1203]) ).

fof(f1946,plain,
    ( ! [X2,X0] :
        ( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
        | c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ozero__class_Ozero(X0)),X2) )
    | ~ spl0_203 ),
    inference(avatar_component_clause,[],[f1945]) ).

fof(f8655,plain,
    ( spl0_609
    | ~ spl0_34
    | ~ spl0_203 ),
    inference(avatar_split_clause,[],[f2035,f1945,f1013,f8653]) ).

fof(f8653,plain,
    ( spl0_609
  <=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_609])]) ).

fof(f1013,plain,
    ( spl0_34
  <=> class_Ring__and__Field_Oring__no__zero__divisors(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).

fof(f2035,plain,
    ( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),X0)
    | ~ spl0_34
    | ~ spl0_203 ),
    inference(resolution,[],[f1946,f1015]) ).

fof(f1015,plain,
    ( class_Ring__and__Field_Oring__no__zero__divisors(tc_Int_Oint)
    | ~ spl0_34 ),
    inference(avatar_component_clause,[],[f1013]) ).

fof(f8651,plain,
    ( spl0_608
    | ~ spl0_72
    | ~ spl0_202 ),
    inference(avatar_split_clause,[],[f2034,f1941,f1203,f8649]) ).

fof(f8649,plain,
    ( spl0_608
  <=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_608])]) ).

fof(f1941,plain,
    ( spl0_202
  <=> ! [X0,X1] :
        ( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
        | c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),c_HOL_Ozero__class_Ozero(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).

fof(f2034,plain,
    ( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))
    | ~ spl0_72
    | ~ spl0_202 ),
    inference(resolution,[],[f1942,f1205]) ).

fof(f1942,plain,
    ( ! [X0,X1] :
        ( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
        | c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),c_HOL_Ozero__class_Ozero(X0)) )
    | ~ spl0_202 ),
    inference(avatar_component_clause,[],[f1941]) ).

fof(f8647,plain,
    ( ~ spl0_606
    | spl0_607
    | ~ spl0_182
    | ~ spl0_526 ),
    inference(avatar_split_clause,[],[f7641,f5994,f1788,f8645,f8641]) ).

fof(f8641,plain,
    ( spl0_606
  <=> c_Parity_Oeven__odd__class_Oeven(c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_606])]) ).

fof(f8645,plain,
    ( spl0_607
  <=> ! [X0] : c_Parity_Oeven__odd__class_Oeven(X0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_607])]) ).

fof(f1788,plain,
    ( spl0_182
  <=> ! [X9,X4] :
        ( ~ c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X4),X9),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).

fof(f7641,plain,
    ( ! [X0] :
        ( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
        | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oone__class_Oone(tc_nat),tc_nat) )
    | ~ spl0_182
    | ~ spl0_526 ),
    inference(superposition,[],[f1789,f5995]) ).

fof(f1789,plain,
    ( ! [X9,X4] :
        ( c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X4),X9),tc_nat)
        | ~ c_Parity_Oeven__odd__class_Oeven(X9,tc_nat) )
    | ~ spl0_182 ),
    inference(avatar_component_clause,[],[f1788]) ).

fof(f8639,plain,
    ( spl0_605
    | ~ spl0_34
    | ~ spl0_202 ),
    inference(avatar_split_clause,[],[f2033,f1941,f1013,f8637]) ).

fof(f8637,plain,
    ( spl0_605
  <=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),X0),c_HOL_Ozero__class_Ozero(tc_Int_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_605])]) ).

fof(f2033,plain,
    ( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),X0),c_HOL_Ozero__class_Ozero(tc_Int_Oint))
    | ~ spl0_34
    | ~ spl0_202 ),
    inference(resolution,[],[f1942,f1015]) ).

fof(f8635,plain,
    ( spl0_604
    | ~ spl0_102
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f2027,f1909,f1353,f8633]) ).

fof(f8633,plain,
    ( spl0_604
  <=> ! [X0] : c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),c_HOL_Ozero__class_Ozero(tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_604])]) ).

fof(f1353,plain,
    ( spl0_102
  <=> class_Power_Opower(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).

fof(f1909,plain,
    ( spl0_194
  <=> ! [X0,X1] :
        ( ~ class_Power_Opower(X0)
        | c_HOL_Oone__class_Oone(X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),c_HOL_Ozero__class_Ozero(tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).

fof(f2027,plain,
    ( ! [X0] : c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),c_HOL_Ozero__class_Ozero(tc_nat))
    | ~ spl0_102
    | ~ spl0_194 ),
    inference(resolution,[],[f1910,f1355]) ).

fof(f1355,plain,
    ( class_Power_Opower(tc_Complex_Ocomplex)
    | ~ spl0_102 ),
    inference(avatar_component_clause,[],[f1353]) ).

fof(f1910,plain,
    ( ! [X0,X1] :
        ( ~ class_Power_Opower(X0)
        | c_HOL_Oone__class_Oone(X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),c_HOL_Ozero__class_Ozero(tc_nat)) )
    | ~ spl0_194 ),
    inference(avatar_component_clause,[],[f1909]) ).

fof(f8631,plain,
    ( spl0_603
    | ~ spl0_69
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f2026,f1909,f1188,f8629]) ).

fof(f8629,plain,
    ( spl0_603
  <=> ! [X0] : c_HOL_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X0),c_HOL_Ozero__class_Ozero(tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_603])]) ).

fof(f1188,plain,
    ( spl0_69
  <=> class_Power_Opower(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).

fof(f2026,plain,
    ( ! [X0] : c_HOL_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X0),c_HOL_Ozero__class_Ozero(tc_nat))
    | ~ spl0_69
    | ~ spl0_194 ),
    inference(resolution,[],[f1910,f1190]) ).

fof(f1190,plain,
    ( class_Power_Opower(tc_Int_Oint)
    | ~ spl0_69 ),
    inference(avatar_component_clause,[],[f1188]) ).

fof(f8627,plain,
    ( spl0_602
    | ~ spl0_26
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f2025,f1909,f973,f8625]) ).

fof(f973,plain,
    ( spl0_26
  <=> class_Power_Opower(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).

fof(f2025,plain,
    ( ! [X0] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X0),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_nat)
    | ~ spl0_26
    | ~ spl0_194 ),
    inference(resolution,[],[f1910,f975]) ).

fof(f975,plain,
    ( class_Power_Opower(tc_nat)
    | ~ spl0_26 ),
    inference(avatar_component_clause,[],[f973]) ).

fof(f7811,plain,
    ( spl0_601
    | ~ spl0_210
    | ~ spl0_526 ),
    inference(avatar_split_clause,[],[f7639,f5994,f1973,f7808]) ).

fof(f7808,plain,
    ( spl0_601
  <=> c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_601])]) ).

fof(f7639,plain,
    ( c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)
    | ~ spl0_210
    | ~ spl0_526 ),
    inference(superposition,[],[f1974,f5995]) ).

fof(f7512,plain,
    spl0_600,
    inference(avatar_split_clause,[],[f517,f7510]) ).

fof(f7510,plain,
    ( spl0_600
  <=> ! [X9,X0,X4] :
        ( ~ class_Int_Onumber__ring(X0)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X4),X9)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X9),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),X0)),X4)),X9)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_600])]) ).

fof(f517,axiom,
    ! [X0,X9,X4] :
      ( ~ class_Int_Onumber__ring(X0)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X4),X9)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X9),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),X0)),X4)),X9)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power2__sum_0) ).

fof(f7502,plain,
    spl0_599,
    inference(avatar_split_clause,[],[f509,f7500]) ).

fof(f7500,plain,
    ( spl0_599
  <=> ! [X9,X0,X4] :
        ( ~ class_Int_Onumber__ring(X0)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ominus__class_Ominus(X4,X9,X0)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X9),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),X0)),X4)),X9),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_599])]) ).

fof(f509,axiom,
    ! [X0,X9,X4] :
      ( ~ class_Int_Onumber__ring(X0)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ominus__class_Ominus(X4,X9,X0)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X9),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),X0)),X4)),X9),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power2__diff_0) ).

fof(f7496,plain,
    spl0_598,
    inference(avatar_split_clause,[],[f22,f7494]) ).

fof(f7494,plain,
    ( spl0_598
  <=> ! [X4,X0,X9,X2,X1] :
        ( ~ class_RealVector_Oreal__normed__algebra(X0)
        | c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X9),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2),X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ominus__class_Ominus(X4,X1,X0)),c_HOL_Ominus__class_Ominus(X9,X2,X0))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ominus__class_Ominus(X4,X1,X0)),X2))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),c_HOL_Ominus__class_Ominus(X9,X2,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_598])]) ).

fof(f22,axiom,
    ! [X2,X0,X1,X9,X4] :
      ( ~ class_RealVector_Oreal__normed__algebra(X0)
      | c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X9),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2),X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ominus__class_Ominus(X4,X1,X0)),c_HOL_Ominus__class_Ominus(X9,X2,X0))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ominus__class_Ominus(X4,X1,X0)),X2))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),c_HOL_Ominus__class_Ominus(X9,X2,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Oprod__diff__prod_0) ).

fof(f7491,plain,
    spl0_597,
    inference(avatar_split_clause,[],[f336,f7489]) ).

fof(f7489,plain,
    ( spl0_597
  <=> ! [X21,X20,X0,X22,X1] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X1
        | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X21),X22)),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X20),X21)),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X22),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X20),X0)),X21) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_597])]) ).

fof(f336,axiom,
    ! [X21,X0,X1,X22,X20] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X1
      | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X21),X22)),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X20),X21)),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X22),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X20),X0)),X21) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__divides__special_0) ).

fof(f7375,plain,
    spl0_596,
    inference(avatar_split_clause,[],[f311,f7373]) ).

fof(f7373,plain,
    ( spl0_596
  <=> ! [X1,X2,X0,X6,X8,X30] :
        ( ~ class_RealVector_Oreal__field(X0)
        | c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X6),X8),X0),X30,X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X2,X8,X0),X30,X0))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X1,X6,X0),X30,X0)),X8)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_596])]) ).

fof(f311,axiom,
    ! [X2,X0,X1,X8,X6,X30] :
      ( ~ class_RealVector_Oreal__field(X0)
      | c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X6),X8),X0),X30,X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X2,X8,X0),X30,X0))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X1,X6,X0),X30,X0)),X8)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DERIV__mult__lemma_0) ).

fof(f7367,plain,
    spl0_595,
    inference(avatar_split_clause,[],[f312,f7365]) ).

fof(f7365,plain,
    ( spl0_595
  <=> ! [X18,X4,X11,X0,X9] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X9
        | c_HOL_Ozero__class_Ozero(X0) = X18
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oinverse__class_Odivide(X4,X9,X0)),c_HOL_Oinverse__class_Odivide(X11,X18,X0)) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X18)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X11),X9)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X9),X18),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_595])]) ).

fof(f312,axiom,
    ! [X0,X11,X18,X9,X4] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X9
      | c_HOL_Ozero__class_Ozero(X0) = X18
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oinverse__class_Odivide(X4,X9,X0)),c_HOL_Oinverse__class_Odivide(X11,X18,X0)) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X18)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X11),X9)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X9),X18),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__frac__eq_0) ).

fof(f6959,plain,
    spl0_594,
    inference(avatar_split_clause,[],[f557,f6957]) ).

fof(f6957,plain,
    ( spl0_594
  <=> ! [X0,X8,X6,X2,X1] :
        ( ~ class_Ring__and__Field_Oidom(X0)
        | ~ class_Int_Onumber__ring(X0)
        | X1 = X2
        | X6 = X8
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X6)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X8)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X8)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X6)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_594])]) ).

fof(f557,axiom,
    ! [X2,X0,X1,X8,X6] :
      ( ~ class_Ring__and__Field_Oidom(X0)
      | ~ class_Int_Onumber__ring(X0)
      | X1 = X2
      | X6 = X8
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X6)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X8)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X8)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X6)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_0) ).

fof(f6955,plain,
    spl0_593,
    inference(avatar_split_clause,[],[f547,f6953]) ).

fof(f6953,plain,
    ( spl0_593
  <=> ! [X22,X21,X19] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X19))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X21),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X22))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(X19)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X21),X22)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_593])]) ).

fof(f547,axiom,
    ! [X21,X19,X22] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X19))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X21),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X22))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(X19)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X21),X22)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_root__cancel1_0) ).

fof(f6951,plain,
    spl0_592,
    inference(avatar_split_clause,[],[f429,f6949]) ).

fof(f6949,plain,
    ( spl0_592
  <=> ! [X18,X4,X11,X0,X9] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X9
        | c_HOL_Ozero__class_Ozero(X0) = X18
        | c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X4,X9,X0),c_HOL_Oinverse__class_Odivide(X11,X18,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X18),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X11),X9),X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X9),X18),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_592])]) ).

fof(f429,axiom,
    ! [X0,X11,X18,X9,X4] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X9
      | c_HOL_Ozero__class_Ozero(X0) = X18
      | c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X4,X9,X0),c_HOL_Oinverse__class_Odivide(X11,X18,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X18),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X11),X9),X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X9),X18),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__frac__eq_0) ).

fof(f6947,plain,
    spl0_591,
    inference(avatar_split_clause,[],[f179,f6945]) ).

fof(f6945,plain,
    ( spl0_591
  <=> ! [X2,X0,X8,X6,X1,X7] :
        ( ~ class_Ring__and__Field_Opordered__ring(X0)
        | ~ c_HOL_Oord__class_Oless(X6,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ominus__class_Ominus(X2,X1,X0)),X7)),X8),X0)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X7)),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X7)),X8),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_591])]) ).

fof(f179,axiom,
    ! [X2,X0,X1,X8,X6,X7] :
      ( ~ class_Ring__and__Field_Opordered__ring(X0)
      | ~ c_HOL_Oord__class_Oless(X6,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ominus__class_Ominus(X2,X1,X0)),X7)),X8),X0)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X7)),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X7)),X8),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__iff2_1) ).

fof(f6943,plain,
    spl0_590,
    inference(avatar_split_clause,[],[f178,f6941]) ).

fof(f6941,plain,
    ( spl0_590
  <=> ! [X2,X0,X8,X6,X1,X7] :
        ( ~ class_Ring__and__Field_Opordered__ring(X0)
        | c_HOL_Oord__class_Oless(X6,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ominus__class_Ominus(X2,X1,X0)),X7)),X8),X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X7)),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X7)),X8),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_590])]) ).

fof(f178,axiom,
    ! [X2,X0,X1,X8,X6,X7] :
      ( ~ class_Ring__and__Field_Opordered__ring(X0)
      | c_HOL_Oord__class_Oless(X6,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ominus__class_Ominus(X2,X1,X0)),X7)),X8),X0)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X7)),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X7)),X8),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__iff2_0) ).

fof(f6939,plain,
    spl0_589,
    inference(avatar_split_clause,[],[f177,f6937]) ).

fof(f6937,plain,
    ( spl0_589
  <=> ! [X2,X1,X0,X6,X8,X7] :
        ( ~ class_Ring__and__Field_Opordered__ring(X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ominus__class_Ominus(X1,X2,X0)),X7)),X6),X8,X0)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X7)),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X7)),X8),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_589])]) ).

fof(f177,axiom,
    ! [X2,X0,X1,X8,X6,X7] :
      ( ~ class_Ring__and__Field_Opordered__ring(X0)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ominus__class_Ominus(X1,X2,X0)),X7)),X6),X8,X0)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X7)),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X7)),X8),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__iff1_1) ).

fof(f6935,plain,
    spl0_588,
    inference(avatar_split_clause,[],[f176,f6933]) ).

fof(f6933,plain,
    ( spl0_588
  <=> ! [X2,X1,X0,X6,X8,X7] :
        ( ~ class_Ring__and__Field_Opordered__ring(X0)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ominus__class_Ominus(X1,X2,X0)),X7)),X6),X8,X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X7)),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X7)),X8),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_588])]) ).

fof(f176,axiom,
    ! [X2,X0,X1,X8,X6,X7] :
      ( ~ class_Ring__and__Field_Opordered__ring(X0)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ominus__class_Ominus(X1,X2,X0)),X7)),X6),X8,X0)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X7)),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X7)),X8),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__iff1_0) ).

fof(f6931,plain,
    ( ~ spl0_587
    | ~ spl0_10
    | ~ spl0_77
    | ~ spl0_94
    | ~ spl0_241
    | ~ spl0_290
    | ~ spl0_300
    | ~ spl0_429
    | ~ spl0_560
    | spl0_586 ),
    inference(avatar_split_clause,[],[f6837,f6828,f6310,f4145,f2838,f2797,f2185,f1313,f1228,f893,f6928]) ).

fof(f2185,plain,
    ( spl0_241
  <=> c_HOL_Oord__class_Oless(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).

fof(f4145,plain,
    ( spl0_429
  <=> ! [X4,X0,X3] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),hAPP(c_Suc,X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).

fof(f6310,plain,
    ( spl0_560
  <=> ! [X21,X1] :
        ( ~ c_HOL_Oord__class_Oless(X21,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat)
        | c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),X1,X21) = hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,X1),X21) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_560])]) ).

fof(f6828,plain,
    ( spl0_586
  <=> hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_Complex_Ocomplex,tc_nat),v_i____)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____))),tc_Complex_Ocomplex)),v_i____)),c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),v_i____))) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_Complex_Ocomplex,tc_nat)),v_i____)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____))),tc_Complex_Ocomplex)),v_i____)),hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat)),v_i____))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_586])]) ).

fof(f6837,plain,
    ( c_HOL_Ominus__class_Ominus(hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_Complex_Ocomplex,tc_nat)),v_i____),c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat)),v_i____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(c_Suc,v_ka____))),tc_Complex_Ocomplex)),v_i____)),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_Complex_Ocomplex,tc_nat)),v_i____)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat)),v_i____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(c_Suc,v_ka____))),tc_Complex_Ocomplex)),v_i____)))
    | ~ spl0_10
    | ~ spl0_77
    | ~ spl0_94
    | ~ spl0_241
    | ~ spl0_290
    | ~ spl0_300
    | ~ spl0_429
    | ~ spl0_560
    | spl0_586 ),
    inference(forward_demodulation,[],[f6836,f6367]) ).

fof(f6367,plain,
    ( ! [X0] : c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),X0,v_i____) = hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,X0),v_i____)
    | ~ spl0_241
    | ~ spl0_560 ),
    inference(resolution,[],[f6311,f2187]) ).

fof(f2187,plain,
    ( c_HOL_Oord__class_Oless(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat)
    | ~ spl0_241 ),
    inference(avatar_component_clause,[],[f2185]) ).

fof(f6311,plain,
    ( ! [X21,X1] :
        ( ~ c_HOL_Oord__class_Oless(X21,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat)
        | c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),X1,X21) = hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,X1),X21) )
    | ~ spl0_560 ),
    inference(avatar_component_clause,[],[f6310]) ).

fof(f6836,plain,
    ( c_HOL_Ominus__class_Ominus(hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_Complex_Ocomplex,tc_nat)),v_i____),c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat)),v_i____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(c_Suc,v_ka____))),tc_Complex_Ocomplex)),v_i____)),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_Complex_Ocomplex,tc_nat),v_i____)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat)),v_i____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(c_Suc,v_ka____))),tc_Complex_Ocomplex)),v_i____)))
    | ~ spl0_10
    | ~ spl0_77
    | ~ spl0_94
    | ~ spl0_241
    | ~ spl0_290
    | ~ spl0_300
    | ~ spl0_429
    | ~ spl0_560
    | spl0_586 ),
    inference(forward_demodulation,[],[f6835,f2955]) ).

fof(f6835,plain,
    ( c_HOL_Ominus__class_Ominus(hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_Complex_Ocomplex,tc_nat)),v_i____),c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat)),v_i____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(c_Suc,v_ka____))),tc_Complex_Ocomplex)),v_i____)),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_Complex_Ocomplex,tc_nat),v_i____)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(c_Suc,v_ka____))),tc_Complex_Ocomplex)),v_i____)),hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat)),v_i____)))
    | ~ spl0_10
    | ~ spl0_77
    | ~ spl0_94
    | ~ spl0_241
    | ~ spl0_290
    | ~ spl0_300
    | ~ spl0_429
    | ~ spl0_560
    | spl0_586 ),
    inference(forward_demodulation,[],[f6834,f6367]) ).

fof(f6834,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_Complex_Ocomplex,tc_nat),v_i____)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(c_Suc,v_ka____))),tc_Complex_Ocomplex)),v_i____)),c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),v_i____))) != c_HOL_Ominus__class_Ominus(hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_Complex_Ocomplex,tc_nat)),v_i____),c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat)),v_i____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(c_Suc,v_ka____))),tc_Complex_Ocomplex)),v_i____)),tc_Complex_Ocomplex),tc_Complex_Ocomplex)
    | ~ spl0_10
    | ~ spl0_77
    | ~ spl0_94
    | ~ spl0_290
    | ~ spl0_300
    | ~ spl0_429
    | spl0_586 ),
    inference(forward_demodulation,[],[f6833,f4404]) ).

fof(f4404,plain,
    ( ! [X0,X1] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X0),hAPP(c_Suc,X1)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X0),X1))
    | ~ spl0_10
    | ~ spl0_429 ),
    inference(resolution,[],[f4146,f895]) ).

fof(f4146,plain,
    ( ! [X3,X0,X4] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),hAPP(c_Suc,X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),X3)) )
    | ~ spl0_429 ),
    inference(avatar_component_clause,[],[f4145]) ).

fof(f6833,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_Complex_Ocomplex,tc_nat),v_i____)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____))),tc_Complex_Ocomplex)),v_i____)),c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),v_i____))) != c_HOL_Ominus__class_Ominus(hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_Complex_Ocomplex,tc_nat)),v_i____),c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat)),v_i____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____))),tc_Complex_Ocomplex)),v_i____)),tc_Complex_Ocomplex),tc_Complex_Ocomplex)
    | ~ spl0_77
    | ~ spl0_94
    | ~ spl0_290
    | ~ spl0_300
    | spl0_586 ),
    inference(forward_demodulation,[],[f6832,f2955]) ).

fof(f6832,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_Complex_Ocomplex,tc_nat),v_i____)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____))),tc_Complex_Ocomplex)),v_i____)),c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),v_i____))) != c_HOL_Ominus__class_Ominus(hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_Complex_Ocomplex,tc_nat)),v_i____),c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____))),tc_Complex_Ocomplex)),v_i____)),hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat)),v_i____)),tc_Complex_Ocomplex),tc_Complex_Ocomplex)
    | ~ spl0_94
    | ~ spl0_290
    | spl0_586 ),
    inference(forward_demodulation,[],[f6830,f2897]) ).

fof(f6830,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_Complex_Ocomplex,tc_nat),v_i____)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____))),tc_Complex_Ocomplex)),v_i____)),c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),v_i____))) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_Complex_Ocomplex,tc_nat)),v_i____)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____))),tc_Complex_Ocomplex)),v_i____)),hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat)),v_i____)))
    | spl0_586 ),
    inference(avatar_component_clause,[],[f6828]) ).

fof(f6831,plain,
    ~ spl0_586,
    inference(avatar_split_clause,[],[f694,f6828]) ).

fof(f694,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_Complex_Ocomplex,tc_nat),v_i____)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____))),tc_Complex_Ocomplex)),v_i____)),c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),v_i____))) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_Complex_Ocomplex,tc_nat)),v_i____)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____))),tc_Complex_Ocomplex)),v_i____)),hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat)),v_i____))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

fof(f6777,plain,
    spl0_585,
    inference(avatar_split_clause,[],[f559,f6775]) ).

fof(f6775,plain,
    ( spl0_585
  <=> ! [X4,X0,X3] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X3))) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),X3))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_585])]) ).

fof(f559,axiom,
    ! [X3,X0,X4] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X3))) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),X3))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I37_J_0) ).

fof(f6773,plain,
    spl0_584,
    inference(avatar_split_clause,[],[f499,f6771]) ).

fof(f6771,plain,
    ( spl0_584
  <=> ! [X15,X17,X4,X3,X0,X13,X12,X16] :
        ( ~ c_Groebner__Basis_Ogb__semiring(X15,X13,X12,X16,X17,X0)
        | hAPP(hAPP(X12,X4),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X3))) = hAPP(hAPP(X13,X4),hAPP(hAPP(X13,hAPP(hAPP(X12,X4),X3)),hAPP(hAPP(X12,X4),X3))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_584])]) ).

fof(f499,axiom,
    ! [X3,X0,X16,X4,X17,X15,X12,X13] :
      ( ~ c_Groebner__Basis_Ogb__semiring(X15,X13,X12,X16,X17,X0)
      | hAPP(hAPP(X12,X4),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X3))) = hAPP(hAPP(X13,X4),hAPP(hAPP(X13,hAPP(hAPP(X12,X4),X3)),hAPP(hAPP(X12,X4),X3))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I37_J_0) ).

fof(f6769,plain,
    spl0_583,
    inference(avatar_split_clause,[],[f16,f6767]) ).

fof(f6767,plain,
    ( spl0_583
  <=> ! [X2,X1,X0,X6,X8,X7] :
        ( ~ class_Ring__and__Field_Oring(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ominus__class_Ominus(X1,X2,X0)),X7)),X6) = X8
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X7)),X6) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X7)),X8) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_583])]) ).

fof(f16,axiom,
    ! [X2,X0,X1,X8,X6,X7] :
      ( ~ class_Ring__and__Field_Oring(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ominus__class_Ominus(X1,X2,X0)),X7)),X6) = X8
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X7)),X6) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X7)),X8) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff1_0) ).

fof(f6750,plain,
    spl0_582,
    inference(avatar_split_clause,[],[f679,f6748]) ).

fof(f6748,plain,
    ( spl0_582
  <=> ! [X1,X0,X6,X2,X7] :
        ( ~ class_Ring__and__Field_Osemiring(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X7)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X7)),X6)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2)),X7)),X6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_582])]) ).

fof(f679,axiom,
    ! [X2,X0,X1,X6,X7] :
      ( ~ class_Ring__and__Field_Osemiring(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X7)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X7)),X6)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2)),X7)),X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_combine__common__factor_0) ).

fof(f6665,plain,
    spl0_581,
    inference(avatar_split_clause,[],[f539,f6663]) ).

fof(f6663,plain,
    ( spl0_581
  <=> ! [X0,X1,X3] :
        ( ~ class_OrderedGroup_Omonoid__mult(X0)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X3))) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_581])]) ).

fof(f539,axiom,
    ! [X3,X0,X1] :
      ( ~ class_OrderedGroup_Omonoid__mult(X0)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X3))) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__odd__eq_0) ).

fof(f6641,plain,
    spl0_580,
    inference(avatar_split_clause,[],[f676,f6639]) ).

fof(f6639,plain,
    ( spl0_580
  <=> ! [X5,X0,X6,X2] :
        ( ~ class_Ring__and__Field_Osemiring(X0)
        | ~ class_Int_Onumber(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_Int_Onumber__class_Onumber__of(X5,X0)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X6)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_Int_Onumber__class_Onumber__of(X5,X0)),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_Int_Onumber__class_Onumber__of(X5,X0)),X6)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_580])]) ).

fof(f676,axiom,
    ! [X2,X0,X6,X5] :
      ( ~ class_Ring__and__Field_Osemiring(X0)
      | ~ class_Int_Onumber(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_Int_Onumber__class_Onumber__of(X5,X0)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X6)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_Int_Onumber__class_Onumber__of(X5,X0)),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_Int_Onumber__class_Onumber__of(X5,X0)),X6)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__distrib__number__of_0) ).

fof(f6637,plain,
    spl0_579,
    inference(avatar_split_clause,[],[f565,f6635]) ).

fof(f6635,plain,
    ( spl0_579
  <=> ! [X0,X5,X2,X1] :
        ( ~ class_Ring__and__Field_Osemiring(X0)
        | ~ class_Int_Onumber(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2)),c_Int_Onumber__class_Onumber__of(X5,X0)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),c_Int_Onumber__class_Onumber__of(X5,X0))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),c_Int_Onumber__class_Onumber__of(X5,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_579])]) ).

fof(f565,axiom,
    ! [X2,X0,X1,X5] :
      ( ~ class_Ring__and__Field_Osemiring(X0)
      | ~ class_Int_Onumber(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2)),c_Int_Onumber__class_Onumber__of(X5,X0)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),c_Int_Onumber__class_Onumber__of(X5,X0))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),c_Int_Onumber__class_Onumber__of(X5,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_left__distrib__number__of_0) ).

fof(f6633,plain,
    spl0_578,
    inference(avatar_split_clause,[],[f17,f6631]) ).

fof(f6631,plain,
    ( spl0_578
  <=> ! [X1,X0,X6,X2,X7] :
        ( ~ class_Ring__and__Field_Oring(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X7)),X6) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X7)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ominus__class_Ominus(X1,X2,X0)),X7)),X6)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_578])]) ).

fof(f17,axiom,
    ! [X2,X0,X1,X6,X7] :
      ( ~ class_Ring__and__Field_Oring(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X7)),X6) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X7)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ominus__class_Ominus(X1,X2,X0)),X7)),X6)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff1_1) ).

fof(f6625,plain,
    spl0_577,
    inference(avatar_split_clause,[],[f653,f6623]) ).

fof(f6623,plain,
    ( spl0_577
  <=> ! [X18,X4,X0,X9] :
        ( ~ class_Ring__and__Field_Oidom(X0)
        | ~ class_Int_Onumber__ring(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X9)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X18)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X18)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X9)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_577])]) ).

fof(f653,axiom,
    ! [X0,X18,X9,X4] :
      ( ~ class_Ring__and__Field_Oidom(X0)
      | ~ class_Int_Onumber__ring(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X9)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X18)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X18)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X9)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_1) ).

fof(f6548,plain,
    spl0_576,
    inference(avatar_split_clause,[],[f640,f6546]) ).

fof(f6546,plain,
    ( spl0_576
  <=> ! [X24,X0,X23,X25,X26] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X23),X26)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X24),X25)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X23),X24)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X26),X25)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_576])]) ).

fof(f640,axiom,
    ! [X0,X26,X24,X25,X23] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X23),X26)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X24),X25)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X23),X24)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X26),X25)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I13_J_0) ).

fof(f6544,plain,
    spl0_575,
    inference(avatar_split_clause,[],[f531,f6542]) ).

fof(f6542,plain,
    ( spl0_575
  <=> ! [X0,X8,X6,X2,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X6),X8)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X6)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X8)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_575])]) ).

fof(f531,axiom,
    ! [X2,X0,X1,X8,X6] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X6),X8)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X6)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X8)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).

fof(f6540,plain,
    spl0_574,
    inference(avatar_split_clause,[],[f501,f6538]) ).

fof(f6538,plain,
    ( spl0_574
  <=> ! [X0,X1,X3] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ouminus__class_Ouminus(X1,X0)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_574])]) ).

fof(f501,axiom,
    ! [X3,X0,X1] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ouminus__class_Ouminus(X1,X0)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__ring__1__class_Opower__minus__even_0) ).

fof(f6536,plain,
    spl0_573,
    inference(avatar_split_clause,[],[f389,f6534]) ).

fof(f6534,plain,
    ( spl0_573
  <=> ! [X15,X17,X4,X3,X0,X13,X12,X16] :
        ( ~ c_Groebner__Basis_Ogb__semiring(X15,X13,X12,X16,X17,X0)
        | hAPP(hAPP(X12,X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X3)) = hAPP(hAPP(X13,hAPP(hAPP(X12,X4),X3)),hAPP(hAPP(X12,X4),X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_573])]) ).

fof(f389,axiom,
    ! [X3,X0,X16,X4,X17,X15,X12,X13] :
      ( ~ c_Groebner__Basis_Ogb__semiring(X15,X13,X12,X16,X17,X0)
      | hAPP(hAPP(X12,X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X3)) = hAPP(hAPP(X13,hAPP(hAPP(X12,X4),X3)),hAPP(hAPP(X12,X4),X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I36_J_0) ).

fof(f6457,plain,
    spl0_572,
    inference(avatar_split_clause,[],[f680,f6455]) ).

fof(f6455,plain,
    ( spl0_572
  <=> ! [X4,X0,X3] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_572])]) ).

fof(f680,axiom,
    ! [X3,X0,X4] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I36_J_0) ).

fof(f6453,plain,
    spl0_571,
    inference(avatar_split_clause,[],[f505,f6451]) ).

fof(f6451,plain,
    ( spl0_571
  <=> ! [X9,X0,X4] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X9
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X9),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_571])]) ).

fof(f505,axiom,
    ! [X0,X9,X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X9
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X9),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__power2__gt__zero__iff_2) ).

fof(f6449,plain,
    spl0_570,
    inference(avatar_split_clause,[],[f504,f6447]) ).

fof(f6447,plain,
    ( spl0_570
  <=> ! [X4,X0,X9] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X4
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X9),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_570])]) ).

fof(f504,axiom,
    ! [X0,X9,X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X4
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X9),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__power2__gt__zero__iff_1) ).

fof(f6445,plain,
    spl0_569,
    inference(avatar_split_clause,[],[f206,f6443]) ).

fof(f6443,plain,
    ( spl0_569
  <=> ! [X16,X0,X26,X24,X25,X17,X15,X12,X23,X13] :
        ( ~ c_Groebner__Basis_Ogb__semiring(X15,X13,X12,X16,X17,X0)
        | hAPP(hAPP(X13,hAPP(hAPP(X13,X23),X26)),hAPP(hAPP(X13,X24),X25)) = hAPP(hAPP(X13,hAPP(hAPP(X13,X23),X24)),hAPP(hAPP(X13,X26),X25)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_569])]) ).

fof(f206,axiom,
    ! [X0,X26,X16,X17,X15,X24,X12,X23,X13,X25] :
      ( ~ c_Groebner__Basis_Ogb__semiring(X15,X13,X12,X16,X17,X0)
      | hAPP(hAPP(X13,hAPP(hAPP(X13,X23),X26)),hAPP(hAPP(X13,X24),X25)) = hAPP(hAPP(X13,hAPP(hAPP(X13,X23),X24)),hAPP(hAPP(X13,X26),X25)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I13_J_0) ).

fof(f6441,plain,
    spl0_568,
    inference(avatar_split_clause,[],[f199,f6439]) ).

fof(f6439,plain,
    ( spl0_568
  <=> ! [X2,X0,X1,X8,X6,X16,X17,X15,X12,X13] :
        ( ~ c_Groebner__Basis_Ogb__semiring(X15,X13,X12,X16,X17,X0)
        | hAPP(hAPP(X15,hAPP(hAPP(X15,X1),X2)),hAPP(hAPP(X15,X6),X8)) = hAPP(hAPP(X15,hAPP(hAPP(X15,X1),X6)),hAPP(hAPP(X15,X2),X8)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_568])]) ).

fof(f199,axiom,
    ! [X2,X0,X1,X8,X6,X16,X17,X15,X12,X13] :
      ( ~ c_Groebner__Basis_Ogb__semiring(X15,X13,X12,X16,X17,X0)
      | hAPP(hAPP(X15,hAPP(hAPP(X15,X1),X2)),hAPP(hAPP(X15,X6),X8)) = hAPP(hAPP(X15,hAPP(hAPP(X15,X1),X6)),hAPP(hAPP(X15,X2),X8)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I20_J_0) ).

fof(f6422,plain,
    spl0_567,
    inference(avatar_split_clause,[],[f20,f6420]) ).

fof(f6420,plain,
    ( spl0_567
  <=> ! [X10,X0,X4,X6,X8] :
        ( ~ class_Ring__and__Field_Oidom(X0)
        | ~ class_Int_Onumber__ring(X0)
        | X6 = X8
        | c_HOL_Ozero__class_Ozero(X0) = X10
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X10),X6)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X10),X8)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_567])]) ).

fof(f20,axiom,
    ! [X10,X0,X8,X6,X4] :
      ( ~ class_Ring__and__Field_Oidom(X0)
      | ~ class_Int_Onumber__ring(X0)
      | X6 = X8
      | c_HOL_Ozero__class_Ozero(X0) = X10
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X10),X6)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X10),X8)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__scale__eq__noteq_0) ).

fof(f6418,plain,
    spl0_566,
    inference(avatar_split_clause,[],[f11,f6416]) ).

fof(f6416,plain,
    ( spl0_566
  <=> ! [X5,X0,X6,X2] :
        ( ~ class_Ring__and__Field_Oring(X0)
        | ~ class_Int_Onumber(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_Int_Onumber__class_Onumber__of(X5,X0)),c_HOL_Ominus__class_Ominus(X2,X6,X0)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_Int_Onumber__class_Onumber__of(X5,X0)),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_Int_Onumber__class_Onumber__of(X5,X0)),X6),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_566])]) ).

fof(f11,axiom,
    ! [X2,X0,X6,X5] :
      ( ~ class_Ring__and__Field_Oring(X0)
      | ~ class_Int_Onumber(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_Int_Onumber__class_Onumber__of(X5,X0)),c_HOL_Ominus__class_Ominus(X2,X6,X0)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_Int_Onumber__class_Onumber__of(X5,X0)),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_Int_Onumber__class_Onumber__of(X5,X0)),X6),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__diff__distrib__number__of_0) ).

fof(f6414,plain,
    spl0_565,
    inference(avatar_split_clause,[],[f10,f6412]) ).

fof(f6412,plain,
    ( spl0_565
  <=> ! [X0,X5,X2,X1] :
        ( ~ class_Ring__and__Field_Oring(X0)
        | ~ class_Int_Onumber(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ominus__class_Ominus(X1,X2,X0)),c_Int_Onumber__class_Onumber__of(X5,X0)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),c_Int_Onumber__class_Onumber__of(X5,X0)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),c_Int_Onumber__class_Onumber__of(X5,X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_565])]) ).

fof(f10,axiom,
    ! [X2,X0,X1,X5] :
      ( ~ class_Ring__and__Field_Oring(X0)
      | ~ class_Int_Onumber(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ominus__class_Ominus(X1,X2,X0)),c_Int_Onumber__class_Onumber__of(X5,X0)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),c_Int_Onumber__class_Onumber__of(X5,X0)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),c_Int_Onumber__class_Onumber__of(X5,X0)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_left__diff__distrib__number__of_0) ).

fof(f6397,plain,
    spl0_564,
    inference(avatar_split_clause,[],[f537,f6395]) ).

fof(f6395,plain,
    ( spl0_564
  <=> ! [X0,X1,X3] :
        ( ~ class_OrderedGroup_Omonoid__mult(X0)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_564])]) ).

fof(f537,axiom,
    ! [X3,X0,X1] :
      ( ~ class_OrderedGroup_Omonoid__mult(X0)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__even__eq_0) ).

fof(f6393,plain,
    spl0_563,
    inference(avatar_split_clause,[],[f496,f6391]) ).

fof(f6391,plain,
    ( spl0_563
  <=> ! [X9,X0,X4] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X9
        | c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X9),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_563])]) ).

fof(f496,axiom,
    ! [X0,X9,X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X9
      | c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X9),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__power2__eq__zero__iff_1) ).

fof(f6389,plain,
    spl0_562,
    inference(avatar_split_clause,[],[f495,f6387]) ).

fof(f6387,plain,
    ( spl0_562
  <=> ! [X4,X0,X9] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X4
        | c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X9),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_562])]) ).

fof(f495,axiom,
    ! [X0,X9,X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X4
      | c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X9),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__power2__eq__zero__iff_0) ).

fof(f6366,plain,
    ( spl0_561
    | ~ spl0_127
    | ~ spl0_247 ),
    inference(avatar_split_clause,[],[f2372,f2210,f1465,f6363]) ).

fof(f6363,plain,
    ( spl0_561
  <=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_561])]) ).

fof(f2372,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)
    | ~ spl0_127
    | ~ spl0_247 ),
    inference(superposition,[],[f1466,f2212]) ).

fof(f6312,plain,
    spl0_560,
    inference(avatar_split_clause,[],[f538,f6310]) ).

fof(f538,axiom,
    ! [X21,X1] :
      ( ~ c_HOL_Oord__class_Oless(X21,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat)
      | c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),X1,X21) = hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,X1),X21) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc_Ohyps_0) ).

fof(f6308,plain,
    spl0_559,
    inference(avatar_split_clause,[],[f506,f6306]) ).

fof(f6306,plain,
    ( spl0_559
  <=> ! [X0] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ozero__class_Ozero(X0)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ozero__class_Ozero(X0)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_559])]) ).

fof(f506,axiom,
    ! [X0] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ozero__class_Ozero(X0)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ozero__class_Ozero(X0)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__power2__gt__zero__iff_0) ).

fof(f6304,plain,
    spl0_558,
    inference(avatar_split_clause,[],[f310,f6302]) ).

fof(f6302,plain,
    ( spl0_558
  <=> ! [X18,X4,X0,X9] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | ~ class_Ring__and__Field_Odivision__by__zero(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X9
        | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X18),X9)),X9,X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X18),c_HOL_Oinverse__class_Odivide(X4,X9,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_558])]) ).

fof(f310,axiom,
    ! [X0,X18,X9,X4] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | ~ class_Ring__and__Field_Odivision__by__zero(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X9
      | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X18),X9)),X9,X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X18),c_HOL_Oinverse__class_Odivide(X4,X9,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__num__frac_0) ).

fof(f6300,plain,
    spl0_557,
    inference(avatar_split_clause,[],[f309,f6298]) ).

fof(f6298,plain,
    ( spl0_557
  <=> ! [X18,X4,X0,X9] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | ~ class_Ring__and__Field_Odivision__by__zero(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X9
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oinverse__class_Odivide(X4,X9,X0)),X18) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X18),X9)),X9,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_557])]) ).

fof(f309,axiom,
    ! [X0,X18,X9,X4] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | ~ class_Ring__and__Field_Odivision__by__zero(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X9
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oinverse__class_Odivide(X4,X9,X0)),X18) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X18),X9)),X9,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__frac__num_0) ).

fof(f6296,plain,
    spl0_556,
    inference(avatar_split_clause,[],[f121,f6294]) ).

fof(f6294,plain,
    ( spl0_556
  <=> ! [X18,X4,X11,X0,X9] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X9
        | c_HOL_Ozero__class_Ozero(X0) = X18
        | c_HOL_Oinverse__class_Odivide(X4,X9,X0) = c_HOL_Oinverse__class_Odivide(X11,X18,X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X18) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X11),X9) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_556])]) ).

fof(f121,axiom,
    ! [X0,X11,X18,X9,X4] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X9
      | c_HOL_Ozero__class_Ozero(X0) = X18
      | c_HOL_Oinverse__class_Odivide(X4,X9,X0) = c_HOL_Oinverse__class_Odivide(X11,X18,X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X18) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X11),X9) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_frac__eq__eq_1) ).

fof(f6292,plain,
    ( spl0_555
    | ~ spl0_91
    | ~ spl0_186 ),
    inference(avatar_split_clause,[],[f1886,f1804,f1298,f6290]) ).

fof(f6290,plain,
    ( spl0_555
  <=> ! [X0] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_555])]) ).

fof(f1804,plain,
    ( spl0_186
  <=> ! [X0,X1] :
        ( ~ class_OrderedGroup_Omonoid__mult(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oone__class_Oone(X0)),X1) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).

fof(f1886,plain,
    ( ! [X0] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),X0) = X0
    | ~ spl0_91
    | ~ spl0_186 ),
    inference(resolution,[],[f1805,f1300]) ).

fof(f1805,plain,
    ( ! [X0,X1] :
        ( ~ class_OrderedGroup_Omonoid__mult(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oone__class_Oone(X0)),X1) = X1 )
    | ~ spl0_186 ),
    inference(avatar_component_clause,[],[f1804]) ).

fof(f6288,plain,
    spl0_554,
    inference(avatar_split_clause,[],[f120,f6286]) ).

fof(f6286,plain,
    ( spl0_554
  <=> ! [X18,X4,X11,X0,X9] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X9
        | c_HOL_Ozero__class_Ozero(X0) = X18
        | c_HOL_Oinverse__class_Odivide(X4,X9,X0) != c_HOL_Oinverse__class_Odivide(X11,X18,X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X18) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X11),X9) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_554])]) ).

fof(f120,axiom,
    ! [X0,X11,X18,X9,X4] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X9
      | c_HOL_Ozero__class_Ozero(X0) = X18
      | c_HOL_Oinverse__class_Odivide(X4,X9,X0) != c_HOL_Oinverse__class_Odivide(X11,X18,X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X18) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X11),X9) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_frac__eq__eq_0) ).

fof(f6265,plain,
    spl0_553,
    inference(avatar_split_clause,[],[f623,f6263]) ).

fof(f6263,plain,
    ( spl0_553
  <=> ! [X18,X4,X11,X0,X9] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | ~ class_Ring__and__Field_Odivision__by__zero(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oinverse__class_Odivide(X4,X9,X0)),c_HOL_Oinverse__class_Odivide(X18,X11,X0)) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X18),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X9),X11),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_553])]) ).

fof(f623,axiom,
    ! [X0,X11,X18,X9,X4] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | ~ class_Ring__and__Field_Odivision__by__zero(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oinverse__class_Odivide(X4,X9,X0)),c_HOL_Oinverse__class_Odivide(X18,X11,X0)) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X18),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X9),X11),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__frac__frac_0) ).

fof(f6261,plain,
    spl0_552,
    inference(avatar_split_clause,[],[f497,f6259]) ).

fof(f6259,plain,
    ( spl0_552
  <=> ! [X0] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ozero__class_Ozero(X0)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ozero__class_Ozero(X0)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_552])]) ).

fof(f497,axiom,
    ! [X0] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ozero__class_Ozero(X0)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ozero__class_Ozero(X0)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__power2__eq__zero__iff_2) ).

fof(f6257,plain,
    spl0_551,
    inference(avatar_split_clause,[],[f340,f6255]) ).

fof(f6255,plain,
    ( spl0_551
  <=> ! [X0,X1,X3] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(X0),X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_551])]) ).

fof(f340,axiom,
    ! [X3,X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(X0),X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__Suc__less_0) ).

fof(f6242,plain,
    ( spl0_550
    | ~ spl0_57
    | ~ spl0_186 ),
    inference(avatar_split_clause,[],[f1885,f1804,f1128,f6240]) ).

fof(f6240,plain,
    ( spl0_550
  <=> ! [X0] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint)),X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_550])]) ).

fof(f1885,plain,
    ( ! [X0] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint)),X0) = X0
    | ~ spl0_57
    | ~ spl0_186 ),
    inference(resolution,[],[f1805,f1130]) ).

fof(f6134,plain,
    ( spl0_549
    | ~ spl0_20
    | ~ spl0_186 ),
    inference(avatar_split_clause,[],[f1884,f1804,f943,f6132]) ).

fof(f1884,plain,
    ( ! [X0] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X0) = X0
    | ~ spl0_20
    | ~ spl0_186 ),
    inference(resolution,[],[f1805,f945]) ).

fof(f6128,plain,
    spl0_548,
    inference(avatar_split_clause,[],[f609,f6126]) ).

fof(f6126,plain,
    ( spl0_548
  <=> ! [X4,X0,X14,X9] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X9)),X14) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),X14)),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X9),X14)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_548])]) ).

fof(f609,axiom,
    ! [X0,X9,X14,X4] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X9)),X14) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),X14)),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X9),X14)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__mul_0) ).

fof(f6124,plain,
    spl0_547,
    inference(avatar_split_clause,[],[f608,f6122]) ).

fof(f6122,plain,
    ( spl0_547
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2)),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_547])]) ).

fof(f608,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2)),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__mult__distrib_0) ).

fof(f6120,plain,
    spl0_546,
    inference(avatar_split_clause,[],[f597,f6118]) ).

fof(f6118,plain,
    ( spl0_546
  <=> ! [X0,X6,X2,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2)),X6) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X6)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X6)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_546])]) ).

fof(f597,axiom,
    ! [X2,X0,X1,X6] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2)),X6) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X6)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X6)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I8_J_0) ).

fof(f6116,plain,
    spl0_545,
    inference(avatar_split_clause,[],[f595,f6114]) ).

fof(f6114,plain,
    ( spl0_545
  <=> ! [X0,X33,X2,X1] :
        ( ~ class_RealVector_Oreal__normed__algebra(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X33)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X33)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_545])]) ).

fof(f595,axiom,
    ! [X2,X0,X1,X33] :
      ( ~ class_RealVector_Oreal__normed__algebra(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X33)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X33)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Oadd__right_0) ).

fof(f6112,plain,
    spl0_544,
    inference(avatar_split_clause,[],[f594,f6110]) ).

fof(f6110,plain,
    ( spl0_544
  <=> ! [X35,X4,X0,X9] :
        ( ~ class_RealVector_Oreal__normed__algebra(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X4),X9)),X35) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X35)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X9),X35)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_544])]) ).

fof(f594,axiom,
    ! [X0,X9,X4,X35] :
      ( ~ class_RealVector_Oreal__normed__algebra(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X4),X9)),X35) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X35)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X9),X35)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Oadd_0) ).

fof(f6108,plain,
    spl0_543,
    inference(avatar_split_clause,[],[f516,f6106]) ).

fof(f6106,plain,
    ( spl0_543
  <=> ! [X0,X6,X2,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2)),X6) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X6)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X6)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_543])]) ).

fof(f516,axiom,
    ! [X2,X0,X1,X6] :
      ( ~ class_Ring__and__Field_Ocomm__semiring(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2)),X6) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X6)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X6)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__semiring__class_Odistrib_0) ).

fof(f6104,plain,
    spl0_542,
    inference(avatar_split_clause,[],[f515,f6102]) ).

fof(f6102,plain,
    ( spl0_542
  <=> ! [X18,X4,X0,X9] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X9),X18)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X9)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X18)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_542])]) ).

fof(f515,axiom,
    ! [X0,X18,X9,X4] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X9),X18)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X9)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X18)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__d_0) ).

fof(f6100,plain,
    spl0_541,
    inference(avatar_split_clause,[],[f503,f6098]) ).

fof(f6098,plain,
    ( spl0_541
  <=> ! [X9,X0,X4] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X9),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_541])]) ).

fof(f503,axiom,
    ! [X0,X9,X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X9),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__sum__power2__lt__zero_0) ).

fof(f6096,plain,
    ( spl0_540
    | ~ spl0_91
    | ~ spl0_185 ),
    inference(avatar_split_clause,[],[f1883,f1800,f1298,f6094]) ).

fof(f6094,plain,
    ( spl0_540
  <=> ! [X0] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_540])]) ).

fof(f1800,plain,
    ( spl0_185
  <=> ! [X0,X1] :
        ( ~ class_OrderedGroup_Omonoid__mult(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),c_HOL_Oone__class_Oone(X0)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).

fof(f1883,plain,
    ( ! [X0] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)) = X0
    | ~ spl0_91
    | ~ spl0_185 ),
    inference(resolution,[],[f1801,f1300]) ).

fof(f1801,plain,
    ( ! [X0,X1] :
        ( ~ class_OrderedGroup_Omonoid__mult(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),c_HOL_Oone__class_Oone(X0)) = X1 )
    | ~ spl0_185 ),
    inference(avatar_component_clause,[],[f1800]) ).

fof(f6092,plain,
    spl0_539,
    inference(avatar_split_clause,[],[f379,f6090]) ).

fof(f6090,plain,
    ( spl0_539
  <=> ! [X20,X8,X3] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat)
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X8),X3))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X8),X20)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(X3)),X20) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_539])]) ).

fof(f379,axiom,
    ! [X3,X8,X20] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat)
      | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X8),X3))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X8),X20)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(X3)),X20) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_root__cancel_0) ).

fof(f6088,plain,
    spl0_538,
    inference(avatar_split_clause,[],[f375,f6086]) ).

fof(f6086,plain,
    ( spl0_538
  <=> ! [X31,X0,X3,X1] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_HOL_Oord__class_Oless(X3,X31,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(X0),X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X31),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_538])]) ).

fof(f375,axiom,
    ! [X31,X3,X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | ~ c_HOL_Oord__class_Oless(X3,X31,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(X0),X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X31),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__decreasing_0) ).

fof(f6084,plain,
    spl0_537,
    inference(avatar_split_clause,[],[f318,f6082]) ).

fof(f6082,plain,
    ( spl0_537
  <=> ! [X0,X1,X3] :
        ( ~ class_Ring__and__Field_Oring__1(X0)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ouminus__class_Ouminus(X1,X0)),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0)),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_537])]) ).

fof(f318,axiom,
    ! [X3,X0,X1] :
      ( ~ class_Ring__and__Field_Oring__1(X0)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ouminus__class_Ouminus(X1,X0)),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0)),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__minus_0) ).

fof(f6080,plain,
    spl0_536,
    inference(avatar_split_clause,[],[f211,f6078]) ).

fof(f6078,plain,
    ( spl0_536
  <=> ! [X2,X0,X1,X6,X16,X17,X15,X12,X13] :
        ( ~ c_Groebner__Basis_Ogb__semiring(X15,X13,X12,X16,X17,X0)
        | hAPP(hAPP(X13,hAPP(hAPP(X15,X1),X2)),X6) = hAPP(hAPP(X15,hAPP(hAPP(X13,X1),X6)),hAPP(hAPP(X13,X2),X6)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_536])]) ).

fof(f211,axiom,
    ! [X2,X0,X1,X6,X16,X17,X15,X12,X13] :
      ( ~ c_Groebner__Basis_Ogb__semiring(X15,X13,X12,X16,X17,X0)
      | hAPP(hAPP(X13,hAPP(hAPP(X15,X1),X2)),X6) = hAPP(hAPP(X15,hAPP(hAPP(X13,X1),X6)),hAPP(hAPP(X13,X2),X6)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I8_J_0) ).

fof(f6076,plain,
    spl0_535,
    inference(avatar_split_clause,[],[f143,f6074]) ).

fof(f6074,plain,
    ( spl0_535
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X2
        | hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Oinverse__class_Odivide(X1,X2,X0)),X3) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_535])]) ).

fof(f143,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X2
      | hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Oinverse__class_Odivide(X1,X2,X0)),X3) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X3),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__power__divide_0) ).

fof(f6072,plain,
    spl0_534,
    inference(avatar_split_clause,[],[f86,f6070]) ).

fof(f6070,plain,
    ( spl0_534
  <=> ! [X0,X18,X9,X16,X4,X17,X15,X12,X13] :
        ( ~ c_Groebner__Basis_Ogb__semiring(X15,X13,X12,X16,X17,X0)
        | hAPP(hAPP(X13,X4),hAPP(hAPP(X15,X9),X18)) = hAPP(hAPP(X15,hAPP(hAPP(X13,X4),X9)),hAPP(hAPP(X13,X4),X18)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_534])]) ).

fof(f86,axiom,
    ! [X0,X18,X9,X16,X4,X17,X15,X12,X13] :
      ( ~ c_Groebner__Basis_Ogb__semiring(X15,X13,X12,X16,X17,X0)
      | hAPP(hAPP(X13,X4),hAPP(hAPP(X15,X9),X18)) = hAPP(hAPP(X15,hAPP(hAPP(X13,X4),X9)),hAPP(hAPP(X13,X4),X18)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Omul__d_0) ).

fof(f6068,plain,
    spl0_533,
    inference(avatar_split_clause,[],[f85,f6066]) ).

fof(f6066,plain,
    ( spl0_533
  <=> ! [X0,X9,X16,X14,X4,X17,X15,X12,X13] :
        ( ~ c_Groebner__Basis_Ogb__semiring(X15,X13,X12,X16,X17,X0)
        | hAPP(hAPP(X12,hAPP(hAPP(X13,X4),X9)),X14) = hAPP(hAPP(X13,hAPP(hAPP(X12,X4),X14)),hAPP(hAPP(X12,X9),X14)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_533])]) ).

fof(f85,axiom,
    ! [X0,X9,X16,X14,X4,X17,X15,X12,X13] :
      ( ~ c_Groebner__Basis_Ogb__semiring(X15,X13,X12,X16,X17,X0)
      | hAPP(hAPP(X12,hAPP(hAPP(X13,X4),X9)),X14) = hAPP(hAPP(X13,hAPP(hAPP(X12,X4),X14)),hAPP(hAPP(X12,X9),X14)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Opwr__mul_0) ).

fof(f6054,plain,
    spl0_532,
    inference(avatar_split_clause,[],[f406,f6052]) ).

fof(f6052,plain,
    ( spl0_532
  <=> ! [X0,X8,X6,X2,X1] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X8),X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ominus__class_Ominus(X1,X2,X0)),c_HOL_Ominus__class_Ominus(X6,X8,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_532])]) ).

fof(f406,axiom,
    ! [X2,X0,X1,X8,X6] :
      ( ~ class_OrderedGroup_Oab__group__add(X0)
      | c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X8),X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ominus__class_Ominus(X1,X2,X0)),c_HOL_Ominus__class_Ominus(X6,X8,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Deriv_Oadd__diff__add_0) ).

fof(f6049,plain,
    ( spl0_531
    | ~ spl0_57
    | ~ spl0_185 ),
    inference(avatar_split_clause,[],[f1882,f1800,f1128,f6047]) ).

fof(f6047,plain,
    ( spl0_531
  <=> ! [X0] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),X0),c_HOL_Oone__class_Oone(tc_Int_Oint)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_531])]) ).

fof(f1882,plain,
    ( ! [X0] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),X0),c_HOL_Oone__class_Oone(tc_Int_Oint)) = X0
    | ~ spl0_57
    | ~ spl0_185 ),
    inference(resolution,[],[f1801,f1130]) ).

fof(f6018,plain,
    spl0_530,
    inference(avatar_split_clause,[],[f636,f6016]) ).

fof(f6016,plain,
    ( spl0_530
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | ~ class_Ring__and__Field_Odivision__by__zero(X0)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Oinverse__class_Odivide(X1,X2,X0)),X3) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_530])]) ).

fof(f636,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | ~ class_Ring__and__Field_Odivision__by__zero(X0)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Oinverse__class_Odivide(X1,X2,X0)),X3) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X3),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__divide_0) ).

fof(f6014,plain,
    spl0_529,
    inference(avatar_split_clause,[],[f541,f6012]) ).

fof(f6012,plain,
    ( spl0_529
  <=> ! [X18,X4,X0,X9,X39] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X4),X18) = X39
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X9),X18)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X9),X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_529])]) ).

fof(f541,axiom,
    ! [X39,X0,X18,X9,X4] :
      ( ~ class_OrderedGroup_Oab__group__add(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X4),X18) = X39
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X9),X18)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X9),X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).

fof(f6010,plain,
    spl0_528,
    inference(avatar_split_clause,[],[f510,f6008]) ).

fof(f6008,plain,
    ( spl0_528
  <=> ! [X0,X1,X3] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X3))),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_528])]) ).

fof(f510,axiom,
    ! [X3,X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X3))),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_odd__power__less__zero_0) ).

fof(f6006,plain,
    spl0_527,
    inference(avatar_split_clause,[],[f330,f6004]) ).

fof(f6004,plain,
    ( spl0_527
  <=> ! [X11,X0,X6,X2] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | ~ class_Ring__and__Field_Odivision__by__zero(X0)
        | ~ class_Int_Onumber(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X6
        | c_HOL_Oinverse__class_Odivide(X2,X6,X0) != c_Int_Onumber__class_Onumber__of(X11,X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_Int_Onumber__class_Onumber__of(X11,X0)),X6) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_527])]) ).

fof(f330,axiom,
    ! [X2,X0,X11,X6] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | ~ class_Ring__and__Field_Odivision__by__zero(X0)
      | ~ class_Int_Onumber(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X6
      | c_HOL_Oinverse__class_Odivide(X2,X6,X0) != c_Int_Onumber__class_Onumber__of(X11,X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_Int_Onumber__class_Onumber__of(X11,X0)),X6) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of_0) ).

fof(f5996,plain,
    ( spl0_526
    | ~ spl0_20
    | ~ spl0_185 ),
    inference(avatar_split_clause,[],[f1881,f1800,f943,f5994]) ).

fof(f1881,plain,
    ( ! [X0] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),c_HOL_Oone__class_Oone(tc_nat)) = X0
    | ~ spl0_20
    | ~ spl0_185 ),
    inference(resolution,[],[f1801,f945]) ).

fof(f5991,plain,
    spl0_525,
    inference(avatar_split_clause,[],[f513,f5989]) ).

fof(f5989,plain,
    ( spl0_525
  <=> ! [X0,X3] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
        | c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0)),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X3))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_525])]) ).

fof(f513,axiom,
    ! [X3,X0] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
      | c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0)),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X3))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__minus1__odd_0) ).

fof(f5987,plain,
    spl0_524,
    inference(avatar_split_clause,[],[f487,f5985]) ).

fof(f5985,plain,
    ( spl0_524
  <=> ! [X38,X0,X16,X14,X4,X17,X15,X12,X13] :
        ( ~ c_Groebner__Basis_Ogb__semiring(X15,X13,X12,X16,X17,X0)
        | hAPP(hAPP(X12,hAPP(hAPP(X12,X4),X38)),X14) = hAPP(hAPP(X12,X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X38),X14)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_524])]) ).

fof(f487,axiom,
    ! [X38,X0,X16,X14,X4,X17,X15,X12,X13] :
      ( ~ c_Groebner__Basis_Ogb__semiring(X15,X13,X12,X16,X17,X0)
      | hAPP(hAPP(X12,hAPP(hAPP(X12,X4),X38)),X14) = hAPP(hAPP(X12,X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X38),X14)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Opwr__pwr_0) ).

fof(f5983,plain,
    spl0_523,
    inference(avatar_split_clause,[],[f112,f5981]) ).

fof(f5981,plain,
    ( spl0_523
  <=> ! [X0,X6,X2,X1] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | ~ class_Ring__and__Field_Odivision__by__zero(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X6
        | c_HOL_Oinverse__class_Odivide(X1,X2,X0) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X6),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X6),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_523])]) ).

fof(f112,axiom,
    ! [X2,X0,X1,X6] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | ~ class_Ring__and__Field_Odivision__by__zero(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X6
      | c_HOL_Oinverse__class_Odivide(X1,X2,X0) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X6),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X6),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__divide__mult__cancel__right_0) ).

fof(f5979,plain,
    spl0_522,
    inference(avatar_split_clause,[],[f111,f5977]) ).

fof(f5977,plain,
    ( spl0_522
  <=> ! [X0,X6,X2,X1] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | ~ class_Ring__and__Field_Odivision__by__zero(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X6
        | c_HOL_Oinverse__class_Odivide(X1,X2,X0) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X6),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X6),X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_522])]) ).

fof(f111,axiom,
    ! [X2,X0,X1,X6] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | ~ class_Ring__and__Field_Odivision__by__zero(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X6
      | c_HOL_Oinverse__class_Odivide(X1,X2,X0) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X6),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X6),X2),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__divide__mult__cancel__left_0) ).

fof(f5931,plain,
    ( spl0_521
    | ~ spl0_93
    | ~ spl0_175 ),
    inference(avatar_split_clause,[],[f1835,f1760,f1308,f5929]) ).

fof(f5929,plain,
    ( spl0_521
  <=> ! [X0] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_521])]) ).

fof(f1308,plain,
    ( spl0_93
  <=> class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).

fof(f1760,plain,
    ( spl0_175
  <=> ! [X0,X1] :
        ( ~ class_OrderedGroup_Omonoid__add(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0)),X1) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).

fof(f1835,plain,
    ( ! [X0] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),X0) = X0
    | ~ spl0_93
    | ~ spl0_175 ),
    inference(resolution,[],[f1761,f1310]) ).

fof(f1310,plain,
    ( class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex)
    | ~ spl0_93 ),
    inference(avatar_component_clause,[],[f1308]) ).

fof(f1761,plain,
    ( ! [X0,X1] :
        ( ~ class_OrderedGroup_Omonoid__add(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0)),X1) = X1 )
    | ~ spl0_175 ),
    inference(avatar_component_clause,[],[f1760]) ).

fof(f5877,plain,
    ( spl0_520
    | ~ spl0_59
    | ~ spl0_175 ),
    inference(avatar_split_clause,[],[f1834,f1760,f1138,f5875]) ).

fof(f5875,plain,
    ( spl0_520
  <=> ! [X0] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_520])]) ).

fof(f1138,plain,
    ( spl0_59
  <=> class_OrderedGroup_Omonoid__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).

fof(f1834,plain,
    ( ! [X0] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),X0) = X0
    | ~ spl0_59
    | ~ spl0_175 ),
    inference(resolution,[],[f1761,f1140]) ).

fof(f1140,plain,
    ( class_OrderedGroup_Omonoid__add(tc_Int_Oint)
    | ~ spl0_59 ),
    inference(avatar_component_clause,[],[f1138]) ).

fof(f5779,plain,
    spl0_519,
    inference(avatar_split_clause,[],[f838,f5777]) ).

fof(f5777,plain,
    ( spl0_519
  <=> ! [X19,X3] :
        ( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X19),X3),tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat),X19,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat),X3,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_519])]) ).

fof(f838,plain,
    ! [X3,X19] :
      ( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X19),X3),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat),X19,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat),X3,tc_nat) ),
    inference(forward_demodulation,[],[f837,f377]) ).

fof(f377,axiom,
    hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_numeral__1__eq__Suc__0_0) ).

fof(f837,plain,
    ! [X3,X19] :
      ( ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat),X19,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat),X3,tc_nat)
      | c_HOL_Oord__class_Oless(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X19),X3),tc_nat) ),
    inference(forward_demodulation,[],[f836,f377]) ).

fof(f836,plain,
    ! [X3,X19] :
      ( ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat),X3,tc_nat)
      | ~ c_HOL_Oord__class_Oless(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),X19,tc_nat)
      | c_HOL_Oord__class_Oless(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X19),X3),tc_nat) ),
    inference(forward_demodulation,[],[f333,f377]) ).

fof(f333,axiom,
    ! [X3,X19] :
      ( ~ c_HOL_Oord__class_Oless(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_nat)
      | ~ c_HOL_Oord__class_Oless(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),X19,tc_nat)
      | c_HOL_Oord__class_Oless(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X19),X3),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__less__mult_0) ).

fof(f5775,plain,
    spl0_518,
    inference(avatar_split_clause,[],[f618,f5773]) ).

fof(f5773,plain,
    ( spl0_518
  <=> ! [X0,X1,X3] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_518])]) ).

fof(f618,axiom,
    ! [X3,X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__power__Suc_0) ).

fof(f5771,plain,
    spl0_517,
    inference(avatar_split_clause,[],[f564,f5769]) ).

fof(f5769,plain,
    ( spl0_517
  <=> ! [X0,X1,X19] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),c_HOL_Oone__class_Oone(X0))),X19) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X19),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X19)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_517])]) ).

fof(f564,axiom,
    ! [X0,X1,X19] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),c_HOL_Oone__class_Oone(X0))),X19) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X19),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X19)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I3_J_0) ).

fof(f5767,plain,
    spl0_516,
    inference(avatar_split_clause,[],[f563,f5765]) ).

fof(f5765,plain,
    ( spl0_516
  <=> ! [X0,X1,X19] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X19)),X19) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),c_HOL_Oone__class_Oone(X0))),X19) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_516])]) ).

fof(f563,axiom,
    ! [X0,X1,X19] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X19)),X19) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),c_HOL_Oone__class_Oone(X0))),X19) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I2_J_0) ).

fof(f5763,plain,
    spl0_515,
    inference(avatar_split_clause,[],[f395,f5761]) ).

fof(f5761,plain,
    ( spl0_515
  <=> ! [X34,X0,X2,X1] :
        ( ~ class_RealVector_Oreal__normed__algebra(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ominus__class_Ominus(X1,X34,X0)),X2) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X34),X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_515])]) ).

fof(f395,axiom,
    ! [X2,X0,X1,X34] :
      ( ~ class_RealVector_Oreal__normed__algebra(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ominus__class_Ominus(X1,X34,X0)),X2) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X34),X2),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Odiff__left_0) ).

fof(f5759,plain,
    spl0_514,
    inference(avatar_split_clause,[],[f293,f5757]) ).

fof(f5757,plain,
    ( spl0_514
  <=> ! [X4,X9,X0,X29] :
        ( ~ class_RealVector_Oreal__normed__algebra(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X29),c_HOL_Ominus__class_Ominus(X4,X9,X0)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X29),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X29),X9),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_514])]) ).

fof(f293,axiom,
    ! [X0,X29,X9,X4] :
      ( ~ class_RealVector_Oreal__normed__algebra(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X29),c_HOL_Ominus__class_Ominus(X4,X9,X0)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X29),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X29),X9),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Odiff_0) ).

fof(f5755,plain,
    ( spl0_513
    | ~ spl0_22
    | ~ spl0_175 ),
    inference(avatar_split_clause,[],[f1833,f1760,f953,f5753]) ).

fof(f5753,plain,
    ( spl0_513
  <=> ! [X0] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_513])]) ).

fof(f953,plain,
    ( spl0_22
  <=> class_OrderedGroup_Omonoid__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).

fof(f1833,plain,
    ( ! [X0] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X0) = X0
    | ~ spl0_22
    | ~ spl0_175 ),
    inference(resolution,[],[f1761,f955]) ).

fof(f955,plain,
    ( class_OrderedGroup_Omonoid__add(tc_nat)
    | ~ spl0_22 ),
    inference(avatar_component_clause,[],[f953]) ).

fof(f5751,plain,
    spl0_512,
    inference(avatar_split_clause,[],[f217,f5749]) ).

fof(f5749,plain,
    ( spl0_512
  <=> ! [X15,X17,X19,X0,X13,X12,X16,X1] :
        ( ~ c_Groebner__Basis_Ogb__semiring(X15,X13,X12,X16,X17,X0)
        | hAPP(hAPP(X13,hAPP(hAPP(X15,X1),X17)),X19) = hAPP(hAPP(X15,hAPP(hAPP(X13,X1),X19)),X19) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_512])]) ).

fof(f217,axiom,
    ! [X0,X1,X19,X16,X17,X15,X12,X13] :
      ( ~ c_Groebner__Basis_Ogb__semiring(X15,X13,X12,X16,X17,X0)
      | hAPP(hAPP(X13,hAPP(hAPP(X15,X1),X17)),X19) = hAPP(hAPP(X15,hAPP(hAPP(X13,X1),X19)),X19) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I2_J_0) ).

fof(f5747,plain,
    spl0_511,
    inference(avatar_split_clause,[],[f216,f5745]) ).

fof(f5745,plain,
    ( spl0_511
  <=> ! [X15,X17,X19,X0,X13,X12,X16,X1] :
        ( ~ c_Groebner__Basis_Ogb__semiring(X15,X13,X12,X16,X17,X0)
        | hAPP(hAPP(X15,X19),hAPP(hAPP(X13,X1),X19)) = hAPP(hAPP(X13,hAPP(hAPP(X15,X1),X17)),X19) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_511])]) ).

fof(f216,axiom,
    ! [X0,X1,X19,X16,X17,X15,X12,X13] :
      ( ~ c_Groebner__Basis_Ogb__semiring(X15,X13,X12,X16,X17,X0)
      | hAPP(hAPP(X15,X19),hAPP(hAPP(X13,X1),X19)) = hAPP(hAPP(X13,hAPP(hAPP(X15,X1),X17)),X19) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I3_J_0) ).

fof(f5743,plain,
    spl0_510,
    inference(avatar_split_clause,[],[f203,f5741]) ).

fof(f5741,plain,
    ( spl0_510
  <=> ! [X16,X0,X26,X24,X17,X15,X12,X23,X13] :
        ( ~ c_Groebner__Basis_Ogb__semiring(X15,X13,X12,X16,X17,X0)
        | hAPP(hAPP(X13,hAPP(hAPP(X13,X23),X26)),X24) = hAPP(hAPP(X13,hAPP(hAPP(X13,X23),X24)),X26) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_510])]) ).

fof(f203,axiom,
    ! [X0,X26,X16,X17,X15,X24,X12,X23,X13] :
      ( ~ c_Groebner__Basis_Ogb__semiring(X15,X13,X12,X16,X17,X0)
      | hAPP(hAPP(X13,hAPP(hAPP(X13,X23),X26)),X24) = hAPP(hAPP(X13,hAPP(hAPP(X13,X23),X24)),X26) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I16_J_0) ).

fof(f5739,plain,
    spl0_509,
    inference(avatar_split_clause,[],[f201,f5737]) ).

fof(f5737,plain,
    ( spl0_509
  <=> ! [X0,X24,X16,X25,X17,X15,X12,X23,X13] :
        ( ~ c_Groebner__Basis_Ogb__semiring(X15,X13,X12,X16,X17,X0)
        | hAPP(hAPP(X13,X23),hAPP(hAPP(X13,X24),X25)) = hAPP(hAPP(X13,hAPP(hAPP(X13,X23),X24)),X25) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_509])]) ).

fof(f201,axiom,
    ! [X0,X16,X17,X15,X24,X12,X23,X13,X25] :
      ( ~ c_Groebner__Basis_Ogb__semiring(X15,X13,X12,X16,X17,X0)
      | hAPP(hAPP(X13,X23),hAPP(hAPP(X13,X24),X25)) = hAPP(hAPP(X13,hAPP(hAPP(X13,X23),X24)),X25) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I18_J_0) ).

fof(f5735,plain,
    spl0_508,
    inference(avatar_split_clause,[],[f200,f5733]) ).

fof(f5733,plain,
    ( spl0_508
  <=> ! [X0,X24,X16,X25,X17,X15,X12,X23,X13] :
        ( ~ c_Groebner__Basis_Ogb__semiring(X15,X13,X12,X16,X17,X0)
        | hAPP(hAPP(X13,X23),hAPP(hAPP(X13,X24),X25)) = hAPP(hAPP(X13,X24),hAPP(hAPP(X13,X23),X25)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_508])]) ).

fof(f200,axiom,
    ! [X0,X16,X17,X15,X24,X12,X23,X13,X25] :
      ( ~ c_Groebner__Basis_Ogb__semiring(X15,X13,X12,X16,X17,X0)
      | hAPP(hAPP(X13,X23),hAPP(hAPP(X13,X24),X25)) = hAPP(hAPP(X13,X24),hAPP(hAPP(X13,X23),X25)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I19_J_0) ).

fof(f5731,plain,
    spl0_507,
    inference(avatar_split_clause,[],[f197,f5729]) ).

fof(f5729,plain,
    ( spl0_507
  <=> ! [X0,X1,X8,X6,X16,X17,X15,X12,X13] :
        ( ~ c_Groebner__Basis_Ogb__semiring(X15,X13,X12,X16,X17,X0)
        | hAPP(hAPP(X15,X1),hAPP(hAPP(X15,X6),X8)) = hAPP(hAPP(X15,X6),hAPP(hAPP(X15,X1),X8)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_507])]) ).

fof(f197,axiom,
    ! [X0,X1,X8,X6,X16,X17,X15,X12,X13] :
      ( ~ c_Groebner__Basis_Ogb__semiring(X15,X13,X12,X16,X17,X0)
      | hAPP(hAPP(X15,X1),hAPP(hAPP(X15,X6),X8)) = hAPP(hAPP(X15,X6),hAPP(hAPP(X15,X1),X8)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I22_J_0) ).

fof(f5727,plain,
    spl0_506,
    inference(avatar_split_clause,[],[f196,f5725]) ).

fof(f5725,plain,
    ( spl0_506
  <=> ! [X2,X0,X1,X6,X16,X17,X15,X12,X13] :
        ( ~ c_Groebner__Basis_Ogb__semiring(X15,X13,X12,X16,X17,X0)
        | hAPP(hAPP(X15,hAPP(hAPP(X15,X1),X2)),X6) = hAPP(hAPP(X15,hAPP(hAPP(X15,X1),X6)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_506])]) ).

fof(f196,axiom,
    ! [X2,X0,X1,X6,X16,X17,X15,X12,X13] :
      ( ~ c_Groebner__Basis_Ogb__semiring(X15,X13,X12,X16,X17,X0)
      | hAPP(hAPP(X15,hAPP(hAPP(X15,X1),X2)),X6) = hAPP(hAPP(X15,hAPP(hAPP(X15,X1),X6)),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I23_J_0) ).

fof(f5723,plain,
    spl0_505,
    inference(avatar_split_clause,[],[f175,f5721]) ).

fof(f5721,plain,
    ( spl0_505
  <=> ! [X0] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ozero__class_Ozero(X0)),c_HOL_Ozero__class_Ozero(X0))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ozero__class_Ozero(X0)),c_HOL_Ozero__class_Ozero(X0))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_505])]) ).

fof(f175,axiom,
    ! [X0] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ozero__class_Ozero(X0)),c_HOL_Ozero__class_Ozero(X0))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ozero__class_Ozero(X0)),c_HOL_Ozero__class_Ozero(X0))),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_0) ).

fof(f5719,plain,
    spl0_504,
    inference(avatar_split_clause,[],[f173,f5717]) ).

fof(f5717,plain,
    ( spl0_504
  <=> ! [X9,X0,X4] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X9
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X9),X9)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_504])]) ).

fof(f173,axiom,
    ! [X0,X9,X4] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X9
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X9),X9)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_2) ).

fof(f5715,plain,
    spl0_503,
    inference(avatar_split_clause,[],[f172,f5713]) ).

fof(f5713,plain,
    ( spl0_503
  <=> ! [X4,X0,X9] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X4
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X9),X9)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_503])]) ).

fof(f172,axiom,
    ! [X0,X9,X4] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X4
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X9),X9)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_1) ).

fof(f5711,plain,
    ( spl0_502
    | ~ spl0_93
    | ~ spl0_174 ),
    inference(avatar_split_clause,[],[f1832,f1756,f1308,f5709]) ).

fof(f5709,plain,
    ( spl0_502
  <=> ! [X0] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),X0),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_502])]) ).

fof(f1756,plain,
    ( spl0_174
  <=> ! [X0,X1] :
        ( ~ class_OrderedGroup_Omonoid__add(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),c_HOL_Ozero__class_Ozero(X0)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).

fof(f1832,plain,
    ( ! [X0] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),X0),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = X0
    | ~ spl0_93
    | ~ spl0_174 ),
    inference(resolution,[],[f1757,f1310]) ).

fof(f1757,plain,
    ( ! [X0,X1] :
        ( ~ class_OrderedGroup_Omonoid__add(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),c_HOL_Ozero__class_Ozero(X0)) = X1 )
    | ~ spl0_174 ),
    inference(avatar_component_clause,[],[f1756]) ).

fof(f5707,plain,
    spl0_501,
    inference(avatar_split_clause,[],[f92,f5705]) ).

fof(f5705,plain,
    ( spl0_501
  <=> ! [X0,X18,X9,X16,X4,X17,X15,X12,X13] :
        ( ~ c_Groebner__Basis_Ogb__semiring(X15,X13,X12,X16,X17,X0)
        | hAPP(hAPP(X15,X4),hAPP(hAPP(X15,X9),X18)) = hAPP(hAPP(X15,hAPP(hAPP(X15,X4),X9)),X18) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_501])]) ).

fof(f92,axiom,
    ! [X0,X18,X9,X16,X4,X17,X15,X12,X13] :
      ( ~ c_Groebner__Basis_Ogb__semiring(X15,X13,X12,X16,X17,X0)
      | hAPP(hAPP(X15,X4),hAPP(hAPP(X15,X9),X18)) = hAPP(hAPP(X15,hAPP(hAPP(X15,X4),X9)),X18) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Oadd__a_0) ).

fof(f5703,plain,
    spl0_500,
    inference(avatar_split_clause,[],[f38,f5701]) ).

fof(f5701,plain,
    ( spl0_500
  <=> ! [X0,X6,X2,X1] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X0),X0)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X6),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X6),X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_500])]) ).

fof(f38,axiom,
    ! [X2,X0,X1,X6] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X0),X0)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X6),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X6),X2),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_0) ).

fof(f5699,plain,
    spl0_499,
    inference(avatar_split_clause,[],[f37,f5697]) ).

fof(f5697,plain,
    ( spl0_499
  <=> ! [X0,X6,X2,X1] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X0),X0)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X6),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X6),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).

fof(f37,axiom,
    ! [X2,X0,X1,X6] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X0),X0)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X6),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X6),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_0) ).

fof(f5616,plain,
    ( spl0_498
    | ~ spl0_59
    | ~ spl0_174 ),
    inference(avatar_split_clause,[],[f1831,f1756,f1138,f5614]) ).

fof(f5614,plain,
    ( spl0_498
  <=> ! [X0] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),X0),c_HOL_Ozero__class_Ozero(tc_Int_Oint)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_498])]) ).

fof(f1831,plain,
    ( ! [X0] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),X0),c_HOL_Ozero__class_Ozero(tc_Int_Oint)) = X0
    | ~ spl0_59
    | ~ spl0_174 ),
    inference(resolution,[],[f1757,f1140]) ).

fof(f5551,plain,
    ( spl0_497
    | ~ spl0_22
    | ~ spl0_174 ),
    inference(avatar_split_clause,[],[f1830,f1756,f953,f5549]) ).

fof(f5549,plain,
    ( spl0_497
  <=> ! [X0] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_HOL_Ozero__class_Ozero(tc_nat)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_497])]) ).

fof(f1830,plain,
    ( ! [X0] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_HOL_Ozero__class_Ozero(tc_nat)) = X0
    | ~ spl0_22
    | ~ spl0_174 ),
    inference(resolution,[],[f1757,f955]) ).

fof(f5244,plain,
    ( spl0_496
    | ~ spl0_94
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1827,f1744,f1313,f5242]) ).

fof(f5242,plain,
    ( spl0_496
  <=> ! [X0] : c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).

fof(f1744,plain,
    ( spl0_171
  <=> ! [X0,X1] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ouminus__class_Ouminus(X1,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(X0),X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).

fof(f1827,plain,
    ( ! [X0] : c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex)
    | ~ spl0_94
    | ~ spl0_171 ),
    inference(resolution,[],[f1745,f1315]) ).

fof(f1745,plain,
    ( ! [X0,X1] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ouminus__class_Ouminus(X1,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(X0),X1,X0) )
    | ~ spl0_171 ),
    inference(avatar_component_clause,[],[f1744]) ).

fof(f5088,plain,
    spl0_495,
    inference(avatar_split_clause,[],[f673,f5086]) ).

fof(f5086,plain,
    ( spl0_495
  <=> ! [X0,X8,X6,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X6),X8)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X8)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).

fof(f673,axiom,
    ! [X0,X1,X8,X6] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X6),X8)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X8)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).

fof(f5084,plain,
    spl0_494,
    inference(avatar_split_clause,[],[f672,f5082]) ).

fof(f5082,plain,
    ( spl0_494
  <=> ! [X0,X6,X2,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2)),X6) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X6)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_494])]) ).

fof(f672,axiom,
    ! [X2,X0,X1,X6] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2)),X6) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X6)),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).

fof(f5080,plain,
    ( spl0_493
    | ~ spl0_60
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1826,f1744,f1143,f5078]) ).

fof(f5078,plain,
    ( spl0_493
  <=> ! [X0] : c_HOL_Ouminus__class_Ouminus(X0,tc_Int_Oint) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_Int_Oint),X0,tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_493])]) ).

fof(f1826,plain,
    ( ! [X0] : c_HOL_Ouminus__class_Ouminus(X0,tc_Int_Oint) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_Int_Oint),X0,tc_Int_Oint)
    | ~ spl0_60
    | ~ spl0_171 ),
    inference(resolution,[],[f1745,f1145]) ).

fof(f5076,plain,
    spl0_492,
    inference(avatar_split_clause,[],[f670,f5074]) ).

fof(f5074,plain,
    ( spl0_492
  <=> ! [X0,X6,X2,X1] :
        ( ~ class_OrderedGroup_Oab__semigroup__add(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X6)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2)),X6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_492])]) ).

fof(f670,axiom,
    ! [X2,X0,X1,X6] :
      ( ~ class_OrderedGroup_Oab__semigroup__add(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X6)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2)),X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).

fof(f5072,plain,
    spl0_491,
    inference(avatar_split_clause,[],[f669,f5070]) ).

fof(f5070,plain,
    ( spl0_491
  <=> ! [X18,X4,X0,X9] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X9),X18)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X4),X18)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).

fof(f669,axiom,
    ! [X0,X18,X9,X4] :
      ( ~ class_OrderedGroup_Oab__group__add(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X9),X18)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X4),X18)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).

fof(f5068,plain,
    spl0_490,
    inference(avatar_split_clause,[],[f668,f5066]) ).

fof(f5066,plain,
    ( spl0_490
  <=> ! [X18,X4,X0,X9] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X9),X18)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X4),X9)),X18) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_490])]) ).

fof(f668,axiom,
    ! [X0,X18,X9,X4] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X9),X18)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X4),X9)),X18) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).

fof(f5064,plain,
    spl0_489,
    inference(avatar_split_clause,[],[f667,f5062]) ).

fof(f5062,plain,
    ( spl0_489
  <=> ! [X0,X6,X2,X1] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X6)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2)),X6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).

fof(f667,axiom,
    ! [X2,X0,X1,X6] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X6)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2)),X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).

fof(f5060,plain,
    spl0_488,
    inference(avatar_split_clause,[],[f666,f5058]) ).

fof(f5058,plain,
    ( spl0_488
  <=> ! [X0,X6,X2,X1] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X6)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X6)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_488])]) ).

fof(f666,axiom,
    ! [X2,X0,X1,X6] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X6)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X6)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).

fof(f5056,plain,
    spl0_487,
    inference(avatar_split_clause,[],[f656,f5054]) ).

fof(f5054,plain,
    ( spl0_487
  <=> ! [X38,X4,X0,X14] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),X38)),X14) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X38),X14)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_487])]) ).

fof(f656,axiom,
    ! [X38,X0,X14,X4] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),X38)),X14) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X38),X14)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__pwr_0) ).

fof(f5052,plain,
    spl0_486,
    inference(avatar_split_clause,[],[f652,f5050]) ).

fof(f5050,plain,
    ( spl0_486
  <=> ! [X0,X1,X3] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | ~ class_Ring__and__Field_Odivision__by__zero(X0)
        | c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X1,X0)),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_486])]) ).

fof(f652,axiom,
    ! [X3,X0,X1] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | ~ class_Ring__and__Field_Odivision__by__zero(X0)
      | c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X1,X0)),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__one__over_0) ).

fof(f5048,plain,
    spl0_485,
    inference(avatar_split_clause,[],[f605,f5046]) ).

fof(f5046,plain,
    ( spl0_485
  <=> ! [X0,X6,X2,X1] :
        ( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2)),X6) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X6)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_485])]) ).

fof(f605,axiom,
    ! [X2,X0,X1,X6] :
      ( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2)),X6) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X6)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).

fof(f5044,plain,
    spl0_484,
    inference(avatar_split_clause,[],[f604,f5042]) ).

fof(f5042,plain,
    ( spl0_484
  <=> ! [X24,X0,X23,X26] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X23),X26)),X24) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X23),X24)),X26) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_484])]) ).

fof(f604,axiom,
    ! [X0,X26,X24,X23] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X23),X26)),X24) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X23),X24)),X26) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).

fof(f5040,plain,
    spl0_483,
    inference(avatar_split_clause,[],[f602,f5038]) ).

fof(f5038,plain,
    ( spl0_483
  <=> ! [X24,X0,X23,X25] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X23),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X24),X25)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X23),X24)),X25) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_483])]) ).

fof(f602,axiom,
    ! [X0,X24,X25,X23] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X23),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X24),X25)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X23),X24)),X25) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I18_J_0) ).

fof(f5015,plain,
    spl0_482,
    inference(avatar_split_clause,[],[f601,f5013]) ).

fof(f5013,plain,
    ( spl0_482
  <=> ! [X24,X0,X23,X25] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X23),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X24),X25)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X24),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X23),X25)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_482])]) ).

fof(f601,axiom,
    ! [X0,X24,X25,X23] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X23),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X24),X25)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X24),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X23),X25)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).

fof(f5011,plain,
    spl0_481,
    inference(avatar_split_clause,[],[f589,f5009]) ).

fof(f5009,plain,
    ( spl0_481
  <=> ! [X0,X3,X19,X1] :
        ( ~ class_OrderedGroup_Omonoid__mult(X0)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X19),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X19)),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_481])]) ).

fof(f589,axiom,
    ! [X3,X0,X1,X19] :
      ( ~ class_OrderedGroup_Omonoid__mult(X0)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X19),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X19)),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__mult_0) ).

fof(f5007,plain,
    spl0_480,
    inference(avatar_split_clause,[],[f580,f5005]) ).

fof(f5005,plain,
    ( spl0_480
  <=> ! [X4,X0,X9,X2] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_HOL_Oord__class_Oless(X4,X9,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X2,X0)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X9),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_480])]) ).

fof(f580,axiom,
    ! [X2,X0,X9,X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | ~ c_HOL_Oord__class_Oless(X4,X9,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X2,X0)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X9),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__increasing__iff_1) ).

fof(f5003,plain,
    spl0_479,
    inference(avatar_split_clause,[],[f579,f5001]) ).

fof(f5001,plain,
    ( spl0_479
  <=> ! [X4,X0,X9,X2] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | c_HOL_Oord__class_Oless(X4,X9,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X2,X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X9),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_479])]) ).

fof(f579,axiom,
    ! [X2,X0,X9,X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | c_HOL_Oord__class_Oless(X4,X9,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X2,X0)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X9),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__increasing__iff_0) ).

fof(f4999,plain,
    spl0_478,
    inference(avatar_split_clause,[],[f553,f4997]) ).

fof(f4997,plain,
    ( spl0_478
  <=> ! [X0,X1,X3] :
        ( ~ class_OrderedGroup_Omonoid__mult(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_478])]) ).

fof(f553,axiom,
    ! [X3,X0,X1] :
      ( ~ class_OrderedGroup_Omonoid__mult(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3)),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__commutes_0) ).

fof(f4995,plain,
    spl0_477,
    inference(avatar_split_clause,[],[f512,f4993]) ).

fof(f4993,plain,
    ( spl0_477
  <=> ! [X0,X3] :
        ( ~ class_Int_Onumber__ring(X0)
        | c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0)),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X3))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_477])]) ).

fof(f512,axiom,
    ! [X3,X0] :
      ( ~ class_Int_Onumber__ring(X0)
      | c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0)),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X3))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__m1__odd_0) ).

fof(f4991,plain,
    spl0_476,
    inference(avatar_split_clause,[],[f382,f4989]) ).

fof(f4989,plain,
    ( spl0_476
  <=> ! [X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ouminus__class_Ouminus(X1,X0)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).

fof(f382,axiom,
    ! [X0,X1] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ouminus__class_Ouminus(X1,X0)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power2__minus_0) ).

fof(f4987,plain,
    spl0_475,
    inference(avatar_split_clause,[],[f58,f4985]) ).

fof(f4985,plain,
    ( spl0_475
  <=> ! [X0,X6,X2,X1] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | c_HOL_Oord__class_Oless(X2,X1,X0)
        | ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X6),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X6),X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).

fof(f58,axiom,
    ! [X2,X0,X1,X6] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | c_HOL_Oord__class_Oless(X2,X1,X0)
      | ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X0),X0)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X6),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X6),X2),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_0) ).

fof(f4983,plain,
    spl0_474,
    inference(avatar_split_clause,[],[f57,f4981]) ).

fof(f4981,plain,
    ( spl0_474
  <=> ! [X0,X6,X2,X1] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | ~ c_HOL_Oord__class_Oless(X2,X1,X0)
        | ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X0),X0)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X6),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X6),X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_474])]) ).

fof(f57,axiom,
    ! [X2,X0,X1,X6] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | ~ c_HOL_Oord__class_Oless(X2,X1,X0)
      | ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X0),X0)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X6),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X6),X2),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_1) ).

fof(f4979,plain,
    spl0_473,
    inference(avatar_split_clause,[],[f56,f4977]) ).

fof(f4977,plain,
    ( spl0_473
  <=> ! [X0,X6,X2,X1] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | c_HOL_Oord__class_Oless(X1,X2,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X6),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X6),X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_473])]) ).

fof(f56,axiom,
    ! [X2,X0,X1,X6] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | c_HOL_Oord__class_Oless(X1,X2,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X6),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X6),X2),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_0) ).

fof(f4954,plain,
    spl0_472,
    inference(avatar_split_clause,[],[f53,f4952]) ).

fof(f4952,plain,
    ( spl0_472
  <=> ! [X0,X6,X2,X1] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
        | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X6),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X6),X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).

fof(f53,axiom,
    ! [X2,X0,X1,X6] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
      | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X6),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X6),X2),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__left__mono_0) ).

fof(f4950,plain,
    spl0_471,
    inference(avatar_split_clause,[],[f52,f4948]) ).

fof(f4948,plain,
    ( spl0_471
  <=> ! [X0,X6,X2,X1] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X6),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X6),X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_471])]) ).

fof(f52,axiom,
    ! [X2,X0,X1,X6] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X6),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X6),X2),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_4) ).

fof(f4946,plain,
    spl0_470,
    inference(avatar_split_clause,[],[f50,f4944]) ).

fof(f4944,plain,
    ( spl0_470
  <=> ! [X0,X6,X2,X1] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | ~ c_HOL_Oord__class_Oless(X2,X1,X0)
        | ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X0),X0)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X6),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X6),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_470])]) ).

fof(f50,axiom,
    ! [X2,X0,X1,X6] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | ~ c_HOL_Oord__class_Oless(X2,X1,X0)
      | ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X0),X0)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X6),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X6),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__right__mono__neg_0) ).

fof(f4942,plain,
    spl0_469,
    inference(avatar_split_clause,[],[f49,f4940]) ).

fof(f4940,plain,
    ( spl0_469
  <=> ! [X0,X6,X2,X1] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
        | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X6),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X6),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).

fof(f49,axiom,
    ! [X2,X0,X1,X6] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
      | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X6),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X6),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__right__mono_0) ).

fof(f4938,plain,
    spl0_468,
    inference(avatar_split_clause,[],[f48,f4936]) ).

fof(f4936,plain,
    ( spl0_468
  <=> ! [X0,X6,X2,X1] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X6),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X6),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).

fof(f48,axiom,
    ! [X2,X0,X1,X6] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X6),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X6),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_4) ).

fof(f4934,plain,
    spl0_467,
    inference(avatar_split_clause,[],[f46,f4932]) ).

fof(f4932,plain,
    ( spl0_467
  <=> ! [X0,X6,X2,X1] :
        ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X0)
        | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X6),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X6),X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).

fof(f46,axiom,
    ! [X2,X0,X1,X6] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X0)
      | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X6),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X6),X2),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__left__mono__comm_0) ).

fof(f4930,plain,
    spl0_466,
    inference(avatar_split_clause,[],[f35,f4928]) ).

fof(f4928,plain,
    ( spl0_466
  <=> ! [X0,X6,X2,X1] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | c_HOL_Oord__class_Oless(X2,X1,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X6),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X6),X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_466])]) ).

fof(f35,axiom,
    ! [X2,X0,X1,X6] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | c_HOL_Oord__class_Oless(X2,X1,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X6),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X6),X2),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_1) ).

fof(f4926,plain,
    spl0_465,
    inference(avatar_split_clause,[],[f34,f4924]) ).

fof(f4924,plain,
    ( spl0_465
  <=> ! [X0,X6,X2,X1] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | c_HOL_Oord__class_Oless(X1,X2,X0)
        | c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X6),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X6),X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_465])]) ).

fof(f34,axiom,
    ! [X2,X0,X1,X6] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | c_HOL_Oord__class_Oless(X1,X2,X0)
      | c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X0),X0)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X6),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X6),X2),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_2) ).

fof(f4922,plain,
    spl0_464,
    inference(avatar_split_clause,[],[f33,f4920]) ).

fof(f4920,plain,
    ( spl0_464
  <=> ! [X0,X6,X2,X1] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | c_HOL_Oord__class_Oless(X2,X1,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X6),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X6),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).

fof(f33,axiom,
    ! [X2,X0,X1,X6] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | c_HOL_Oord__class_Oless(X2,X1,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X6),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X6),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_1) ).

fof(f4918,plain,
    spl0_463,
    inference(avatar_split_clause,[],[f32,f4916]) ).

fof(f4916,plain,
    ( spl0_463
  <=> ! [X0,X6,X2,X1] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | c_HOL_Oord__class_Oless(X1,X2,X0)
        | c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X6),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X6),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).

fof(f32,axiom,
    ! [X2,X0,X1,X6] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | c_HOL_Oord__class_Oless(X1,X2,X0)
      | c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X0),X0)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X6),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X6),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_2) ).

fof(f4899,plain,
    spl0_462,
    inference(avatar_split_clause,[],[f19,f4897]) ).

fof(f4897,plain,
    ( spl0_462
  <=> ! [X4,X0,X9] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X4
        | c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X9),X9)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).

fof(f19,axiom,
    ! [X0,X9,X4] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X4
      | c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X9),X9)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_0) ).

fof(f4895,plain,
    spl0_461,
    inference(avatar_split_clause,[],[f18,f4893]) ).

fof(f4893,plain,
    ( spl0_461
  <=> ! [X9,X0,X4] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X9
        | c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X9),X9)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).

fof(f18,axiom,
    ! [X0,X9,X4] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X9
      | c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X9),X9)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_1) ).

fof(f4891,plain,
    spl0_460,
    inference(avatar_split_clause,[],[f14,f4889]) ).

fof(f4889,plain,
    ( spl0_460
  <=> ! [X0] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ozero__class_Ozero(X0)),c_HOL_Ozero__class_Ozero(X0))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ozero__class_Ozero(X0)),c_HOL_Ozero__class_Ozero(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).

fof(f14,axiom,
    ! [X0] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ozero__class_Ozero(X0)),c_HOL_Ozero__class_Ozero(X0))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ozero__class_Ozero(X0)),c_HOL_Ozero__class_Ozero(X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_2) ).

fof(f4815,plain,
    ( spl0_459
    | ~ spl0_222
    | ~ spl0_340 ),
    inference(avatar_split_clause,[],[f4073,f3324,f2041,f4812]) ).

fof(f4812,plain,
    ( spl0_459
  <=> c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).

fof(f2041,plain,
    ( spl0_222
  <=> ! [X0] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).

fof(f3324,plain,
    ( spl0_340
  <=> c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).

fof(f4073,plain,
    ( c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
    | ~ spl0_222
    | ~ spl0_340 ),
    inference(superposition,[],[f2042,f3326]) ).

fof(f3326,plain,
    ( c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_Complex_Ocomplex)
    | ~ spl0_340 ),
    inference(avatar_component_clause,[],[f3324]) ).

fof(f2042,plain,
    ( ! [X0] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0
    | ~ spl0_222 ),
    inference(avatar_component_clause,[],[f2041]) ).

fof(f4776,plain,
    spl0_458,
    inference(avatar_split_clause,[],[f689,f4774]) ).

fof(f4774,plain,
    ( spl0_458
  <=> ! [X35,X4,X0,X9] :
        ( ~ class_RealVector_Oreal__normed__field(X0)
        | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X4),X9),X35,X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oinverse__class_Odivide(X4,X35,X0)),c_HOL_Oinverse__class_Odivide(X9,X35,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_458])]) ).

fof(f689,axiom,
    ! [X0,X9,X4,X35] :
      ( ~ class_RealVector_Oreal__normed__field(X0)
      | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X4),X9),X35,X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oinverse__class_Odivide(X4,X35,X0)),c_HOL_Oinverse__class_Odivide(X9,X35,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide_Oadd_0) ).

fof(f4772,plain,
    spl0_457,
    inference(avatar_split_clause,[],[f688,f4770]) ).

fof(f4770,plain,
    ( spl0_457
  <=> ! [X0,X6,X2,X1] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2),X6,X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oinverse__class_Odivide(X1,X6,X0)),c_HOL_Oinverse__class_Odivide(X2,X6,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_457])]) ).

fof(f688,axiom,
    ! [X2,X0,X1,X6] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2),X6,X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oinverse__class_Odivide(X1,X6,X0)),c_HOL_Oinverse__class_Odivide(X2,X6,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__divide__distrib_0) ).

fof(f4768,plain,
    spl0_456,
    inference(avatar_split_clause,[],[f677,f4766]) ).

fof(f4766,plain,
    ( spl0_456
  <=> ! [X0,X1] :
        ( ~ class_OrderedGroup_Omonoid__mult(X0)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X1)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).

fof(f677,axiom,
    ! [X0,X1] :
      ( ~ class_OrderedGroup_Omonoid__mult(X0)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X1)),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power3__eq__cube_0) ).

fof(f4764,plain,
    spl0_455,
    inference(avatar_split_clause,[],[f571,f4762]) ).

fof(f4762,plain,
    ( spl0_455
  <=> ! [X0,X8,X6,X2,X1] :
        ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
        | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
        | ~ c_HOL_Oord__class_Oless(X6,X8,X0)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X8),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).

fof(f571,axiom,
    ! [X2,X0,X1,X8,X6] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
      | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
      | ~ c_HOL_Oord__class_Oless(X6,X8,X0)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X8),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).

fof(f4760,plain,
    spl0_454,
    inference(avatar_split_clause,[],[f527,f4758]) ).

fof(f4758,plain,
    ( spl0_454
  <=> ! [X0,X6,X2,X1] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | c_HOL_Oord__class_Oless(X1,X2,X0)
        | c_HOL_Oord__class_Oless(X2,X1,X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X6),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X6),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_454])]) ).

fof(f527,axiom,
    ! [X2,X0,X1,X6] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | c_HOL_Oord__class_Oless(X1,X2,X0)
      | c_HOL_Oord__class_Oless(X2,X1,X0)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X6),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X6),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_3) ).

fof(f4756,plain,
    spl0_453,
    inference(avatar_split_clause,[],[f526,f4754]) ).

fof(f4754,plain,
    ( spl0_453
  <=> ! [X0,X6,X2,X1] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | c_HOL_Oord__class_Oless(X1,X2,X0)
        | c_HOL_Oord__class_Oless(X2,X1,X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X6),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X6),X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).

fof(f526,axiom,
    ! [X2,X0,X1,X6] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | c_HOL_Oord__class_Oless(X1,X2,X0)
      | c_HOL_Oord__class_Oless(X2,X1,X0)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X6),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X6),X2),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_3) ).

fof(f4752,plain,
    spl0_452,
    inference(avatar_split_clause,[],[f445,f4750]) ).

fof(f4750,plain,
    ( spl0_452
  <=> ! [X15,X17,X4,X0,X13,X14,X12,X16] :
        ( ~ c_Groebner__Basis_Ogb__semiring(X15,X13,X12,X16,X17,X0)
        | hAPP(hAPP(X12,X4),hAPP(c_Suc,X14)) = hAPP(hAPP(X13,hAPP(hAPP(X12,X4),X14)),X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).

fof(f445,axiom,
    ! [X0,X16,X14,X4,X17,X15,X12,X13] :
      ( ~ c_Groebner__Basis_Ogb__semiring(X15,X13,X12,X16,X17,X0)
      | hAPP(hAPP(X12,X4),hAPP(c_Suc,X14)) = hAPP(hAPP(X13,hAPP(hAPP(X12,X4),X14)),X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I28_J_0) ).

fof(f4748,plain,
    ( spl0_451
    | ~ spl0_221
    | ~ spl0_339 ),
    inference(avatar_split_clause,[],[f4015,f3276,f2022,f4745]) ).

fof(f4745,plain,
    ( spl0_451
  <=> c_HOL_Oone__class_Oone(tc_Int_Oint) = c_HOL_Ouminus__class_Ouminus(c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_Int_Oint),tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).

fof(f2022,plain,
    ( spl0_221
  <=> ! [X0] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_Int_Oint),tc_Int_Oint) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).

fof(f3276,plain,
    ( spl0_339
  <=> c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).

fof(f4015,plain,
    ( c_HOL_Oone__class_Oone(tc_Int_Oint) = c_HOL_Ouminus__class_Ouminus(c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_Int_Oint),tc_Int_Oint)
    | ~ spl0_221
    | ~ spl0_339 ),
    inference(superposition,[],[f2023,f3278]) ).

fof(f3278,plain,
    ( c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_Int_Oint)
    | ~ spl0_339 ),
    inference(avatar_component_clause,[],[f3276]) ).

fof(f2023,plain,
    ( ! [X0] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_Int_Oint),tc_Int_Oint) = X0
    | ~ spl0_221 ),
    inference(avatar_component_clause,[],[f2022]) ).

fof(f4743,plain,
    spl0_450,
    inference(avatar_split_clause,[],[f443,f4741]) ).

fof(f4741,plain,
    ( spl0_450
  <=> ! [X15,X17,X4,X3,X0,X13,X12,X16] :
        ( ~ c_Groebner__Basis_Ogb__semiring(X15,X13,X12,X16,X17,X0)
        | hAPP(hAPP(X12,X4),hAPP(c_Suc,X3)) = hAPP(hAPP(X13,X4),hAPP(hAPP(X12,X4),X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).

fof(f443,axiom,
    ! [X3,X0,X16,X4,X17,X15,X12,X13] :
      ( ~ c_Groebner__Basis_Ogb__semiring(X15,X13,X12,X16,X17,X0)
      | hAPP(hAPP(X12,X4),hAPP(c_Suc,X3)) = hAPP(hAPP(X13,X4),hAPP(hAPP(X12,X4),X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Opwr__Suc_0) ).

fof(f4739,plain,
    spl0_449,
    inference(avatar_split_clause,[],[f373,f4737]) ).

fof(f4737,plain,
    ( spl0_449
  <=> ! [X0,X1,X3] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(X0),X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),hAPP(c_Suc,X3)),c_HOL_Oone__class_Oone(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).

fof(f373,axiom,
    ! [X3,X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(X0),X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),hAPP(c_Suc,X3)),c_HOL_Oone__class_Oone(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__Suc__less__one_0) ).

fof(f4735,plain,
    spl0_448,
    inference(avatar_split_clause,[],[f238,f4733]) ).

fof(f4733,plain,
    ( spl0_448
  <=> ! [X4,X0,X3] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | c_Parity_Oeven__odd__class_Oeven(X3,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X3
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X4,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).

fof(f238,axiom,
    ! [X3,X0,X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_Parity_Oeven__odd__class_Oeven(X3,tc_nat)
      | c_HOL_Ozero__class_Ozero(tc_nat) = X3
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X4,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),X3),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power__eq_0) ).

fof(f4601,plain,
    ( spl0_447
    | ~ spl0_166
    | ~ spl0_176 ),
    inference(avatar_split_clause,[],[f1807,f1764,f1668,f4599]) ).

fof(f4599,plain,
    ( spl0_447
  <=> ! [X0] : ~ c_HOL_Oord__class_Oless(hAPP(c_Suc,hAPP(c_Suc,X0)),X0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).

fof(f1764,plain,
    ( spl0_176
  <=> ! [X0] : ~ c_HOL_Oord__class_Oless(hAPP(c_Suc,X0),X0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).

fof(f1807,plain,
    ( ! [X0] : ~ c_HOL_Oord__class_Oless(hAPP(c_Suc,hAPP(c_Suc,X0)),X0,tc_nat)
    | ~ spl0_166
    | ~ spl0_176 ),
    inference(resolution,[],[f1765,f1669]) ).

fof(f1765,plain,
    ( ! [X0] : ~ c_HOL_Oord__class_Oless(hAPP(c_Suc,X0),X0,tc_nat)
    | ~ spl0_176 ),
    inference(avatar_component_clause,[],[f1764]) ).

fof(f4501,plain,
    spl0_446,
    inference(avatar_split_clause,[],[f835,f4499]) ).

fof(f4499,plain,
    ( spl0_446
  <=> ! [X3,X19] :
        ( ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat),X19,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat),X3,tc_nat)
        | c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X3),X19),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_446])]) ).

fof(f835,plain,
    ! [X3,X19] :
      ( ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat),X19,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat),X3,tc_nat)
      | c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X3),X19),tc_nat) ),
    inference(forward_demodulation,[],[f834,f377]) ).

fof(f834,plain,
    ! [X3,X19] :
      ( ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat),X3,tc_nat)
      | ~ c_HOL_Oord__class_Oless(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),X19,tc_nat)
      | c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X3),X19),tc_nat) ),
    inference(forward_demodulation,[],[f334,f377]) ).

fof(f334,axiom,
    ! [X3,X19] :
      ( ~ c_HOL_Oord__class_Oless(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_nat)
      | ~ c_HOL_Oord__class_Oless(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),X19,tc_nat)
      | c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X3),X19),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__less__n__mult__m_0) ).

fof(f4497,plain,
    spl0_445,
    inference(avatar_split_clause,[],[f833,f4495]) ).

fof(f4495,plain,
    ( spl0_445
  <=> ! [X3,X19] :
        ( ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat),X19,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat),X3,tc_nat)
        | c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X19),X3),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).

fof(f833,plain,
    ! [X3,X19] :
      ( ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat),X19,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat),X3,tc_nat)
      | c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X19),X3),tc_nat) ),
    inference(forward_demodulation,[],[f832,f377]) ).

fof(f832,plain,
    ! [X3,X19] :
      ( ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat),X3,tc_nat)
      | ~ c_HOL_Oord__class_Oless(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),X19,tc_nat)
      | c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X19),X3),tc_nat) ),
    inference(forward_demodulation,[],[f335,f377]) ).

fof(f335,axiom,
    ! [X3,X19] :
      ( ~ c_HOL_Oord__class_Oless(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_nat)
      | ~ c_HOL_Oord__class_Oless(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),X19,tc_nat)
      | c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X19),X3),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__less__m__mult__n_0) ).

fof(f4493,plain,
    spl0_444,
    inference(avatar_split_clause,[],[f687,f4491]) ).

fof(f4491,plain,
    ( spl0_444
  <=> ! [X18,X4,X0,X9] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | ~ class_Ring__and__Field_Odivision__by__zero(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oinverse__class_Odivide(X4,X9,X0)),X18) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X18),X9,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).

fof(f687,axiom,
    ! [X0,X18,X9,X4] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | ~ class_Ring__and__Field_Odivision__by__zero(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oinverse__class_Odivide(X4,X9,X0)),X18) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X18),X9,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__frac__num_0) ).

fof(f4489,plain,
    spl0_443,
    inference(avatar_split_clause,[],[f600,f4487]) ).

fof(f4487,plain,
    ( spl0_443
  <=> ! [X20,X19,X3] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X19),X3)),X20) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X19),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X3),X20)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).

fof(f600,axiom,
    ! [X3,X19,X20] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X19),X3)),X20) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X19),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X3),X20)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__assoc_0) ).

fof(f4485,plain,
    spl0_442,
    inference(avatar_split_clause,[],[f574,f4483]) ).

fof(f574,axiom,
    ! [X3,X0,X1,X19] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | X3 = X19
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3) != hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X19) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__inject__exp_0) ).

fof(f4481,plain,
    spl0_441,
    inference(avatar_split_clause,[],[f525,f4479]) ).

fof(f4479,plain,
    ( spl0_441
  <=> ! [X0,X11] :
        ( ~ class_Int_Onumber__ring(X0)
        | c_Int_Onumber__class_Onumber__of(c_Int_OBit1(X11),X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oone__class_Oone(X0)),c_Int_Onumber__class_Onumber__of(X11,X0))),c_Int_Onumber__class_Onumber__of(X11,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).

fof(f525,axiom,
    ! [X0,X11] :
      ( ~ class_Int_Onumber__ring(X0)
      | c_Int_Onumber__class_Onumber__of(c_Int_OBit1(X11),X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oone__class_Oone(X0)),c_Int_Onumber__class_Onumber__of(X11,X0))),c_Int_Onumber__class_Onumber__of(X11,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_number__of__Bit1_0) ).

fof(f4477,plain,
    spl0_440,
    inference(avatar_split_clause,[],[f507,f4475]) ).

fof(f4475,plain,
    ( spl0_440
  <=> ! [X0,X3] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
        | c_HOL_Oone__class_Oone(X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).

fof(f507,axiom,
    ! [X3,X0] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
      | c_HOL_Oone__class_Oone(X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__minus1__even_0) ).

fof(f4473,plain,
    spl0_439,
    inference(avatar_split_clause,[],[f424,f4471]) ).

fof(f4471,plain,
    ( spl0_439
  <=> ! [X0,X3] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X3
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ozero__class_Ozero(X0)),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).

fof(f424,axiom,
    ! [X3,X0] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_HOL_Ozero__class_Ozero(tc_nat) = X3
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ozero__class_Ozero(X0)),X3),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power__eq_2) ).

fof(f4469,plain,
    spl0_438,
    inference(avatar_split_clause,[],[f317,f4467]) ).

fof(f4467,plain,
    ( spl0_438
  <=> ! [X0,X11] :
        ( ~ class_Int_Onumber__ring(X0)
        | c_Int_Onumber__class_Onumber__of(c_Int_OBit0(X11),X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0)),c_Int_Onumber__class_Onumber__of(X11,X0))),c_Int_Onumber__class_Onumber__of(X11,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).

fof(f317,axiom,
    ! [X0,X11] :
      ( ~ class_Int_Onumber__ring(X0)
      | c_Int_Onumber__class_Onumber__of(c_Int_OBit0(X11),X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0)),c_Int_Onumber__class_Onumber__of(X11,X0))),c_Int_Onumber__class_Onumber__of(X11,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_number__of__Bit0_0) ).

fof(f4465,plain,
    spl0_437,
    inference(avatar_split_clause,[],[f292,f4463]) ).

fof(f4463,plain,
    ( spl0_437
  <=> ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Oidom(X0)
        | X1 = X2
        | c_HOL_Ouminus__class_Ouminus(X2,X0) = X1
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X1) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).

fof(f292,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Ring__and__Field_Oidom(X0)
      | X1 = X2
      | c_HOL_Ouminus__class_Ouminus(X2,X0) = X1
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X1) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_square__eq__iff_0) ).

fof(f4461,plain,
    spl0_436,
    inference(avatar_split_clause,[],[f166,f4459]) ).

fof(f4459,plain,
    ( spl0_436
  <=> ! [X21,X19,X3] :
        ( c_HOL_Oord__class_Oless(X19,X3,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X21,tc_nat)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X21),X19),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X21),X3),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).

fof(f166,axiom,
    ! [X21,X3,X19] :
      ( c_HOL_Oord__class_Oless(X19,X3,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X21,tc_nat)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X21),X19),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X21),X3),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__power__less__imp__less_0) ).

fof(f4457,plain,
    spl0_435,
    inference(avatar_split_clause,[],[f152,f4455]) ).

fof(f4455,plain,
    ( spl0_435
  <=> ! [X22,X20,X21] :
        ( ~ c_HOL_Oord__class_Oless(X21,X22,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X20,tc_nat)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X20),X21),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X20),X22),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).

fof(f152,axiom,
    ! [X21,X22,X20] :
      ( ~ c_HOL_Oord__class_Oless(X21,X22,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X20,tc_nat)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X20),X21),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X20),X22),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__mono2_0) ).

fof(f4453,plain,
    spl0_434,
    inference(avatar_split_clause,[],[f150,f4451]) ).

fof(f4451,plain,
    ( spl0_434
  <=> ! [X20,X19,X3] :
        ( ~ c_HOL_Oord__class_Oless(X19,X3,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X20,tc_nat)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X19),X20),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X3),X20),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).

fof(f150,axiom,
    ! [X3,X19,X20] :
      ( ~ c_HOL_Oord__class_Oless(X19,X3,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X20,tc_nat)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X19),X20),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X3),X20),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel2_2) ).

fof(f4163,plain,
    spl0_433,
    inference(avatar_split_clause,[],[f690,f4161]) ).

fof(f4161,plain,
    ( spl0_433
  <=> ! [X3,X0,X19] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X19,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X3,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X19),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_433])]) ).

fof(f690,axiom,
    ! [X3,X0,X19] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X19,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X3,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X19),X3),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__1__mult_0) ).

fof(f4159,plain,
    spl0_432,
    inference(avatar_split_clause,[],[f682,f4157]) ).

fof(f4157,plain,
    ( spl0_432
  <=> ! [X20,X19,X3] :
        ( ~ c_HOL_Oord__class_Oless(X19,X3,tc_nat)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,X20)),X19),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,X20)),X3),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).

fof(f682,axiom,
    ! [X3,X19,X20] :
      ( ~ c_HOL_Oord__class_Oless(X19,X3,tc_nat)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,X20)),X19),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,X20)),X3),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mult__less__cancel1_1) ).

fof(f4155,plain,
    spl0_431,
    inference(avatar_split_clause,[],[f659,f4153]) ).

fof(f4153,plain,
    ( spl0_431
  <=> ! [X0,X1,X3] :
        ( ~ class_Power_Opower(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),hAPP(c_Suc,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).

fof(f659,axiom,
    ! [X3,X0,X1] :
      ( ~ class_Power_Opower(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),hAPP(c_Suc,X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__Suc_0) ).

fof(f4151,plain,
    spl0_430,
    inference(avatar_split_clause,[],[f658,f4149]) ).

fof(f4149,plain,
    ( spl0_430
  <=> ! [X0,X1,X3] :
        ( ~ class_OrderedGroup_Omonoid__mult(X0)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),hAPP(c_Suc,X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).

fof(f658,axiom,
    ! [X3,X0,X1] :
      ( ~ class_OrderedGroup_Omonoid__mult(X0)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),hAPP(c_Suc,X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3)),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__Suc2_0) ).

fof(f4147,plain,
    spl0_429,
    inference(avatar_split_clause,[],[f657,f4145]) ).

fof(f657,axiom,
    ! [X3,X0,X4] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),hAPP(c_Suc,X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__Suc_0) ).

fof(f4143,plain,
    spl0_428,
    inference(avatar_split_clause,[],[f645,f4141]) ).

fof(f4141,plain,
    ( spl0_428
  <=> ! [X0,X11] :
        ( ~ class_Int_Onumber__ring(X0)
        | c_Int_Onumber__class_Onumber__of(c_Int_OBit0(X11),X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oone__class_Oone(X0)),c_HOL_Oone__class_Oone(X0))),c_Int_Onumber__class_Onumber__of(X11,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).

fof(f645,axiom,
    ! [X0,X11] :
      ( ~ class_Int_Onumber__ring(X0)
      | c_Int_Onumber__class_Onumber__of(c_Int_OBit0(X11),X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oone__class_Oone(X0)),c_HOL_Oone__class_Oone(X0))),c_Int_Onumber__class_Onumber__of(X11,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__number__of__Bit0_0) ).

fof(f4139,plain,
    spl0_427,
    inference(avatar_split_clause,[],[f635,f4137]) ).

fof(f4137,plain,
    ( spl0_427
  <=> ! [X0,X1,X3] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).

fof(f635,axiom,
    ! [X3,X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__gt1__lemma_0) ).

fof(f4131,plain,
    spl0_426,
    inference(avatar_split_clause,[],[f576,f4129]) ).

fof(f4129,plain,
    ( spl0_426
  <=> ! [X4,X0,X14] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),hAPP(c_Suc,X14)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),X14)),X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).

fof(f576,axiom,
    ! [X0,X14,X4] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),hAPP(c_Suc,X14)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),X14)),X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I28_J_0) ).

fof(f4127,plain,
    spl0_425,
    inference(avatar_split_clause,[],[f554,f4125]) ).

fof(f4125,plain,
    ( spl0_425
  <=> ! [X0,X19] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X19),X19) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oone__class_Oone(X0)),c_HOL_Oone__class_Oone(X0))),X19) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).

fof(f554,axiom,
    ! [X0,X19] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X19),X19) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oone__class_Oone(X0)),c_HOL_Oone__class_Oone(X0))),X19) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I4_J_0) ).

fof(f4123,plain,
    spl0_424,
    inference(avatar_split_clause,[],[f511,f4121]) ).

fof(f4121,plain,
    ( spl0_424
  <=> ! [X0,X3] :
        ( ~ class_Int_Onumber__ring(X0)
        | c_HOL_Oone__class_Oone(X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).

fof(f511,axiom,
    ! [X3,X0] :
      ( ~ class_Int_Onumber__ring(X0)
      | c_HOL_Oone__class_Oone(X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__m1__even_0) ).

fof(f4119,plain,
    spl0_423,
    inference(avatar_split_clause,[],[f378,f4117]) ).

fof(f4117,plain,
    ( spl0_423
  <=> ! [X15,X17,X4,X0,X13,X12,X16] :
        ( ~ c_Groebner__Basis_Ogb__semiring(X15,X13,X12,X16,X17,X0)
        | hAPP(hAPP(X13,X4),X4) = hAPP(hAPP(X12,X4),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).

fof(f378,axiom,
    ! [X0,X16,X4,X17,X15,X12,X13] :
      ( ~ c_Groebner__Basis_Ogb__semiring(X15,X13,X12,X16,X17,X0)
      | hAPP(hAPP(X13,X4),X4) = hAPP(hAPP(X12,X4),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I29_J_0) ).

fof(f4115,plain,
    spl0_422,
    inference(avatar_split_clause,[],[f374,f4113]) ).

fof(f4113,plain,
    ( spl0_422
  <=> ! [X0,X1,X3] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).

fof(f374,axiom,
    ! [X3,X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__less__power_0) ).

fof(f4111,plain,
    spl0_421,
    inference(avatar_split_clause,[],[f229,f4109]) ).

fof(f4109,plain,
    ( spl0_421
  <=> ! [X0,X3] :
        ( ~ class_Ring__and__Field_Ozero__neq__one(X0)
        | ~ class_Ring__and__Field_Ono__zero__divisors(X0)
        | ~ class_Ring__and__Field_Omult__zero(X0)
        | ~ class_Power_Opower(X0)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X3
        | c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ozero__class_Ozero(X0)),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).

fof(f229,axiom,
    ! [X3,X0] :
      ( ~ class_Ring__and__Field_Ozero__neq__one(X0)
      | ~ class_Ring__and__Field_Ono__zero__divisors(X0)
      | ~ class_Ring__and__Field_Omult__zero(X0)
      | ~ class_Power_Opower(X0)
      | c_HOL_Ozero__class_Ozero(tc_nat) = X3
      | c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ozero__class_Ozero(X0)),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_2) ).

fof(f4107,plain,
    spl0_420,
    inference(avatar_split_clause,[],[f215,f4105]) ).

fof(f4105,plain,
    ( spl0_420
  <=> ! [X15,X17,X19,X0,X13,X12,X16] :
        ( ~ c_Groebner__Basis_Ogb__semiring(X15,X13,X12,X16,X17,X0)
        | hAPP(hAPP(X15,X19),X19) = hAPP(hAPP(X13,hAPP(hAPP(X15,X17),X17)),X19) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).

fof(f215,axiom,
    ! [X0,X19,X16,X17,X15,X12,X13] :
      ( ~ c_Groebner__Basis_Ogb__semiring(X15,X13,X12,X16,X17,X0)
      | hAPP(hAPP(X15,X19),X19) = hAPP(hAPP(X13,hAPP(hAPP(X15,X17),X17)),X19) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I4_J_0) ).

fof(f4103,plain,
    spl0_419,
    inference(avatar_split_clause,[],[f174,f4101]) ).

fof(f4101,plain,
    ( spl0_419
  <=> ! [X9,X0,X4] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X9),X9)),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).

fof(f174,axiom,
    ! [X0,X9,X4] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X9),X9)),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__sum__squares__lt__zero_0) ).

fof(f4099,plain,
    spl0_418,
    inference(avatar_split_clause,[],[f76,f4097]) ).

fof(f4097,plain,
    ( spl0_418
  <=> ! [X4,X0,X3] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
        | c_Parity_Oeven__odd__class_Oeven(X3,tc_nat)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ouminus__class_Ouminus(X4,X0)),X3) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).

fof(f76,axiom,
    ! [X3,X0,X4] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
      | c_Parity_Oeven__odd__class_Oeven(X3,tc_nat)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ouminus__class_Ouminus(X4,X0)),X3) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),X3),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__power__if_1) ).

fof(f4095,plain,
    spl0_417,
    inference(avatar_split_clause,[],[f45,f4093]) ).

fof(f4093,plain,
    ( spl0_417
  <=> ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).

fof(f45,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
      | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__neg__neg_0) ).

fof(f4072,plain,
    spl0_416,
    inference(avatar_split_clause,[],[f44,f4070]) ).

fof(f4070,plain,
    ( spl0_416
  <=> ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).

fof(f44,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pos__pos_0) ).

fof(f4068,plain,
    spl0_415,
    inference(avatar_split_clause,[],[f43,f4066]) ).

fof(f4066,plain,
    ( spl0_415
  <=> ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).

fof(f43,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__mult__pos_0) ).

fof(f4064,plain,
    spl0_414,
    inference(avatar_split_clause,[],[f42,f4062]) ).

fof(f4062,plain,
    ( spl0_414
  <=> ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).

fof(f42,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__mult__pos2_0) ).

fof(f4060,plain,
    spl0_413,
    inference(avatar_split_clause,[],[f41,f4058]) ).

fof(f4058,plain,
    ( spl0_413
  <=> ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
        | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).

fof(f41,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
      | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__neg__pos_0) ).

fof(f4056,plain,
    spl0_412,
    inference(avatar_split_clause,[],[f40,f4054]) ).

fof(f4054,plain,
    ( spl0_412
  <=> ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
        | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).

fof(f40,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
      | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pos__neg_0) ).

fof(f4052,plain,
    spl0_411,
    inference(avatar_split_clause,[],[f31,f4050]) ).

fof(f4050,plain,
    ( spl0_411
  <=> ! [X2,X0,X1] :
        ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
        | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).

fof(f31,axiom,
    ! [X2,X0,X1] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
      | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
      | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).

fof(f4048,plain,
    spl0_410,
    inference(avatar_split_clause,[],[f23,f4046]) ).

fof(f4046,plain,
    ( spl0_410
  <=> ! [X2,X0,X1] :
        ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).

fof(f23,axiom,
    ! [X2,X0,X1] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).

fof(f3997,plain,
    spl0_409,
    inference(avatar_split_clause,[],[f831,f3995]) ).

fof(f3995,plain,
    ( spl0_409
  <=> ! [X4,X19] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X4),X19) != c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat)
        | c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat) = X4
        | c_HOL_Ozero__class_Ozero(tc_nat) = X19 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).

fof(f831,plain,
    ! [X19,X4] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X4),X19) != c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat)
      | c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat) = X4
      | c_HOL_Ozero__class_Ozero(tc_nat) = X19 ),
    inference(forward_demodulation,[],[f830,f377]) ).

fof(f830,plain,
    ! [X19,X4] :
      ( c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat) = X4
      | c_HOL_Ozero__class_Ozero(tc_nat) = X19
      | hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X4),X19) ),
    inference(forward_demodulation,[],[f165,f377]) ).

fof(f165,axiom,
    ! [X19,X4] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X19
      | hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = X4
      | hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X4),X19) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__power__eq__Suc__0__iff_0) ).

fof(f3993,plain,
    spl0_408,
    inference(avatar_split_clause,[],[f455,f3991]) ).

fof(f3991,plain,
    ( spl0_408
  <=> ! [X0,X1,X3] :
        ( ~ class_Ring__and__Field_Ozero__neq__one(X0)
        | ~ class_Ring__and__Field_Ono__zero__divisors(X0)
        | ~ class_Ring__and__Field_Omult__zero(X0)
        | ~ class_Power_Opower(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X1
        | c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_408])]) ).

fof(f455,axiom,
    ! [X3,X0,X1] :
      ( ~ class_Ring__and__Field_Ozero__neq__one(X0)
      | ~ class_Ring__and__Field_Ono__zero__divisors(X0)
      | ~ class_Ring__and__Field_Omult__zero(X0)
      | ~ class_Power_Opower(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X1
      | c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_0) ).

fof(f3989,plain,
    spl0_407,
    inference(avatar_split_clause,[],[f398,f3987]) ).

fof(f3987,plain,
    ( spl0_407
  <=> ! [X2,X0,X1] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2),X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ouminus__class_Ouminus(X2,X0)),c_HOL_Ouminus__class_Ouminus(X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_407])]) ).

fof(f398,axiom,
    ! [X2,X0,X1] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2),X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ouminus__class_Ouminus(X2,X0)),c_HOL_Ouminus__class_Ouminus(X1,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add_0) ).

fof(f3985,plain,
    spl0_406,
    inference(avatar_split_clause,[],[f397,f3983]) ).

fof(f3983,plain,
    ( spl0_406
  <=> ! [X2,X0,X1] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2),X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ouminus__class_Ouminus(X1,X0)),c_HOL_Ouminus__class_Ouminus(X2,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).

fof(f397,axiom,
    ! [X2,X0,X1] :
      ( ~ class_OrderedGroup_Oab__group__add(X0)
      | c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2),X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ouminus__class_Ouminus(X1,X0)),c_HOL_Ouminus__class_Ouminus(X2,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add__distrib_0) ).

fof(f3981,plain,
    spl0_405,
    inference(avatar_split_clause,[],[f160,f3979]) ).

fof(f3979,plain,
    ( spl0_405
  <=> ! [X20,X3,X19] :
        ( X3 = X19
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X20,tc_nat)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X20),X19) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X20),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).

fof(f160,axiom,
    ! [X3,X19,X20] :
      ( X3 = X19
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X20,tc_nat)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X20),X19) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X20),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__eq__cancel1_0) ).

fof(f3977,plain,
    spl0_404,
    inference(avatar_split_clause,[],[f131,f3975]) ).

fof(f3975,plain,
    ( spl0_404
  <=> ! [X2,X0,X11] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | ~ class_Ring__and__Field_Odivision__by__zero(X0)
        | ~ class_Int_Onumber(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_Int_Onumber__class_Onumber__of(X11,X0)
        | c_Int_Onumber__class_Onumber__of(X11,X0) != c_HOL_Oinverse__class_Odivide(X2,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).

fof(f131,axiom,
    ! [X2,X0,X11] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | ~ class_Ring__and__Field_Odivision__by__zero(X0)
      | ~ class_Int_Onumber(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_Int_Onumber__class_Onumber__of(X11,X0)
      | c_Int_Onumber__class_Onumber__of(X11,X0) != c_HOL_Oinverse__class_Odivide(X2,c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of_1) ).

fof(f3865,plain,
    ( ~ spl0_403
    | ~ spl0_119
    | ~ spl0_247 ),
    inference(avatar_split_clause,[],[f2370,f2210,f1433,f3862]) ).

fof(f3862,plain,
    ( spl0_403
  <=> c_HOL_Ozero__class_Ozero(tc_nat) = c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).

fof(f1433,plain,
    ( spl0_119
  <=> ! [X19] : c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(c_Suc,X19) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).

fof(f2370,plain,
    ( c_HOL_Ozero__class_Ozero(tc_nat) != c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat)
    | ~ spl0_119
    | ~ spl0_247 ),
    inference(superposition,[],[f1434,f2212]) ).

fof(f1434,plain,
    ( ! [X19] : c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(c_Suc,X19)
    | ~ spl0_119 ),
    inference(avatar_component_clause,[],[f1433]) ).

fof(f3764,plain,
    spl0_402,
    inference(avatar_split_clause,[],[f612,f3762]) ).

fof(f3762,plain,
    ( spl0_402
  <=> ! [X20,X3,X19] :
        ( X3 = X19
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,X20)),X19) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,X20)),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).

fof(f612,axiom,
    ! [X3,X19,X20] :
      ( X3 = X19
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,X20)),X19) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,X20)),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mult__cancel1_0) ).

fof(f3760,plain,
    spl0_401,
    inference(avatar_split_clause,[],[f586,f3758]) ).

fof(f3758,plain,
    ( spl0_401
  <=> ! [X0,X6,X2,X1] :
        ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
        | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X6),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).

fof(f586,axiom,
    ! [X2,X0,X1,X6] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
      | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X6),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).

fof(f3756,plain,
    spl0_400,
    inference(avatar_split_clause,[],[f585,f3754]) ).

fof(f3754,plain,
    ( spl0_400
  <=> ! [X0,X6,X2,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
        | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X6),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).

fof(f585,axiom,
    ! [X2,X0,X1,X6] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
      | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X6),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).

fof(f3752,plain,
    spl0_399,
    inference(avatar_split_clause,[],[f584,f3750]) ).

fof(f584,axiom,
    ! [X2,X0,X1,X6] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
      | c_HOL_Oord__class_Oless(X1,X2,X0)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X6),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).

fof(f3748,plain,
    spl0_398,
    inference(avatar_split_clause,[],[f583,f3746]) ).

fof(f3746,plain,
    ( spl0_398
  <=> ! [X0,X6,X2,X1] :
        ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
        | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X6),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X6),X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).

fof(f583,axiom,
    ! [X2,X0,X1,X6] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
      | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X6),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X6),X2),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).

fof(f3744,plain,
    spl0_397,
    inference(avatar_split_clause,[],[f582,f3742]) ).

fof(f582,axiom,
    ! [X2,X0,X1,X6] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
      | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X6),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X6),X2),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).

fof(f3740,plain,
    spl0_396,
    inference(avatar_split_clause,[],[f581,f3738]) ).

fof(f3738,plain,
    ( spl0_396
  <=> ! [X0,X6,X2,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
        | c_HOL_Oord__class_Oless(X1,X2,X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X6),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X6),X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).

fof(f581,axiom,
    ! [X2,X0,X1,X6] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
      | c_HOL_Oord__class_Oless(X1,X2,X0)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X6),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X6),X2),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).

fof(f3736,plain,
    spl0_395,
    inference(avatar_split_clause,[],[f533,f3734]) ).

fof(f3734,plain,
    ( spl0_395
  <=> ! [X18,X4,X0,X9] :
        ( ~ class_Ring__and__Field_Oidom(X0)
        | ~ class_Int_Onumber__ring(X0)
        | X9 = X18
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X4),X9) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X4),X18) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).

fof(f533,axiom,
    ! [X0,X18,X9,X4] :
      ( ~ class_Ring__and__Field_Oidom(X0)
      | ~ class_Int_Onumber__ring(X0)
      | X9 = X18
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X4),X9) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X4),X18) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).

fof(f3732,plain,
    spl0_394,
    inference(avatar_split_clause,[],[f484,f3730]) ).

fof(f3730,plain,
    ( spl0_394
  <=> ! [X20,X3,X19] :
        ( X3 = X19
        | c_HOL_Ozero__class_Ozero(tc_nat) = X20
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X19),X20) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X3),X20) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).

fof(f484,axiom,
    ! [X3,X19,X20] :
      ( X3 = X19
      | c_HOL_Ozero__class_Ozero(tc_nat) = X20
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X19),X20) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X3),X20) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__cancel2_0) ).

fof(f3728,plain,
    spl0_393,
    inference(avatar_split_clause,[],[f482,f3726]) ).

fof(f3726,plain,
    ( spl0_393
  <=> ! [X20,X3,X19] :
        ( X3 = X19
        | c_HOL_Ozero__class_Ozero(tc_nat) = X20
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X20),X19) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X20),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).

fof(f482,axiom,
    ! [X3,X19,X20] :
      ( X3 = X19
      | c_HOL_Ozero__class_Ozero(tc_nat) = X20
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X20),X19) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X20),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__eq__cancel__disj_0) ).

fof(f3724,plain,
    ( ~ spl0_392
    | ~ spl0_132
    | spl0_380 ),
    inference(avatar_split_clause,[],[f3675,f3594,f1488,f3721]) ).

fof(f3721,plain,
    ( spl0_392
  <=> class_Ring__and__Field_Oordered__semidom(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).

fof(f1488,plain,
    ( spl0_132
  <=> ! [X0] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).

fof(f3594,plain,
    ( spl0_380
  <=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).

fof(f3675,plain,
    ( ~ class_Ring__and__Field_Oordered__semidom(tc_Complex_Ocomplex)
    | ~ spl0_132
    | spl0_380 ),
    inference(resolution,[],[f3595,f1489]) ).

fof(f1489,plain,
    ( ! [X0] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0)
        | ~ class_Ring__and__Field_Oordered__semidom(X0) )
    | ~ spl0_132 ),
    inference(avatar_component_clause,[],[f1488]) ).

fof(f3595,plain,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex)
    | spl0_380 ),
    inference(avatar_component_clause,[],[f3594]) ).

fof(f3719,plain,
    spl0_391,
    inference(avatar_split_clause,[],[f470,f3717]) ).

fof(f3717,plain,
    ( spl0_391
  <=> ! [X35,X4,X0,X9] :
        ( ~ class_RealVector_Oreal__normed__field(X0)
        | c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X4,X9,X0),X35,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X4,X35,X0),c_HOL_Oinverse__class_Odivide(X9,X35,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).

fof(f470,axiom,
    ! [X0,X9,X4,X35] :
      ( ~ class_RealVector_Oreal__normed__field(X0)
      | c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X4,X9,X0),X35,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X4,X35,X0),c_HOL_Oinverse__class_Odivide(X9,X35,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide_Odiff_0) ).

fof(f3715,plain,
    spl0_390,
    inference(avatar_split_clause,[],[f469,f3713]) ).

fof(f3713,plain,
    ( spl0_390
  <=> ! [X0,X6,X2,X1] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X1,X2,X0),X6,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X1,X6,X0),c_HOL_Oinverse__class_Odivide(X2,X6,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).

fof(f469,axiom,
    ! [X2,X0,X1,X6] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X1,X2,X0),X6,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X1,X6,X0),c_HOL_Oinverse__class_Odivide(X2,X6,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__divide__distrib_0) ).

fof(f3711,plain,
    spl0_389,
    inference(avatar_split_clause,[],[f422,f3709]) ).

fof(f3709,plain,
    ( spl0_389
  <=> ! [X4,X0,X3] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | c_Parity_Oeven__odd__class_Oeven(X3,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X0),X0)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),X3),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).

fof(f422,axiom,
    ! [X3,X0,X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_Parity_Oeven__odd__class_Oeven(X3,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X0),X0)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),X3),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__zero__eq_2) ).

fof(f3707,plain,
    spl0_388,
    inference(avatar_split_clause,[],[f420,f3705]) ).

fof(f3705,plain,
    ( spl0_388
  <=> ! [X4,X0,X3] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | c_Parity_Oeven__odd__class_Oeven(X3,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X4,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).

fof(f420,axiom,
    ! [X3,X0,X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_Parity_Oeven__odd__class_Oeven(X3,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X4,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),X3),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power__eq_5) ).

fof(f3703,plain,
    spl0_387,
    inference(avatar_split_clause,[],[f407,f3701]) ).

fof(f3701,plain,
    ( spl0_387
  <=> ! [X18,X4,X0,X9] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_HOL_Ouminus__class_Ouminus(X18,X0) = X4
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X9),X18)) != X9 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).

fof(f407,axiom,
    ! [X0,X18,X9,X4] :
      ( ~ class_OrderedGroup_Oab__group__add(X0)
      | c_HOL_Ouminus__class_Ouminus(X18,X0) = X4
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X9),X18)) != X9 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__end_0) ).

fof(f3699,plain,
    spl0_386,
    inference(avatar_split_clause,[],[f392,f3697]) ).

fof(f3697,plain,
    ( spl0_386
  <=> ! [X0,X1] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X1
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).

fof(f392,axiom,
    ! [X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X1
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power2_1) ).

fof(f3695,plain,
    spl0_385,
    inference(avatar_split_clause,[],[f227,f3693]) ).

fof(f3693,plain,
    ( spl0_385
  <=> ! [X0,X3] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | ~ c_Parity_Oeven__odd__class_Oeven(X3,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X3
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ozero__class_Ozero(X0)),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).

fof(f227,axiom,
    ! [X3,X0] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | ~ c_Parity_Oeven__odd__class_Oeven(X3,tc_nat)
      | c_HOL_Ozero__class_Ozero(tc_nat) = X3
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ozero__class_Ozero(X0)),X3),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power__eq_1) ).

fof(f3691,plain,
    spl0_384,
    inference(avatar_split_clause,[],[f161,f3689]) ).

fof(f3689,plain,
    ( spl0_384
  <=> ! [X3,X19] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X19,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X19),X3),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).

fof(f161,axiom,
    ! [X3,X19] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X19,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X19),X3),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_2) ).

fof(f3687,plain,
    spl0_383,
    inference(avatar_split_clause,[],[f83,f3685]) ).

fof(f3685,plain,
    ( spl0_383
  <=> ! [X4,X0,X3] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
        | ~ c_Parity_Oeven__odd__class_Oeven(X3,tc_nat)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ouminus__class_Ouminus(X4,X0)),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).

fof(f83,axiom,
    ! [X3,X0,X4] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
      | ~ c_Parity_Oeven__odd__class_Oeven(X3,tc_nat)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ouminus__class_Ouminus(X4,X0)),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__power__if_0) ).

fof(f3683,plain,
    spl0_382,
    inference(avatar_split_clause,[],[f61,f3681]) ).

fof(f3681,plain,
    ( spl0_382
  <=> ! [X4,X0] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | ~ class_Ring__and__Field_Odivision__by__zero(X0)
        | ~ class_Int_Onumber__ring(X0)
        | c_HOL_Oinverse__class_Odivide(c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0),X4,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X4,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).

fof(f61,axiom,
    ! [X0,X4] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | ~ class_Ring__and__Field_Odivision__by__zero(X0)
      | ~ class_Int_Onumber__ring(X0)
      | c_HOL_Oinverse__class_Odivide(c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0),X4,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X4,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus1__divide_0) ).

fof(f3674,plain,
    spl0_381,
    inference(avatar_split_clause,[],[f26,f3672]) ).

fof(f3672,plain,
    ( spl0_381
  <=> ! [X0,X6,X2,X1] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_HOL_Oord__class_Oless(X2,X6,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X6),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).

fof(f26,axiom,
    ! [X2,X0,X1,X6] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | ~ c_HOL_Oord__class_Oless(X2,X6,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
      | c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X6),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).

fof(f3597,plain,
    ( ~ spl0_379
    | spl0_380
    | ~ spl0_167
    | ~ spl0_236 ),
    inference(avatar_split_clause,[],[f2249,f2164,f1672,f3594,f3590]) ).

fof(f3590,plain,
    ( spl0_379
  <=> class_Ring__and__Field_Oordered__idom(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).

fof(f1672,plain,
    ( spl0_167
  <=> ! [X3] : c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(X3)),X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).

fof(f2164,plain,
    ( spl0_236
  <=> ! [X4,X0] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),c_HOL_Ozero__class_Ozero(tc_nat)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).

fof(f2249,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex)
    | ~ class_Ring__and__Field_Oordered__idom(tc_Complex_Ocomplex)
    | ~ spl0_167
    | ~ spl0_236 ),
    inference(superposition,[],[f2165,f1673]) ).

fof(f1673,plain,
    ( ! [X3] : c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(X3)),X3)
    | ~ spl0_167 ),
    inference(avatar_component_clause,[],[f1672]) ).

fof(f2165,plain,
    ( ! [X0,X4] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),c_HOL_Ozero__class_Ozero(tc_nat)),X0)
        | ~ class_Ring__and__Field_Oordered__idom(X0) )
    | ~ spl0_236 ),
    inference(avatar_component_clause,[],[f2164]) ).

fof(f3540,plain,
    spl0_378,
    inference(avatar_split_clause,[],[f685,f3538]) ).

fof(f3538,plain,
    ( spl0_378
  <=> ! [X18,X0] :
        ( ~ class_Int_Onumber__ring(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X18),X18) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X18),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).

fof(f685,axiom,
    ! [X0,X18] :
      ( ~ class_Int_Onumber__ring(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X18),X18) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X18),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__2__right_0) ).

fof(f3536,plain,
    spl0_377,
    inference(avatar_split_clause,[],[f684,f3534]) ).

fof(f3534,plain,
    ( spl0_377
  <=> ! [X18,X0] :
        ( ~ class_Int_Onumber__ring(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),X0)),X18) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X18),X18) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).

fof(f684,axiom,
    ! [X0,X18] :
      ( ~ class_Int_Onumber__ring(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),X0)),X18) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X18),X18) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__2_0) ).

fof(f3532,plain,
    spl0_376,
    inference(avatar_split_clause,[],[f607,f3530]) ).

fof(f3530,plain,
    ( spl0_376
  <=> ! [X0,X1] :
        ( ~ class_OrderedGroup_Omonoid__mult(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).

fof(f607,axiom,
    ! [X0,X1] :
      ( ~ class_OrderedGroup_Omonoid__mult(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power2__eq__square_0) ).

fof(f3528,plain,
    spl0_375,
    inference(avatar_split_clause,[],[f588,f3526]) ).

fof(f3526,plain,
    ( spl0_375
  <=> ! [X4,X0] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X4) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).

fof(f588,axiom,
    ! [X0,X4] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X4) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I29_J_0) ).

fof(f3524,plain,
    spl0_374,
    inference(avatar_split_clause,[],[f572,f3522]) ).

fof(f3522,plain,
    ( spl0_374
  <=> ! [X0,X1,X3] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),hAPP(c_Suc,X3)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).

fof(f572,axiom,
    ! [X3,X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),hAPP(c_Suc,X3)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__gt1_0) ).

fof(f3520,plain,
    ( ~ spl0_373
    | ~ spl0_119
    | ~ spl0_220 ),
    inference(avatar_split_clause,[],[f2099,f2013,f1433,f3517]) ).

fof(f3517,plain,
    ( spl0_373
  <=> c_HOL_Ozero__class_Ozero(tc_nat) = c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).

fof(f2099,plain,
    ( c_HOL_Ozero__class_Ozero(tc_nat) != c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)
    | ~ spl0_119
    | ~ spl0_220 ),
    inference(superposition,[],[f1434,f2015]) ).

fof(f3515,plain,
    spl0_372,
    inference(avatar_split_clause,[],[f433,f3513]) ).

fof(f3513,plain,
    ( spl0_372
  <=> ! [X4,X0] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
        | c_Parity_Oeven__odd__class_Oeven(X4,tc_nat)
        | c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0)),X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).

fof(f433,axiom,
    ! [X0,X4] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
      | c_Parity_Oeven__odd__class_Oeven(X4,tc_nat)
      | c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0)),X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__one__odd__power_0) ).

fof(f3511,plain,
    spl0_371,
    inference(avatar_split_clause,[],[f419,f3509]) ).

fof(f3509,plain,
    ( spl0_371
  <=> ! [X4,X0,X3] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | ~ c_Parity_Oeven__odd__class_Oeven(X3,tc_nat)
        | c_HOL_Ozero__class_Ozero(X0) = X4
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).

fof(f419,axiom,
    ! [X3,X0,X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | ~ c_Parity_Oeven__odd__class_Oeven(X3,tc_nat)
      | c_HOL_Ozero__class_Ozero(X0) = X4
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),X3),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power__eq_4) ).

fof(f3507,plain,
    spl0_370,
    inference(avatar_split_clause,[],[f383,f3505]) ).

fof(f3505,plain,
    ( spl0_370
  <=> ! [X0,X1] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X1
        | c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).

fof(f383,axiom,
    ! [X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X1
      | c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__eq__power2_0) ).

fof(f3503,plain,
    spl0_369,
    inference(avatar_split_clause,[],[f291,f3501]) ).

fof(f3501,plain,
    ( spl0_369
  <=> ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Ono__zero__divisors(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X2
        | c_HOL_Ozero__class_Ozero(X0) = X1
        | c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).

fof(f291,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Ring__and__Field_Ono__zero__divisors(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X2
      | c_HOL_Ozero__class_Ozero(X0) = X1
      | c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_no__zero__divirors__neq0_0) ).

fof(f3499,plain,
    spl0_368,
    inference(avatar_split_clause,[],[f289,f3497]) ).

fof(f3497,plain,
    ( spl0_368
  <=> ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X1
        | c_HOL_Ozero__class_Ozero(X0) = X2
        | c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).

fof(f289,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X1
      | c_HOL_Ozero__class_Ozero(X0) = X2
      | c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_0) ).

fof(f3495,plain,
    spl0_367,
    inference(avatar_split_clause,[],[f288,f3493]) ).

fof(f3493,plain,
    ( spl0_367
  <=> ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Oring(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ouminus__class_Ouminus(X1,X0)),X2) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).

fof(f288,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Ring__and__Field_Oring(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ouminus__class_Ouminus(X1,X0)),X2) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__left_0) ).

fof(f3491,plain,
    spl0_366,
    inference(avatar_split_clause,[],[f287,f3489]) ).

fof(f3489,plain,
    ( spl0_366
  <=> ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Oring(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),c_HOL_Ouminus__class_Ouminus(X2,X0)) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).

fof(f287,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Ring__and__Field_Oring(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),c_HOL_Ouminus__class_Ouminus(X2,X0)) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__right_0) ).

fof(f3487,plain,
    spl0_365,
    inference(avatar_split_clause,[],[f285,f3485]) ).

fof(f3485,plain,
    ( spl0_365
  <=> ! [X9,X0,X4] :
        ( ~ class_RealVector_Oreal__normed__algebra(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ouminus__class_Ouminus(X4,X0)),X9) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X9),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).

fof(f285,axiom,
    ! [X0,X9,X4] :
      ( ~ class_RealVector_Oreal__normed__algebra(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ouminus__class_Ouminus(X4,X0)),X9) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X9),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Ominus_0) ).

fof(f3483,plain,
    spl0_364,
    inference(avatar_split_clause,[],[f283,f3481]) ).

fof(f3481,plain,
    ( spl0_364
  <=> ! [X29,X4,X0] :
        ( ~ class_RealVector_Oreal__normed__algebra(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X29),c_HOL_Ouminus__class_Ouminus(X4,X0)) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X29),X4),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).

fof(f283,axiom,
    ! [X0,X29,X4] :
      ( ~ class_RealVector_Oreal__normed__algebra(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X29),c_HOL_Ouminus__class_Ouminus(X4,X0)) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X29),X4),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Ominus_0) ).

fof(f3479,plain,
    spl0_363,
    inference(avatar_split_clause,[],[f282,f3477]) ).

fof(f3477,plain,
    ( spl0_363
  <=> ! [X2,X0] :
        ( ~ class_Ring__and__Field_Oidom(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ouminus__class_Ouminus(X2,X0)),c_HOL_Ouminus__class_Ouminus(X2,X0)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).

fof(f282,axiom,
    ! [X2,X0] :
      ( ~ class_Ring__and__Field_Oidom(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ouminus__class_Ouminus(X2,X0)),c_HOL_Ouminus__class_Ouminus(X2,X0)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_square__eq__iff_1) ).

fof(f3475,plain,
    ( spl0_362
    | ~ spl0_159
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1727,f1668,f1640,f3473]) ).

fof(f3473,plain,
    ( spl0_362
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).

fof(f1727,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat) )
    | ~ spl0_159
    | ~ spl0_166 ),
    inference(resolution,[],[f1669,f1641]) ).

fof(f3471,plain,
    spl0_361,
    inference(avatar_split_clause,[],[f281,f3469]) ).

fof(f3469,plain,
    ( spl0_361
  <=> ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Oring(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ouminus__class_Ouminus(X1,X0)),c_HOL_Ouminus__class_Ouminus(X2,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).

fof(f281,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Ring__and__Field_Oring(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ouminus__class_Ouminus(X1,X0)),c_HOL_Ouminus__class_Ouminus(X2,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__minus_0) ).

fof(f3467,plain,
    spl0_360,
    inference(avatar_split_clause,[],[f269,f3465]) ).

fof(f3465,plain,
    ( spl0_360
  <=> ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Oring(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ouminus__class_Ouminus(X1,X0)),X2) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),c_HOL_Ouminus__class_Ouminus(X2,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).

fof(f269,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Ring__and__Field_Oring(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ouminus__class_Ouminus(X1,X0)),X2) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),c_HOL_Ouminus__class_Ouminus(X2,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__commute_0) ).

fof(f3463,plain,
    spl0_359,
    inference(avatar_split_clause,[],[f261,f3461]) ).

fof(f3461,plain,
    ( spl0_359
  <=> ! [X4,X0,X9,X27,X28] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
        | ~ c_HOL_Oord__class_Oless(X4,X9,X0)
        | c_HOL_Oord__class_Oless(X27,X28,X0)
        | c_HOL_Ominus__class_Ominus(X4,X9,X0) != c_HOL_Ominus__class_Ominus(X27,X28,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).

fof(f261,axiom,
    ! [X28,X0,X9,X27,X4] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
      | ~ c_HOL_Oord__class_Oless(X4,X9,X0)
      | c_HOL_Oord__class_Oless(X27,X28,X0)
      | c_HOL_Ominus__class_Ominus(X4,X9,X0) != c_HOL_Ominus__class_Ominus(X27,X28,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eqI_0) ).

fof(f3459,plain,
    spl0_358,
    inference(avatar_split_clause,[],[f239,f3457]) ).

fof(f3457,plain,
    ( spl0_358
  <=> ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X2
        | c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) = c_HOL_Oinverse__class_Odivide(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).

fof(f239,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X2
      | c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) = c_HOL_Oinverse__class_Odivide(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__minus__divide__right_0) ).

fof(f3455,plain,
    spl0_357,
    inference(avatar_split_clause,[],[f219,f3453]) ).

fof(f3453,plain,
    ( spl0_357
  <=> ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X2
        | c_HOL_Oinverse__class_Odivide(X1,X2,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).

fof(f219,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X2
      | c_HOL_Oinverse__class_Odivide(X1,X2,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__minus__divide__divide_0) ).

fof(f3451,plain,
    spl0_356,
    inference(avatar_split_clause,[],[f168,f3449]) ).

fof(f3449,plain,
    ( spl0_356
  <=> ! [X4,X3] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X3
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X4),X3),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).

fof(f168,axiom,
    ! [X3,X4] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X3
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X4),X3),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__zero__less__power__iff_0) ).

fof(f3447,plain,
    spl0_355,
    inference(avatar_split_clause,[],[f159,f3445]) ).

fof(f3445,plain,
    ( spl0_355
  <=> ! [X20,X19,X3] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X20,tc_nat)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X20),X19),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X20),X3),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).

fof(f159,axiom,
    ! [X3,X19,X20] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X20,tc_nat)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X20),X19),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X20),X3),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel1_0) ).

fof(f3443,plain,
    spl0_354,
    inference(avatar_split_clause,[],[f158,f3441]) ).

fof(f3441,plain,
    ( spl0_354
  <=> ! [X20,X19,X3] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X20,tc_nat)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X19),X20),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X3),X20),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).

fof(f158,axiom,
    ! [X3,X19,X20] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X20,tc_nat)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X19),X20),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X3),X20),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel2_0) ).

fof(f3439,plain,
    spl0_353,
    inference(avatar_split_clause,[],[f119,f3437]) ).

fof(f3437,plain,
    ( spl0_353
  <=> ! [X6,X2,X0] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | ~ class_Ring__and__Field_Odivision__by__zero(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X6
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oinverse__class_Odivide(X2,X6,X0)),X6) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).

fof(f119,axiom,
    ! [X2,X0,X6] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | ~ class_Ring__and__Field_Odivision__by__zero(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X6
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oinverse__class_Odivide(X2,X6,X0)),X6) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq_0) ).

fof(f3425,plain,
    ( spl0_352
    | ~ spl0_123
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1724,f1664,f1449,f3423]) ).

fof(f3423,plain,
    ( spl0_352
  <=> ! [X0] : c_HOL_Oord__class_Oless(X0,hAPP(c_Suc,hAPP(c_Suc,X0)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).

fof(f1724,plain,
    ( ! [X0] : c_HOL_Oord__class_Oless(X0,hAPP(c_Suc,hAPP(c_Suc,X0)),tc_nat)
    | ~ spl0_123
    | ~ spl0_165 ),
    inference(resolution,[],[f1665,f1450]) ).

fof(f3376,plain,
    spl0_351,
    inference(avatar_split_clause,[],[f826,f3374]) ).

fof(f3374,plain,
    ( spl0_351
  <=> ! [X3] :
        ( c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat) = X3
        | c_HOL_Ozero__class_Ozero(tc_nat) = X3
        | ~ c_HOL_Oord__class_Oless(X3,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).

fof(f826,plain,
    ! [X3] :
      ( c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat) = X3
      | c_HOL_Ozero__class_Ozero(tc_nat) = X3
      | ~ c_HOL_Oord__class_Oless(X3,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) ),
    inference(forward_demodulation,[],[f498,f377]) ).

fof(f498,axiom,
    ! [X3] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X3
      | hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = X3
      | ~ c_HOL_Oord__class_Oless(X3,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__2__cases_0) ).

fof(f3372,plain,
    ( spl0_350
    | ~ spl0_97
    | ~ spl0_155 ),
    inference(avatar_split_clause,[],[f1682,f1624,f1328,f3370]) ).

fof(f3370,plain,
    ( spl0_350
  <=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).

fof(f1624,plain,
    ( spl0_155
  <=> ! [X0,X1] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X0),X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).

fof(f1682,plain,
    ( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex)
    | ~ spl0_97
    | ~ spl0_155 ),
    inference(resolution,[],[f1625,f1330]) ).

fof(f1625,plain,
    ( ! [X0,X1] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X0),X1,X0) )
    | ~ spl0_155 ),
    inference(avatar_component_clause,[],[f1624]) ).

fof(f3368,plain,
    spl0_349,
    inference(avatar_split_clause,[],[f622,f3366]) ).

fof(f3366,plain,
    ( spl0_349
  <=> ! [X20,X19,X3] :
        ( c_HOL_Oord__class_Oless(X19,X3,tc_nat)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X19),X20),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X3),X20),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).

fof(f622,axiom,
    ! [X3,X19,X20] :
      ( c_HOL_Oord__class_Oless(X19,X3,tc_nat)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X19),X20),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X3),X20),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel2_1) ).

fof(f3364,plain,
    spl0_348,
    inference(avatar_split_clause,[],[f621,f3362]) ).

fof(f3362,plain,
    ( spl0_348
  <=> ! [X20,X19,X3] :
        ( c_HOL_Oord__class_Oless(X19,X3,tc_nat)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X20),X19),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X20),X3),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).

fof(f621,axiom,
    ! [X3,X19,X20] :
      ( c_HOL_Oord__class_Oless(X19,X3,tc_nat)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X20),X19),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X20),X3),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel1_1) ).

fof(f3360,plain,
    spl0_347,
    inference(avatar_split_clause,[],[f536,f3358]) ).

fof(f3358,plain,
    ( spl0_347
  <=> ! [X0,X6,X2,X1] :
        ( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
        | X2 = X6
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X6),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).

fof(f536,axiom,
    ! [X2,X0,X1,X6] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
      | X2 = X6
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X6),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).

fof(f3356,plain,
    spl0_346,
    inference(avatar_split_clause,[],[f535,f3354]) ).

fof(f3354,plain,
    ( spl0_346
  <=> ! [X0,X6,X2,X1] :
        ( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
        | X2 = X6
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).

fof(f535,axiom,
    ! [X2,X0,X1,X6] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
      | X2 = X6
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).

fof(f3352,plain,
    spl0_345,
    inference(avatar_split_clause,[],[f534,f3350]) ).

fof(f3350,plain,
    ( spl0_345
  <=> ! [X0,X6,X2,X1] :
        ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X0)
        | X2 = X6
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).

fof(f534,axiom,
    ! [X2,X0,X1,X6] :
      ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X0)
      | X2 = X6
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).

fof(f3348,plain,
    spl0_344,
    inference(avatar_split_clause,[],[f243,f3346]) ).

fof(f3346,plain,
    ( spl0_344
  <=> ! [X0,X1] :
        ( ~ class_Ring__and__Field_Ozero__neq__one(X0)
        | ~ class_Ring__and__Field_Ono__zero__divisors(X0)
        | ~ class_Ring__and__Field_Omult__zero(X0)
        | ~ class_Power_Opower(X0)
        | c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),c_HOL_Ozero__class_Ozero(tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).

fof(f243,axiom,
    ! [X0,X1] :
      ( ~ class_Ring__and__Field_Ozero__neq__one(X0)
      | ~ class_Ring__and__Field_Ono__zero__divisors(X0)
      | ~ class_Ring__and__Field_Omult__zero(X0)
      | ~ class_Power_Opower(X0)
      | c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_1) ).

fof(f3344,plain,
    spl0_343,
    inference(avatar_split_clause,[],[f228,f3342]) ).

fof(f3342,plain,
    ( spl0_343
  <=> ! [X0,X3] :
        ( ~ class_Ring__and__Field_Osemiring__0(X0)
        | ~ class_Power_Opower(X0)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X3
        | c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ozero__class_Ozero(X0)),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).

fof(f228,axiom,
    ! [X3,X0] :
      ( ~ class_Ring__and__Field_Osemiring__0(X0)
      | ~ class_Power_Opower(X0)
      | c_HOL_Ozero__class_Ozero(tc_nat) = X3
      | c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ozero__class_Ozero(X0)),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0__left_1) ).

fof(f3340,plain,
    spl0_342,
    inference(avatar_split_clause,[],[f195,f3338]) ).

fof(f3338,plain,
    ( spl0_342
  <=> ! [X15,X17,X0,X13,X6,X12,X16,X1] :
        ( ~ c_Groebner__Basis_Ogb__semiring(X15,X13,X12,X16,X17,X0)
        | hAPP(hAPP(X15,X1),X6) = hAPP(hAPP(X15,X6),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).

fof(f195,axiom,
    ! [X0,X1,X6,X16,X17,X15,X12,X13] :
      ( ~ c_Groebner__Basis_Ogb__semiring(X15,X13,X12,X16,X17,X0)
      | hAPP(hAPP(X15,X1),X6) = hAPP(hAPP(X15,X6),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I24_J_0) ).

fof(f3336,plain,
    spl0_341,
    inference(avatar_split_clause,[],[f87,f3334]) ).

fof(f3334,plain,
    ( spl0_341
  <=> ! [X15,X17,X4,X9,X0,X13,X12,X16] :
        ( ~ c_Groebner__Basis_Ogb__semiring(X15,X13,X12,X16,X17,X0)
        | hAPP(hAPP(X13,X4),X9) = hAPP(hAPP(X13,X9),X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).

fof(f87,axiom,
    ! [X0,X9,X16,X4,X17,X15,X12,X13] :
      ( ~ c_Groebner__Basis_Ogb__semiring(X15,X13,X12,X16,X17,X0)
      | hAPP(hAPP(X13,X4),X9) = hAPP(hAPP(X13,X9),X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Omul__c_0) ).

fof(f3327,plain,
    ( spl0_340
    | ~ spl0_101
    | ~ spl0_154 ),
    inference(avatar_split_clause,[],[f1681,f1620,f1348,f3324]) ).

fof(f1620,plain,
    ( spl0_154
  <=> ! [X0] :
        ( ~ class_Int_Onumber__ring(X0)
        | c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0) = c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).

fof(f1681,plain,
    ( c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_Complex_Ocomplex)
    | ~ spl0_101
    | ~ spl0_154 ),
    inference(resolution,[],[f1621,f1350]) ).

fof(f1621,plain,
    ( ! [X0] :
        ( ~ class_Int_Onumber__ring(X0)
        | c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0) = c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0) )
    | ~ spl0_154 ),
    inference(avatar_component_clause,[],[f1620]) ).

fof(f3279,plain,
    ( spl0_339
    | ~ spl0_68
    | ~ spl0_154 ),
    inference(avatar_split_clause,[],[f1680,f1620,f1183,f3276]) ).

fof(f1680,plain,
    ( c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_Int_Oint)
    | ~ spl0_68
    | ~ spl0_154 ),
    inference(resolution,[],[f1621,f1185]) ).

fof(f3205,plain,
    ( spl0_338
    | ~ spl0_127
    | ~ spl0_148 ),
    inference(avatar_split_clause,[],[f1607,f1567,f1465,f3202]) ).

fof(f3202,plain,
    ( spl0_338
  <=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).

fof(f1607,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat),tc_nat)
    | ~ spl0_127
    | ~ spl0_148 ),
    inference(superposition,[],[f1466,f1569]) ).

fof(f3180,plain,
    spl0_337,
    inference(avatar_split_clause,[],[f824,f3178]) ).

fof(f3178,plain,
    ( spl0_337
  <=> ! [X19,X3] :
        ( hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X19),X3) != c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat)
        | c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).

fof(f824,plain,
    ! [X3,X19] :
      ( hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X19),X3) != c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat)
      | c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat) = X3 ),
    inference(forward_demodulation,[],[f823,f377]) ).

fof(f823,plain,
    ! [X3,X19] :
      ( c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat) = X3
      | hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X19),X3) ),
    inference(forward_demodulation,[],[f147,f377]) ).

fof(f147,axiom,
    ! [X3,X19] :
      ( hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = X3
      | hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X19),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__1__iff_1) ).

fof(f3176,plain,
    spl0_336,
    inference(avatar_split_clause,[],[f822,f3174]) ).

fof(f3174,plain,
    ( spl0_336
  <=> ! [X19,X3] :
        ( hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X19),X3) != c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat)
        | c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat) = X19 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).

fof(f822,plain,
    ! [X3,X19] :
      ( hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X19),X3) != c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat)
      | c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat) = X19 ),
    inference(forward_demodulation,[],[f821,f377]) ).

fof(f821,plain,
    ! [X3,X19] :
      ( c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat) = X19
      | hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X19),X3) ),
    inference(forward_demodulation,[],[f148,f377]) ).

fof(f148,axiom,
    ! [X3,X19] :
      ( hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = X19
      | hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X19),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__1__iff_0) ).

fof(f3172,plain,
    spl0_335,
    inference(avatar_split_clause,[],[f818,f3169]) ).

fof(f3169,plain,
    ( spl0_335
  <=> c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat)),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).

fof(f818,plain,
    c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat)),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat)),
    inference(forward_demodulation,[],[f149,f377]) ).

fof(f149,axiom,
    hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__1__iff_2) ).

fof(f3167,plain,
    spl0_334,
    inference(avatar_split_clause,[],[f490,f3165]) ).

fof(f3165,plain,
    ( spl0_334
  <=> ! [X3,X19] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X19
        | c_HOL_Ozero__class_Ozero(tc_nat) = X3
        | c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X19),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).

fof(f490,axiom,
    ! [X3,X19] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X19
      | c_HOL_Ozero__class_Ozero(tc_nat) = X3
      | c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X19),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__is__0_0) ).

fof(f3163,plain,
    spl0_333,
    inference(avatar_split_clause,[],[f471,f3161]) ).

fof(f3161,plain,
    ( spl0_333
  <=> ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | ~ class_Ring__and__Field_Odivision__by__zero(X0)
        | c_HOL_Oinverse__class_Odivide(X1,X2,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).

fof(f471,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | ~ class_Ring__and__Field_Odivision__by__zero(X0)
      | c_HOL_Oinverse__class_Odivide(X1,X2,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__divide__divide_0) ).

fof(f3159,plain,
    spl0_332,
    inference(avatar_split_clause,[],[f468,f3157]) ).

fof(f3157,plain,
    ( spl0_332
  <=> ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | ~ class_Ring__and__Field_Odivision__by__zero(X0)
        | c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) = c_HOL_Oinverse__class_Odivide(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).

fof(f468,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | ~ class_Ring__and__Field_Odivision__by__zero(X0)
      | c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) = c_HOL_Oinverse__class_Odivide(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__divide__right_0) ).

fof(f3155,plain,
    spl0_331,
    inference(avatar_split_clause,[],[f435,f3153]) ).

fof(f3153,plain,
    ( spl0_331
  <=> ! [X4,X0] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
        | ~ c_Parity_Oeven__odd__class_Oeven(X4,tc_nat)
        | c_HOL_Oone__class_Oone(X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0)),X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).

fof(f435,axiom,
    ! [X0,X4] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
      | ~ c_Parity_Oeven__odd__class_Oeven(X4,tc_nat)
      | c_HOL_Oone__class_Oone(X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0)),X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__one__even__power_0) ).

fof(f3151,plain,
    spl0_330,
    inference(avatar_split_clause,[],[f432,f3149]) ).

fof(f3149,plain,
    ( spl0_330
  <=> ! [X4,X0] :
        ( ~ class_Int_Onumber__ring(X0)
        | c_Parity_Oeven__odd__class_Oeven(X4,tc_nat)
        | c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0)),X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).

fof(f432,axiom,
    ! [X0,X4] :
      ( ~ class_Int_Onumber__ring(X0)
      | c_Parity_Oeven__odd__class_Oeven(X4,tc_nat)
      | c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0)),X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__one__odd__power_0) ).

fof(f3145,plain,
    spl0_329,
    inference(avatar_split_clause,[],[f401,f3143]) ).

fof(f401,axiom,
    ! [X2,X0,X1] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ouminus__class_Ouminus(X1,X0)),X2)) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__minus__cancel_0) ).

fof(f3141,plain,
    spl0_328,
    inference(avatar_split_clause,[],[f400,f3139]) ).

fof(f3139,plain,
    ( spl0_328
  <=> ! [X9,X0,X18] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ouminus__class_Ouminus(X18,X0)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X9),X18)) = X9 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).

fof(f400,axiom,
    ! [X0,X18,X9] :
      ( ~ class_OrderedGroup_Oab__group__add(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ouminus__class_Ouminus(X18,X0)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X9),X18)) = X9 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__end_1) ).

fof(f3137,plain,
    spl0_327,
    inference(avatar_split_clause,[],[f399,f3135]) ).

fof(f3135,plain,
    ( spl0_327
  <=> ! [X2,X0,X1] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ouminus__class_Ouminus(X1,X0)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2)) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).

fof(f399,axiom,
    ! [X2,X0,X1] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ouminus__class_Ouminus(X1,X0)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2)) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add__cancel_0) ).

fof(f3133,plain,
    spl0_326,
    inference(avatar_split_clause,[],[f393,f3131]) ).

fof(f393,axiom,
    ! [X0] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ozero__class_Ozero(X0)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power2_0) ).

fof(f3129,plain,
    spl0_325,
    inference(avatar_split_clause,[],[f117,f3127]) ).

fof(f3127,plain,
    ( spl0_325
  <=> ! [X6,X0] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | ~ class_Ring__and__Field_Odivision__by__zero(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ozero__class_Ozero(X0)),X6),X6,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).

fof(f117,axiom,
    ! [X0,X6] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | ~ class_Ring__and__Field_Odivision__by__zero(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ozero__class_Ozero(X0)),X6),X6,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq_4) ).

fof(f3125,plain,
    spl0_324,
    inference(avatar_split_clause,[],[f115,f3123]) ).

fof(f3123,plain,
    ( spl0_324
  <=> ! [X6,X0,X1] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X6
        | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X6),X6,X0) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).

fof(f115,axiom,
    ! [X0,X1,X6] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X6
      | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X6),X6,X0) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__imp_0) ).

fof(f3121,plain,
    spl0_323,
    inference(avatar_split_clause,[],[f73,f3119]) ).

fof(f73,axiom,
    ! [X2,X0,X1] :
      ( ~ class_OrderedGroup_Oab__group__add(X0)
      | c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X1,X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Lim_Ominus__diff__minus_0) ).

fof(f3117,plain,
    spl0_322,
    inference(avatar_split_clause,[],[f30,f3115]) ).

fof(f3115,plain,
    ( spl0_322
  <=> ! [X0,X1] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X1),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).

fof(f30,axiom,
    ! [X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X1),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_1) ).

fof(f3113,plain,
    spl0_321,
    inference(avatar_split_clause,[],[f29,f3111]) ).

fof(f3111,plain,
    ( spl0_321
  <=> ! [X0,X1] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X1),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).

fof(f29,axiom,
    ! [X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X1),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_0) ).

fof(f3109,plain,
    spl0_320,
    inference(avatar_split_clause,[],[f28,f3107]) ).

fof(f3107,plain,
    ( spl0_320
  <=> ! [X0,X1] :
        ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
        | c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X1),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).

fof(f28,axiom,
    ! [X0,X1] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
      | c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X1),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_0) ).

fof(f3103,plain,
    spl0_319,
    inference(avatar_split_clause,[],[f27,f3101]) ).

fof(f3101,plain,
    ( spl0_319
  <=> ! [X0,X1] :
        ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
        | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X1),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).

fof(f27,axiom,
    ! [X0,X1] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
      | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X1),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_1) ).

fof(f3099,plain,
    spl0_318,
    inference(avatar_split_clause,[],[f25,f3097]) ).

fof(f3097,plain,
    ( spl0_318
  <=> ! [X0,X1] :
        ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).

fof(f25,axiom,
    ! [X0,X1] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X1),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_0) ).

fof(f3095,plain,
    spl0_317,
    inference(avatar_split_clause,[],[f24,f3093]) ).

fof(f3093,plain,
    ( spl0_317
  <=> ! [X0,X1] :
        ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).

fof(f24,axiom,
    ! [X0,X1] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X1),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_1) ).

fof(f3091,plain,
    spl0_316,
    inference(avatar_split_clause,[],[f8,f3089]) ).

fof(f3089,plain,
    ( spl0_316
  <=> ! [X4,X0,X3] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),X3),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).

fof(f8,axiom,
    ! [X3,X0,X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X0),X0)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),X3),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__zero__eq_1) ).

fof(f3087,plain,
    spl0_315,
    inference(avatar_split_clause,[],[f7,f3085]) ).

fof(f7,axiom,
    ! [X3,X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power_0) ).

fof(f3049,plain,
    spl0_314,
    inference(avatar_split_clause,[],[f641,f3047]) ).

fof(f3047,plain,
    ( spl0_314
  <=> ! [X0] :
        ( ~ class_Ring__and__Field_Osemiring__1(X0)
        | c_HOL_Oone__class_Oone(X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Oone__class_Oone(X0)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).

fof(f641,axiom,
    ! [X0] :
      ( ~ class_Ring__and__Field_Osemiring__1(X0)
      | c_HOL_Oone__class_Oone(X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Oone__class_Oone(X0)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__power2_0) ).

fof(f3045,plain,
    spl0_313,
    inference(avatar_split_clause,[],[f520,f3043]) ).

fof(f3043,plain,
    ( spl0_313
  <=> ! [X0] :
        ( ~ class_Int_Onumber__ring(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oone__class_Oone(X0)),c_HOL_Oone__class_Oone(X0)) = c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).

fof(f520,axiom,
    ! [X0] :
      ( ~ class_Int_Onumber__ring(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oone__class_Oone(X0)),c_HOL_Oone__class_Oone(X0)) = c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__add__one__is__two_0) ).

fof(f3041,plain,
    spl0_312,
    inference(avatar_split_clause,[],[f494,f3039]) ).

fof(f3039,plain,
    ( spl0_312
  <=> ! [X0,X1] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).

fof(f494,axiom,
    ! [X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power2__less__0_0) ).

fof(f3037,plain,
    spl0_311,
    inference(avatar_split_clause,[],[f491,f3035]) ).

fof(f3035,plain,
    ( spl0_311
  <=> ! [X4,X9] :
        ( ~ c_Parity_Oeven__odd__class_Oeven(X4,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X9,tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X4),X9),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).

fof(f491,axiom,
    ! [X9,X4] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X9,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X4),X9),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__power__nat_2) ).

fof(f3033,plain,
    spl0_310,
    inference(avatar_split_clause,[],[f436,f3031]) ).

fof(f3031,plain,
    ( spl0_310
  <=> ! [X4,X0] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | ~ class_Ring__and__Field_Odivision__by__zero(X0)
        | ~ class_Int_Onumber__ring(X0)
        | c_HOL_Ouminus__class_Ouminus(X4,X0) = c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).

fof(f436,axiom,
    ! [X0,X4] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | ~ class_Ring__and__Field_Odivision__by__zero(X0)
      | ~ class_Int_Onumber__ring(X0)
      | c_HOL_Ouminus__class_Ouminus(X4,X0) = c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__minus1_0) ).

fof(f3029,plain,
    spl0_309,
    inference(avatar_split_clause,[],[f403,f3027]) ).

fof(f3027,plain,
    ( spl0_309
  <=> ! [X4,X0,X1] :
        ( ~ class_Ring__and__Field_Oidom(X0)
        | ~ class_Int_Onumber__ring(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X1
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X4),X1) != X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).

fof(f403,axiom,
    ! [X0,X1,X4] :
      ( ~ class_Ring__and__Field_Oidom(X0)
      | ~ class_Int_Onumber__ring(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X1
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X4),X1) != X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).

fof(f3025,plain,
    spl0_308,
    inference(avatar_split_clause,[],[f385,f3023]) ).

fof(f3023,plain,
    ( spl0_308
  <=> ! [X0] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ozero__class_Ozero(X0)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).

fof(f385,axiom,
    ! [X0] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ozero__class_Ozero(X0)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__eq__power2_1) ).

fof(f3021,plain,
    spl0_307,
    inference(avatar_split_clause,[],[f384,f3019]) ).

fof(f3019,plain,
    ( spl0_307
  <=> ! [X0] :
        ( ~ class_Ring__and__Field_Osemiring__1(X0)
        | c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ozero__class_Ozero(X0)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).

fof(f384,axiom,
    ! [X0] :
      ( ~ class_Ring__and__Field_Osemiring__1(X0)
      | c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ozero__class_Ozero(X0)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__power2_0) ).

fof(f3017,plain,
    spl0_306,
    inference(avatar_split_clause,[],[f137,f3015]) ).

fof(f3015,plain,
    ( spl0_306
  <=> ! [X0,X3] :
        ( ~ class_Ring__and__Field_Osemiring__0(X0)
        | ~ class_Power_Opower(X0)
        | c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ozero__class_Ozero(X0)),hAPP(c_Suc,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).

fof(f137,axiom,
    ! [X3,X0] :
      ( ~ class_Ring__and__Field_Osemiring__0(X0)
      | ~ class_Power_Opower(X0)
      | c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ozero__class_Ozero(X0)),hAPP(c_Suc,X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0__Suc_0) ).

fof(f3013,plain,
    spl0_305,
    inference(avatar_split_clause,[],[f136,f3011]) ).

fof(f3011,plain,
    ( spl0_305
  <=> ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | X1 = X2
        | c_HOL_Ozero__class_Ozero(X0) = X2
        | c_HOL_Oinverse__class_Odivide(X1,X2,X0) != c_HOL_Oone__class_Oone(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).

fof(f136,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | X1 = X2
      | c_HOL_Ozero__class_Ozero(X0) = X2
      | c_HOL_Oinverse__class_Odivide(X1,X2,X0) != c_HOL_Oone__class_Oone(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__inverse__eq_0) ).

fof(f3009,plain,
    spl0_304,
    inference(avatar_split_clause,[],[f81,f3007]) ).

fof(f3007,plain,
    ( spl0_304
  <=> ! [X2,X0,X1] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ouminus__class_Ouminus(X1,X0) = X2
        | c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).

fof(f81,axiom,
    ! [X2,X0,X1] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Ouminus__class_Ouminus(X1,X0) = X2
      | c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__unique_0) ).

fof(f3005,plain,
    spl0_303,
    inference(avatar_split_clause,[],[f80,f3003]) ).

fof(f3003,plain,
    ( spl0_303
  <=> ! [X2,X0,X1] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ouminus__class_Ouminus(X2,X0) = X1
        | c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).

fof(f80,axiom,
    ! [X2,X0,X1] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Ouminus__class_Ouminus(X2,X0) = X1
      | c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__neg__iff__add__eq__0_1) ).

fof(f2981,plain,
    spl0_302,
    inference(avatar_split_clause,[],[f68,f2979]) ).

fof(f2979,plain,
    ( spl0_302
  <=> ! [X4,X0] :
        ( ~ class_Int_Onumber__ring(X0)
        | ~ c_Parity_Oeven__odd__class_Oeven(X4,tc_nat)
        | c_HOL_Oone__class_Oone(X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0)),X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).

fof(f68,axiom,
    ! [X0,X4] :
      ( ~ class_Int_Onumber__ring(X0)
      | ~ c_Parity_Oeven__odd__class_Oeven(X4,tc_nat)
      | c_HOL_Oone__class_Oone(X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0)),X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__one__even__power_0) ).

fof(f2844,plain,
    spl0_301,
    inference(avatar_split_clause,[],[f683,f2842]) ).

fof(f2842,plain,
    ( spl0_301
  <=> ! [X19,X3] :
        ( ~ c_HOL_Oord__class_Oless(X19,X3,tc_nat)
        | hAPP(c_Suc,X19) = X3
        | c_HOL_Oord__class_Oless(hAPP(c_Suc,X19),X3,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).

fof(f683,axiom,
    ! [X3,X19] :
      ( ~ c_HOL_Oord__class_Oless(X19,X3,tc_nat)
      | hAPP(c_Suc,X19) = X3
      | c_HOL_Oord__class_Oless(hAPP(c_Suc,X19),X3,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__lessI_0) ).

fof(f2840,plain,
    spl0_300,
    inference(avatar_split_clause,[],[f663,f2838]) ).

fof(f663,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).

fof(f2836,plain,
    spl0_299,
    inference(avatar_split_clause,[],[f598,f2833]) ).

fof(f2833,plain,
    ( spl0_299
  <=> c_HOL_Oord__class_Oless(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(c_Suc,v_ka____)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).

fof(f598,axiom,
    c_HOL_Oord__class_Oless(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(c_Suc,v_ka____)),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_i_0) ).

fof(f2831,plain,
    spl0_298,
    inference(avatar_split_clause,[],[f551,f2829]) ).

fof(f2829,plain,
    ( spl0_298
  <=> ! [X2,X0,X1] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).

fof(f551,axiom,
    ! [X2,X0,X1] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).

fof(f2827,plain,
    spl0_297,
    inference(avatar_split_clause,[],[f550,f2825]) ).

fof(f550,axiom,
    ! [X0,X9,X4] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X4),X9) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X9),X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).

fof(f2823,plain,
    spl0_296,
    inference(avatar_split_clause,[],[f472,f2821]) ).

fof(f2821,plain,
    ( spl0_296
  <=> ! [X9,X0,X4] :
        ( ~ class_RealVector_Oreal__normed__field(X0)
        | c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X4,X0),X9,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X4,X9,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).

fof(f472,axiom,
    ! [X0,X9,X4] :
      ( ~ class_RealVector_Oreal__normed__field(X0)
      | c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X4,X0),X9,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X4,X9,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide_Ominus_0) ).

fof(f2819,plain,
    spl0_295,
    inference(avatar_split_clause,[],[f467,f2817]) ).

fof(f467,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__divide__left_0) ).

fof(f2815,plain,
    spl0_294,
    inference(avatar_split_clause,[],[f454,f2813]) ).

fof(f2813,plain,
    ( spl0_294
  <=> ! [X0,X1,X3] :
        ( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X1
        | c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).

fof(f454,axiom,
    ! [X3,X0,X1] :
      ( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X1
      | c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_field__power__not__zero_0) ).

fof(f2811,plain,
    spl0_293,
    inference(avatar_split_clause,[],[f423,f2809]) ).

fof(f2809,plain,
    ( spl0_293
  <=> ! [X4,X0,X3] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | ~ c_Parity_Oeven__odd__class_Oeven(X3,tc_nat)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),X3),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).

fof(f423,axiom,
    ! [X3,X0,X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | ~ c_Parity_Oeven__odd__class_Oeven(X3,tc_nat)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),X3),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__zero__eq_0) ).

fof(f2807,plain,
    spl0_292,
    inference(avatar_split_clause,[],[f402,f2805]) ).

fof(f2805,plain,
    ( spl0_292
  <=> ! [X0,X1] :
        ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X1
        | c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).

fof(f402,axiom,
    ! [X0,X1] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X1
      | c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).

fof(f2803,plain,
    spl0_291,
    inference(avatar_split_clause,[],[f332,f2801]) ).

fof(f2801,plain,
    ( spl0_291
  <=> ! [X4,X0] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | ~ class_Ring__and__Field_Odivision__by__zero(X0)
        | ~ class_Int_Onumber__ring(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(c_Int_OPls,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).

fof(f332,axiom,
    ! [X0,X4] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | ~ class_Ring__and__Field_Odivision__by__zero(X0)
      | ~ class_Int_Onumber__ring(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(c_Int_OPls,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__Numeral0_0) ).

fof(f2799,plain,
    spl0_290,
    inference(avatar_split_clause,[],[f254,f2797]) ).

fof(f254,axiom,
    ! [X2,X0,X1] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2) = c_HOL_Ominus__class_Ominus(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__minus__eq__add_0) ).

fof(f2795,plain,
    spl0_289,
    inference(avatar_split_clause,[],[f226,f2793]) ).

fof(f2793,plain,
    ( spl0_289
  <=> ! [X15,X17,X4,X0,X13,X12,X16] :
        ( ~ c_Groebner__Basis_Ogb__semiring(X15,X13,X12,X16,X17,X0)
        | hAPP(hAPP(X12,X4),c_HOL_Ozero__class_Ozero(tc_nat)) = X17 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).

fof(f226,axiom,
    ! [X0,X16,X4,X17,X15,X12,X13] :
      ( ~ c_Groebner__Basis_Ogb__semiring(X15,X13,X12,X16,X17,X0)
      | hAPP(hAPP(X12,X4),c_HOL_Ozero__class_Ozero(tc_nat)) = X17 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Opwr__0_0) ).

fof(f2791,plain,
    spl0_288,
    inference(avatar_split_clause,[],[f223,f2789]) ).

fof(f2789,plain,
    ( spl0_288
  <=> ! [X9,X0,X4] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_HOL_Ominus__class_Ominus(X4,X9,X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X4),c_HOL_Ouminus__class_Ouminus(X9,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).

fof(f223,axiom,
    ! [X0,X9,X4] :
      ( ~ class_OrderedGroup_Oab__group__add(X0)
      | c_HOL_Ominus__class_Ominus(X4,X9,X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X4),c_HOL_Ouminus__class_Ouminus(X9,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__def_0) ).

fof(f2787,plain,
    spl0_287,
    inference(avatar_split_clause,[],[f222,f2785]) ).

fof(f2785,plain,
    ( spl0_287
  <=> ! [X9,X0,X4] :
        ( ~ class_Int_Onumber__ring(X0)
        | c_HOL_Ominus__class_Ominus(X4,X9,X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X4),c_HOL_Ouminus__class_Ouminus(X9,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).

fof(f222,axiom,
    ! [X0,X9,X4] :
      ( ~ class_Int_Onumber__ring(X0)
      | c_HOL_Ominus__class_Ominus(X4,X9,X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X4),c_HOL_Ouminus__class_Ouminus(X9,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ring_Osub__add_0) ).

fof(f2783,plain,
    spl0_286,
    inference(avatar_split_clause,[],[f221,f2781]) ).

fof(f221,axiom,
    ! [X2,X0,X1] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Ominus__class_Ominus(X1,X2,X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),c_HOL_Ouminus__class_Ouminus(X2,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__minus_0) ).

fof(f2779,plain,
    spl0_285,
    inference(avatar_split_clause,[],[f170,f2777]) ).

fof(f2777,plain,
    ( spl0_285
  <=> ! [X4,X3] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X4),X3),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).

fof(f170,axiom,
    ! [X3,X4] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X4),X3),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power__nat__eq_2) ).

fof(f2775,plain,
    spl0_284,
    inference(avatar_split_clause,[],[f157,f2773]) ).

fof(f157,axiom,
    ! [X3,X19] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X19,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X19),X3),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_0) ).

fof(f2771,plain,
    spl0_283,
    inference(avatar_split_clause,[],[f156,f2769]) ).

fof(f156,axiom,
    ! [X3,X19] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X19),X3),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_1) ).

fof(f2767,plain,
    ( ~ spl0_282
    | ~ spl0_148
    | ~ spl0_158
    | ~ spl0_272 ),
    inference(avatar_split_clause,[],[f2674,f2492,f1636,f1567,f2764]) ).

fof(f2764,plain,
    ( spl0_282
  <=> c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).

fof(f1636,plain,
    ( spl0_158
  <=> ! [X19] : c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X19),c_HOL_Ozero__class_Ozero(tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).

fof(f2674,plain,
    ( ~ c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat),tc_nat)
    | ~ spl0_148
    | ~ spl0_158
    | ~ spl0_272 ),
    inference(forward_demodulation,[],[f2671,f1569]) ).

fof(f2671,plain,
    ( ~ c_Parity_Oeven__odd__class_Oeven(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)
    | ~ spl0_158
    | ~ spl0_272 ),
    inference(superposition,[],[f2493,f1637]) ).

fof(f1637,plain,
    ( ! [X19] : c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X19),c_HOL_Ozero__class_Ozero(tc_nat))
    | ~ spl0_158 ),
    inference(avatar_component_clause,[],[f1636]) ).

fof(f2762,plain,
    spl0_281,
    inference(avatar_split_clause,[],[f9,f2760]) ).

fof(f2760,plain,
    ( spl0_281
  <=> ! [X4,X0] :
        ( ~ class_Int_Onumber__ring(X0)
        | c_HOL_Ouminus__class_Ouminus(X4,X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0)),X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).

fof(f9,axiom,
    ! [X0,X4] :
      ( ~ class_Int_Onumber__ring(X0)
      | c_HOL_Ouminus__class_Ouminus(X4,X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0)),X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ring_Oneg__mul_0) ).

fof(f2573,plain,
    ( ~ spl0_279
    | spl0_280
    | ~ spl0_112
    | ~ spl0_253 ),
    inference(avatar_split_clause,[],[f2550,f2412,f1401,f2571,f2567]) ).

fof(f2567,plain,
    ( spl0_279
  <=> class_OrderedGroup_Opordered__ab__group__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).

fof(f2571,plain,
    ( spl0_280
  <=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).

fof(f1401,plain,
    ( spl0_112
  <=> ! [X3] : ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).

fof(f2412,plain,
    ( spl0_253
  <=> ! [X2,X0,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
        | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).

fof(f2550,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ class_OrderedGroup_Opordered__ab__group__add(tc_nat) )
    | ~ spl0_112
    | ~ spl0_253 ),
    inference(resolution,[],[f2413,f1402]) ).

fof(f1402,plain,
    ( ! [X3] : ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
    | ~ spl0_112 ),
    inference(avatar_component_clause,[],[f1401]) ).

fof(f2413,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
        | ~ class_OrderedGroup_Opordered__ab__group__add(X0) )
    | ~ spl0_253 ),
    inference(avatar_component_clause,[],[f2412]) ).

fof(f2518,plain,
    spl0_278,
    inference(avatar_split_clause,[],[f810,f2516]) ).

fof(f810,plain,
    ! [X19] : c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat)),X19),
    inference(forward_demodulation,[],[f164,f377]) ).

fof(f164,axiom,
    ! [X19] : hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))),X19),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__power__eq__Suc__0__iff_2) ).

fof(f2514,plain,
    spl0_277,
    inference(avatar_split_clause,[],[f802,f2512]) ).

fof(f2512,plain,
    ( spl0_277
  <=> ! [X41,X43,X42,X0,X44,X45] : hAPP(c_COMBB(X41,X42,X43,X0,X44),X45) = hAPP(X41,hAPP(X42,X45)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).

fof(f802,axiom,
    ! [X41,X0,X44,X45,X42,X43] : hAPP(c_COMBB(X41,X42,X43,X0,X44),X45) = hAPP(X41,hAPP(X42,X45)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBB__def_0) ).

fof(f2510,plain,
    spl0_276,
    inference(avatar_split_clause,[],[f678,f2508]) ).

fof(f678,axiom,
    ! [X0,X9,X4] :
      ( ~ class_Int_Oring__char__0(X0)
      | ~ class_Int_Onumber__ring(X0)
      | X4 = X9
      | c_Int_Onumber__class_Onumber__of(X4,X0) != c_Int_Onumber__class_Onumber__of(X9,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__number__of_0) ).

fof(f2506,plain,
    spl0_275,
    inference(avatar_split_clause,[],[f665,f2504]) ).

fof(f2504,plain,
    ( spl0_275
  <=> ! [X18,X4,X0,X9] :
        ( ~ class_Orderings_Opreorder(X0)
        | ~ c_HOL_Oord__class_Oless(X4,X9,X0)
        | ~ c_HOL_Oord__class_Oless(X9,X18,X0)
        | c_HOL_Oord__class_Oless(X4,X18,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).

fof(f665,axiom,
    ! [X0,X18,X9,X4] :
      ( ~ class_Orderings_Opreorder(X0)
      | ~ c_HOL_Oord__class_Oless(X4,X9,X0)
      | ~ c_HOL_Oord__class_Oless(X9,X18,X0)
      | c_HOL_Oord__class_Oless(X4,X18,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__trans_0) ).

fof(f2502,plain,
    spl0_274,
    inference(avatar_split_clause,[],[f664,f2500]) ).

fof(f664,axiom,
    ! [X0,X18,X9,X4] :
      ( ~ class_Orderings_Oorder(X0)
      | ~ c_HOL_Oord__class_Oless(X9,X4,X0)
      | ~ c_HOL_Oord__class_Oless(X18,X9,X0)
      | c_HOL_Oord__class_Oless(X18,X4,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).

fof(f2498,plain,
    spl0_273,
    inference(avatar_split_clause,[],[f626,f2496]) ).

fof(f2496,plain,
    ( spl0_273
  <=> ! [X22,X20,X21] :
        ( ~ c_HOL_Oord__class_Oless(X21,X22,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X22,X20,tc_nat)
        | c_HOL_Oord__class_Oless(hAPP(c_Suc,X21),X20,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).

fof(f626,axiom,
    ! [X21,X22,X20] :
      ( ~ c_HOL_Oord__class_Oless(X21,X22,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X22,X20,tc_nat)
      | c_HOL_Oord__class_Oless(hAPP(c_Suc,X21),X20,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__trans__Suc_0) ).

fof(f2494,plain,
    spl0_272,
    inference(avatar_split_clause,[],[f500,f2492]) ).

fof(f500,axiom,
    ! [X4] : ~ c_Parity_Oeven__odd__class_Oeven(hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X4)),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_odd__Suc__mult__two__ex_1) ).

fof(f2490,plain,
    spl0_271,
    inference(avatar_split_clause,[],[f479,f2488]) ).

fof(f2488,plain,
    ( spl0_271
  <=> ! [X9,X4] :
        ( c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(X4,tc_nat)
        | ~ c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X4),X9),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).

fof(f479,axiom,
    ! [X9,X4] :
      ( c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(X4,tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X4),X9),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__product__nat_0) ).

fof(f2486,plain,
    spl0_270,
    inference(avatar_split_clause,[],[f418,f2484]) ).

fof(f418,axiom,
    ! [X0,X18] :
      ( ~ class_Int_Onumber__ring(X0)
      | c_HOL_Ouminus__class_Ouminus(X18,X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X18),c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__minus1__right_0) ).

fof(f2480,plain,
    spl0_269,
    inference(avatar_split_clause,[],[f417,f2478]) ).

fof(f417,axiom,
    ! [X0,X18] :
      ( ~ class_Int_Onumber__ring(X0)
      | c_HOL_Ouminus__class_Ouminus(X18,X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0)),X18) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__minus1_0) ).

fof(f2476,plain,
    spl0_268,
    inference(avatar_split_clause,[],[f268,f2474]) ).

fof(f2474,plain,
    ( spl0_268
  <=> ! [X2,X0,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
        | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0)
        | c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).

fof(f268,axiom,
    ! [X2,X0,X1] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
      | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0)
      | c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__minus__iff_0) ).

fof(f2472,plain,
    spl0_267,
    inference(avatar_split_clause,[],[f266,f2470]) ).

fof(f2470,plain,
    ( spl0_267
  <=> ! [X2,X0,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X0),X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).

fof(f266,axiom,
    ! [X2,X0,X1] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X0),X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__less__iff_0) ).

fof(f2468,plain,
    spl0_266,
    inference(avatar_split_clause,[],[f264,f2466]) ).

fof(f2466,plain,
    ( spl0_266
  <=> ! [X2,X0,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
        | c_HOL_Oord__class_Oless(X1,X2,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).

fof(f264,axiom,
    ! [X2,X0,X1] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
      | c_HOL_Oord__class_Oless(X1,X2,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__iff__less_0) ).

fof(f2464,plain,
    spl0_265,
    inference(avatar_split_clause,[],[f263,f2462]) ).

fof(f2462,plain,
    ( spl0_265
  <=> ! [X2,X0,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
        | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).

fof(f263,axiom,
    ! [X2,X0,X1] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
      | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__iff__less_1) ).

fof(f2460,plain,
    spl0_264,
    inference(avatar_split_clause,[],[f252,f2458]) ).

fof(f2458,plain,
    ( spl0_264
  <=> ! [X9,X0,X4] :
        ( ~ class_Ring__and__Field_Oidom(X0)
        | ~ class_Int_Onumber__ring(X0)
        | X4 = X9
        | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X4,X9,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).

fof(f252,axiom,
    ! [X0,X9,X4] :
      ( ~ class_Ring__and__Field_Oidom(X0)
      | ~ class_Int_Onumber__ring(X0)
      | X4 = X9
      | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X4,X9,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_0) ).

fof(f2456,plain,
    spl0_263,
    inference(avatar_split_clause,[],[f244,f2454]) ).

fof(f2454,plain,
    ( spl0_263
  <=> ! [X4,X0,X27,X28] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | X27 = X28
        | c_HOL_Ominus__class_Ominus(X4,X4,X0) != c_HOL_Ominus__class_Ominus(X27,X28,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).

fof(f244,axiom,
    ! [X28,X0,X27,X4] :
      ( ~ class_OrderedGroup_Oab__group__add(X0)
      | X27 = X28
      | c_HOL_Ominus__class_Ominus(X4,X4,X0) != c_HOL_Ominus__class_Ominus(X27,X28,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_0) ).

fof(f2452,plain,
    spl0_262,
    inference(avatar_split_clause,[],[f241,f2450]) ).

fof(f2450,plain,
    ( spl0_262
  <=> ! [X0,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).

fof(f241,axiom,
    ! [X0,X1] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__0__iff__less_0) ).

fof(f2448,plain,
    spl0_261,
    inference(avatar_split_clause,[],[f240,f2446]) ).

fof(f2446,plain,
    ( spl0_261
  <=> ! [X0,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).

fof(f240,axiom,
    ! [X0,X1] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__0__iff__less_1) ).

fof(f2444,plain,
    spl0_260,
    inference(avatar_split_clause,[],[f213,f2442]) ).

fof(f2442,plain,
    ( spl0_260
  <=> ! [X15,X17,X0,X13,X12,X16,X1] :
        ( ~ c_Groebner__Basis_Ogb__semiring(X15,X13,X12,X16,X17,X0)
        | hAPP(hAPP(X15,X1),X16) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).

fof(f213,axiom,
    ! [X0,X1,X16,X17,X15,X12,X13] :
      ( ~ c_Groebner__Basis_Ogb__semiring(X15,X13,X12,X16,X17,X0)
      | hAPP(hAPP(X15,X1),X16) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I6_J_0) ).

fof(f2438,plain,
    spl0_259,
    inference(avatar_split_clause,[],[f210,f2436]) ).

fof(f2436,plain,
    ( spl0_259
  <=> ! [X15,X17,X0,X13,X12,X16,X1] :
        ( ~ c_Groebner__Basis_Ogb__semiring(X15,X13,X12,X16,X17,X0)
        | hAPP(hAPP(X13,X16),X1) = X16 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).

fof(f210,axiom,
    ! [X0,X1,X16,X17,X15,X12,X13] :
      ( ~ c_Groebner__Basis_Ogb__semiring(X15,X13,X12,X16,X17,X0)
      | hAPP(hAPP(X13,X16),X1) = X16 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I9_J_0) ).

fof(f2434,plain,
    spl0_258,
    inference(avatar_split_clause,[],[f209,f2432]) ).

fof(f2432,plain,
    ( spl0_258
  <=> ! [X15,X17,X0,X13,X12,X16,X1] :
        ( ~ c_Groebner__Basis_Ogb__semiring(X15,X13,X12,X16,X17,X0)
        | hAPP(hAPP(X13,X1),X16) = X16 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).

fof(f209,axiom,
    ! [X0,X1,X16,X17,X15,X12,X13] :
      ( ~ c_Groebner__Basis_Ogb__semiring(X15,X13,X12,X16,X17,X0)
      | hAPP(hAPP(X13,X1),X16) = X16 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I10_J_0) ).

fof(f2430,plain,
    spl0_257,
    inference(avatar_split_clause,[],[f208,f2428]) ).

fof(f2428,plain,
    ( spl0_257
  <=> ! [X15,X17,X0,X13,X12,X16,X1] :
        ( ~ c_Groebner__Basis_Ogb__semiring(X15,X13,X12,X16,X17,X0)
        | hAPP(hAPP(X13,X17),X1) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).

fof(f208,axiom,
    ! [X0,X1,X16,X17,X15,X12,X13] :
      ( ~ c_Groebner__Basis_Ogb__semiring(X15,X13,X12,X16,X17,X0)
      | hAPP(hAPP(X13,X17),X1) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I11_J_0) ).

fof(f2426,plain,
    spl0_256,
    inference(avatar_split_clause,[],[f207,f2424]) ).

fof(f2424,plain,
    ( spl0_256
  <=> ! [X15,X17,X0,X13,X12,X16,X1] :
        ( ~ c_Groebner__Basis_Ogb__semiring(X15,X13,X12,X16,X17,X0)
        | hAPP(hAPP(X13,X1),X17) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).

fof(f207,axiom,
    ! [X0,X1,X16,X17,X15,X12,X13] :
      ( ~ c_Groebner__Basis_Ogb__semiring(X15,X13,X12,X16,X17,X0)
      | hAPP(hAPP(X13,X1),X17) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I12_J_0) ).

fof(f2422,plain,
    spl0_255,
    inference(avatar_split_clause,[],[f180,f2420]) ).

fof(f2420,plain,
    ( spl0_255
  <=> ! [X0] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oone__class_Oone(X0)),c_HOL_Oone__class_Oone(X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).

fof(f180,axiom,
    ! [X0] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oone__class_Oone(X0)),c_HOL_Oone__class_Oone(X0)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__two_0) ).

fof(f2418,plain,
    spl0_254,
    inference(avatar_split_clause,[],[f93,f2416]) ).

fof(f2416,plain,
    ( spl0_254
  <=> ! [X15,X17,X4,X0,X13,X12,X16] :
        ( ~ c_Groebner__Basis_Ogb__semiring(X15,X13,X12,X16,X17,X0)
        | hAPP(hAPP(X15,X16),X4) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).

fof(f93,axiom,
    ! [X0,X16,X4,X17,X15,X12,X13] :
      ( ~ c_Groebner__Basis_Ogb__semiring(X15,X13,X12,X16,X17,X0)
      | hAPP(hAPP(X15,X16),X4) = X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Oadd__0_0) ).

fof(f2414,plain,
    spl0_253,
    inference(avatar_split_clause,[],[f79,f2412]) ).

fof(f79,axiom,
    ! [X2,X0,X1] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
      | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_0) ).

fof(f2410,plain,
    spl0_252,
    inference(avatar_split_clause,[],[f78,f2408]) ).

fof(f2408,plain,
    ( spl0_252
  <=> ! [X2,X0,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
        | c_HOL_Oord__class_Oless(X1,X2,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).

fof(f78,axiom,
    ! [X2,X0,X1] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
      | c_HOL_Oord__class_Oless(X1,X2,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_1) ).

fof(f2406,plain,
    spl0_251,
    inference(avatar_split_clause,[],[f72,f2404]) ).

fof(f2404,plain,
    ( spl0_251
  <=> ! [X0,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
        | c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).

fof(f72,axiom,
    ! [X0,X1] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
      | c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__less__iff__less_0) ).

fof(f2402,plain,
    spl0_250,
    inference(avatar_split_clause,[],[f71,f2400]) ).

fof(f2400,plain,
    ( spl0_250
  <=> ! [X0,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
        | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).

fof(f71,axiom,
    ! [X0,X1] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
      | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__less__iff__less_1) ).

fof(f2390,plain,
    spl0_249,
    inference(avatar_split_clause,[],[f6,f2388]) ).

fof(f2388,plain,
    ( spl0_249
  <=> ! [X0] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_Groebner__Basis_Ogb__semiring(c_HOL_Oplus__class_Oplus(X0),c_HOL_Otimes__class_Otimes(X0),c_Power_Opower__class_Opower(X0),c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).

fof(f6,axiom,
    ! [X0] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_Groebner__Basis_Ogb__semiring(c_HOL_Oplus__class_Oplus(X0),c_HOL_Otimes__class_Otimes(X0),c_Power_Opower__class_Opower(X0),c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Ogb__semiring__axioms_H_0) ).

fof(f2229,plain,
    ( spl0_248
    | ~ spl0_101
    | ~ spl0_153 ),
    inference(avatar_split_clause,[],[f1618,f1590,f1348,f2226]) ).

fof(f2226,plain,
    ( spl0_248
  <=> c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).

fof(f1590,plain,
    ( spl0_153
  <=> ! [X0] :
        ( ~ class_Int_Onumber__ring(X0)
        | c_HOL_Oone__class_Oone(X0) = c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).

fof(f1618,plain,
    ( c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_Complex_Ocomplex)
    | ~ spl0_101
    | ~ spl0_153 ),
    inference(resolution,[],[f1591,f1350]) ).

fof(f1591,plain,
    ( ! [X0] :
        ( ~ class_Int_Onumber__ring(X0)
        | c_HOL_Oone__class_Oone(X0) = c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X0) )
    | ~ spl0_153 ),
    inference(avatar_component_clause,[],[f1590]) ).

fof(f2213,plain,
    spl0_247,
    inference(avatar_split_clause,[],[f813,f2210]) ).

fof(f813,plain,
    c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat) = hAPP(c_Suc,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),
    inference(forward_demodulation,[],[f812,f806]) ).

fof(f806,plain,
    c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat) = hAPP(c_Suc,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat)),
    inference(forward_demodulation,[],[f381,f377]) ).

fof(f381,axiom,
    hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))) = c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_numeral__2__eq__2_0) ).

fof(f812,plain,
    c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat) = hAPP(c_Suc,hAPP(c_Suc,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat))),
    inference(forward_demodulation,[],[f376,f377]) ).

fof(f376,axiom,
    c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat) = hAPP(c_Suc,hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_numeral__3__eq__3_0) ).

fof(f2208,plain,
    spl0_246,
    inference(avatar_split_clause,[],[f662,f2206]) ).

fof(f662,axiom,
    ! [X3,X19] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X19),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X3),X19),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__commute_0) ).

fof(f2204,plain,
    spl0_245,
    inference(avatar_split_clause,[],[f643,f2202]) ).

fof(f2202,plain,
    ( spl0_245
  <=> ! [X0,X1] :
        ( ~ class_Int_Onumber__ring(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X0)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).

fof(f643,axiom,
    ! [X0,X1] :
      ( ~ class_Int_Onumber__ring(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X0)) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__numeral__1__right_0) ).

fof(f2200,plain,
    spl0_244,
    inference(avatar_split_clause,[],[f642,f2198]) ).

fof(f2198,plain,
    ( spl0_244
  <=> ! [X0,X1] :
        ( ~ class_Int_Onumber__ring(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X0)),X1) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).

fof(f642,axiom,
    ! [X0,X1] :
      ( ~ class_Int_Onumber__ring(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X0)),X1) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__numeral__1_0) ).

fof(f2196,plain,
    spl0_243,
    inference(avatar_split_clause,[],[f634,f2194]) ).

fof(f2194,plain,
    ( spl0_243
  <=> ! [X9,X0,X4] :
        ( ~ class_Orderings_Olinorder(X0)
        | X4 = X9
        | c_HOL_Oord__class_Oless(X4,X9,X0)
        | c_HOL_Oord__class_Oless(X9,X4,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).

fof(f634,axiom,
    ! [X0,X9,X4] :
      ( ~ class_Orderings_Olinorder(X0)
      | X4 = X9
      | c_HOL_Oord__class_Oless(X4,X9,X0)
      | c_HOL_Oord__class_Oless(X9,X4,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).

fof(f2192,plain,
    spl0_242,
    inference(avatar_split_clause,[],[f627,f2190]) ).

fof(f2190,plain,
    ( spl0_242
  <=> ! [X9,X0,X4] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | X4 = X9
        | c_HOL_Oord__class_Oless(X4,X9,X0)
        | c_HOL_Oord__class_Oless(X9,X4,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).

fof(f627,axiom,
    ! [X0,X9,X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | X4 = X9
      | c_HOL_Oord__class_Oless(X4,X9,X0)
      | c_HOL_Oord__class_Oless(X9,X4,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).

fof(f2188,plain,
    spl0_241,
    inference(avatar_split_clause,[],[f587,f2185]) ).

fof(f587,axiom,
    c_HOL_Oord__class_Oless(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_True_0) ).

fof(f2183,plain,
    ( spl0_240
    | ~ spl0_68
    | ~ spl0_153 ),
    inference(avatar_split_clause,[],[f1617,f1590,f1183,f2180]) ).

fof(f2180,plain,
    ( spl0_240
  <=> c_HOL_Oone__class_Oone(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).

fof(f1617,plain,
    ( c_HOL_Oone__class_Oone(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_Int_Oint)
    | ~ spl0_68
    | ~ spl0_153 ),
    inference(resolution,[],[f1591,f1185]) ).

fof(f2178,plain,
    spl0_239,
    inference(avatar_split_clause,[],[f560,f2176]) ).

fof(f2176,plain,
    ( spl0_239
  <=> ! [X3,X19] :
        ( X3 = X19
        | c_HOL_Oord__class_Oless(X3,X19,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X3,hAPP(c_Suc,X19),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).

fof(f560,axiom,
    ! [X3,X19] :
      ( X3 = X19
      | c_HOL_Oord__class_Oless(X3,X19,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X3,hAPP(c_Suc,X19),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_0) ).

fof(f2174,plain,
    spl0_238,
    inference(avatar_split_clause,[],[f543,f2172]) ).

fof(f2172,plain,
    ( spl0_238
  <=> ! [X4,X0] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | ~ class_Int_Onumber__ring(X0)
        | c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X0),X0) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).

fof(f543,axiom,
    ! [X0,X4] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | ~ class_Int_Onumber__ring(X0)
      | c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X0),X0) = X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__Numeral1_0) ).

fof(f2170,plain,
    spl0_237,
    inference(avatar_split_clause,[],[f492,f2168]) ).

fof(f2168,plain,
    ( spl0_237
  <=> ! [X9,X4] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X9,tc_nat)
        | ~ c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X4),X9),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).

fof(f492,axiom,
    ! [X9,X4] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X9,tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X4),X9),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__power__nat_1) ).

fof(f2166,plain,
    spl0_236,
    inference(avatar_split_clause,[],[f421,f2164]) ).

fof(f421,axiom,
    ! [X0,X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),c_HOL_Ozero__class_Ozero(tc_nat)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power__eq_3) ).

fof(f2162,plain,
    spl0_235,
    inference(avatar_split_clause,[],[f416,f2160]) ).

fof(f416,axiom,
    ! [X2,X0,X1] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2),X2,X0) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).

fof(f2158,plain,
    spl0_234,
    inference(avatar_split_clause,[],[f411,f2156]) ).

fof(f2156,plain,
    ( spl0_234
  <=> ! [X4,X0] :
        ( ~ class_Ring__and__Field_Oidom(X0)
        | ~ class_Int_Onumber__ring(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X4),c_HOL_Ozero__class_Ozero(X0)) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).

fof(f411,axiom,
    ! [X0,X4] :
      ( ~ class_Ring__and__Field_Oidom(X0)
      | ~ class_Int_Onumber__ring(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X4),c_HOL_Ozero__class_Ozero(X0)) = X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).

fof(f2154,plain,
    spl0_233,
    inference(avatar_split_clause,[],[f405,f2152]) ).

fof(f2152,plain,
    ( spl0_233
  <=> ! [X0] :
        ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
        | c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0)),c_HOL_Ozero__class_Ozero(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).

fof(f405,axiom,
    ! [X0] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
      | c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0)),c_HOL_Ozero__class_Ozero(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).

fof(f2150,plain,
    spl0_232,
    inference(avatar_split_clause,[],[f404,f2148]) ).

fof(f404,axiom,
    ! [X2,X0,X1] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ominus__class_Ominus(X1,X2,X0)),X2) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).

fof(f2146,plain,
    spl0_231,
    inference(avatar_split_clause,[],[f260,f2144]) ).

fof(f260,axiom,
    ! [X2,X0,X1] :
      ( ~ class_OrderedGroup_Oab__group__add(X0)
      | c_HOL_Ominus__class_Ominus(X2,X1,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X1,X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__diff__eq_0) ).

fof(f2142,plain,
    spl0_230,
    inference(avatar_split_clause,[],[f248,f2140]) ).

fof(f248,axiom,
    ! [X0,X1] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),c_HOL_Ouminus__class_Ouminus(X1,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus_0) ).

fof(f2138,plain,
    ( spl0_229
    | ~ spl0_97
    | ~ spl0_152 ),
    inference(avatar_split_clause,[],[f1616,f1586,f1328,f2136]) ).

fof(f2136,plain,
    ( spl0_229
  <=> ! [X0] : c_HOL_Oinverse__class_Odivide(X0,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).

fof(f1586,plain,
    ( spl0_152
  <=> ! [X0,X1] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Oinverse__class_Odivide(X1,c_HOL_Oone__class_Oone(X0),X0) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).

fof(f1616,plain,
    ( ! [X0] : c_HOL_Oinverse__class_Odivide(X0,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0
    | ~ spl0_97
    | ~ spl0_152 ),
    inference(resolution,[],[f1587,f1330]) ).

fof(f1587,plain,
    ( ! [X0,X1] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Oinverse__class_Odivide(X1,c_HOL_Oone__class_Oone(X0),X0) = X1 )
    | ~ spl0_152 ),
    inference(avatar_component_clause,[],[f1586]) ).

fof(f2134,plain,
    spl0_228,
    inference(avatar_split_clause,[],[f247,f2132]) ).

fof(f2132,plain,
    ( spl0_228
  <=> ! [X0,X1] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ouminus__class_Ouminus(X1,X0)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).

fof(f247,axiom,
    ! [X0,X1] :
      ( ~ class_OrderedGroup_Oab__group__add(X0)
      | c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ouminus__class_Ouminus(X1,X0)),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__left__minus_0) ).

fof(f2130,plain,
    spl0_227,
    inference(avatar_split_clause,[],[f246,f2128]) ).

fof(f246,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ouminus__class_Ouminus(X2,X0)),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__neg__iff__add__eq__0_0) ).

fof(f2126,plain,
    spl0_226,
    inference(avatar_split_clause,[],[f135,f2124]) ).

fof(f135,axiom,
    ! [X0,X4] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X4
      | c_HOL_Oone__class_Oone(X0) = c_HOL_Oinverse__class_Odivide(X4,X4,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__inverse__eq_1) ).

fof(f2122,plain,
    spl0_225,
    inference(avatar_split_clause,[],[f70,f2120]) ).

fof(f2120,plain,
    ( spl0_225
  <=> ! [X0,X1] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).

fof(f70,axiom,
    ! [X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
      | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__minus__self__iff_0) ).

fof(f2118,plain,
    spl0_224,
    inference(avatar_split_clause,[],[f69,f2116]) ).

fof(f2116,plain,
    ( spl0_224
  <=> ! [X0,X1] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
        | c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).

fof(f69,axiom,
    ! [X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
      | c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__minus__self__iff_1) ).

fof(f2072,plain,
    ( ~ spl0_223
    | ~ spl0_119
    | ~ spl0_148 ),
    inference(avatar_split_clause,[],[f1609,f1567,f1433,f2069]) ).

fof(f1609,plain,
    ( c_HOL_Ozero__class_Ozero(tc_nat) != c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat)
    | ~ spl0_119
    | ~ spl0_148 ),
    inference(superposition,[],[f1434,f1569]) ).

fof(f2043,plain,
    ( spl0_222
    | ~ spl0_94
    | ~ spl0_146 ),
    inference(avatar_split_clause,[],[f1603,f1559,f1313,f2041]) ).

fof(f1559,plain,
    ( spl0_146
  <=> ! [X0,X1] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).

fof(f1603,plain,
    ( ! [X0] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0
    | ~ spl0_94
    | ~ spl0_146 ),
    inference(resolution,[],[f1560,f1315]) ).

fof(f1560,plain,
    ( ! [X0,X1] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = X1 )
    | ~ spl0_146 ),
    inference(avatar_component_clause,[],[f1559]) ).

fof(f2024,plain,
    ( spl0_221
    | ~ spl0_60
    | ~ spl0_146 ),
    inference(avatar_split_clause,[],[f1602,f1559,f1143,f2022]) ).

fof(f1602,plain,
    ( ! [X0] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_Int_Oint),tc_Int_Oint) = X0
    | ~ spl0_60
    | ~ spl0_146 ),
    inference(resolution,[],[f1560,f1145]) ).

fof(f2016,plain,
    spl0_220,
    inference(avatar_split_clause,[],[f806,f2013]) ).

fof(f2011,plain,
    spl0_219,
    inference(avatar_split_clause,[],[f805,f2009]) ).

fof(f805,plain,
    ! [X4] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X4),c_HOL_Ozero__class_Ozero(tc_nat)) = c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat),
    inference(forward_demodulation,[],[f162,f377]) ).

fof(f162,axiom,
    ! [X4] : hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X4),c_HOL_Ozero__class_Ozero(tc_nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__power__eq__Suc__0__iff_1) ).

fof(f2007,plain,
    spl0_218,
    inference(avatar_split_clause,[],[f693,f2005]) ).

fof(f2005,plain,
    ( spl0_218
  <=> ! [X4,X3] :
        ( ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat)
        | c_HOL_Oord__class_Oless(hAPP(c_Suc,X4),hAPP(c_Suc,X3),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).

fof(f693,axiom,
    ! [X3,X4] :
      ( ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat)
      | c_HOL_Oord__class_Oless(hAPP(c_Suc,X4),hAPP(c_Suc,X3),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__0__disj_3) ).

fof(f2003,plain,
    spl0_217,
    inference(avatar_split_clause,[],[f692,f2001]) ).

fof(f2001,plain,
    ( spl0_217
  <=> ! [X19,X3] :
        ( c_HOL_Oord__class_Oless(X19,X3,tc_nat)
        | ~ c_HOL_Oord__class_Oless(hAPP(c_Suc,X19),hAPP(c_Suc,X3),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).

fof(f692,axiom,
    ! [X3,X19] :
      ( c_HOL_Oord__class_Oless(X19,X3,tc_nat)
      | ~ c_HOL_Oord__class_Oless(hAPP(c_Suc,X19),hAPP(c_Suc,X3),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__less__eq_0) ).

fof(f1999,plain,
    spl0_216,
    inference(avatar_split_clause,[],[f620,f1997]) ).

fof(f1997,plain,
    ( spl0_216
  <=> ! [X0,X1] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),c_HOL_Oone__class_Oone(X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).

fof(f620,axiom,
    ! [X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),c_HOL_Oone__class_Oone(X0)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__one_0) ).

fof(f1995,plain,
    spl0_215,
    inference(avatar_split_clause,[],[f611,f1993]) ).

fof(f1993,plain,
    ( spl0_215
  <=> ! [X0,X1] :
        ( ~ class_Int_Onumber__ring(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),c_Int_Onumber__class_Onumber__of(c_Int_OPls,X0)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).

fof(f611,axiom,
    ! [X0,X1] :
      ( ~ class_Int_Onumber__ring(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),c_Int_Onumber__class_Onumber__of(c_Int_OPls,X0)) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__numeral__0__right_0) ).

fof(f1991,plain,
    spl0_214,
    inference(avatar_split_clause,[],[f610,f1989]) ).

fof(f1989,plain,
    ( spl0_214
  <=> ! [X0,X1] :
        ( ~ class_Int_Onumber__ring(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_Int_Onumber__class_Onumber__of(c_Int_OPls,X0)),X1) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).

fof(f610,axiom,
    ! [X0,X1] :
      ( ~ class_Int_Onumber__ring(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_Int_Onumber__class_Onumber__of(c_Int_OPls,X0)),X1) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__numeral__0_0) ).

fof(f1987,plain,
    spl0_213,
    inference(avatar_split_clause,[],[f540,f1985]) ).

fof(f540,axiom,
    ! [X3,X0] :
      ( ~ class_OrderedGroup_Omonoid__mult(X0)
      | c_HOL_Oone__class_Oone(X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Oone__class_Oone(X0)),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__one_0) ).

fof(f1983,plain,
    spl0_212,
    inference(avatar_split_clause,[],[f465,f1981]) ).

fof(f465,axiom,
    ! [X2,X0] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | ~ class_Ring__and__Field_Odivision__by__zero(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(X2,c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq_2) ).

fof(f1979,plain,
    ( spl0_211
    | ~ spl0_94
    | ~ spl0_145 ),
    inference(avatar_split_clause,[],[f1601,f1555,f1313,f1977]) ).

fof(f1977,plain,
    ( spl0_211
  <=> ! [X0] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).

fof(f1555,plain,
    ( spl0_145
  <=> ! [X0,X1] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).

fof(f1601,plain,
    ( ! [X0] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0
    | ~ spl0_94
    | ~ spl0_145 ),
    inference(resolution,[],[f1556,f1315]) ).

fof(f1556,plain,
    ( ! [X0,X1] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 )
    | ~ spl0_145 ),
    inference(avatar_component_clause,[],[f1555]) ).

fof(f1975,plain,
    spl0_210,
    inference(avatar_split_clause,[],[f387,f1973]) ).

fof(f387,axiom,
    ! [X4] : c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X4),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__mult__two__ex_1) ).

fof(f1971,plain,
    spl0_209,
    inference(avatar_split_clause,[],[f280,f1969]) ).

fof(f1969,plain,
    ( spl0_209
  <=> ! [X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ozero__class_Ozero(X0)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).

fof(f280,axiom,
    ! [X0,X1] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ozero__class_Ozero(X0)),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I9_J_0) ).

fof(f1967,plain,
    spl0_208,
    inference(avatar_split_clause,[],[f279,f1965]) ).

fof(f1965,plain,
    ( spl0_208
  <=> ! [X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),c_HOL_Ozero__class_Ozero(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).

fof(f279,axiom,
    ! [X0,X1] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),c_HOL_Ozero__class_Ozero(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).

fof(f1963,plain,
    spl0_207,
    inference(avatar_split_clause,[],[f277,f1961]) ).

fof(f1961,plain,
    ( spl0_207
  <=> ! [X2,X0] :
        ( ~ class_RealVector_Oreal__normed__algebra(X0)
        | c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ozero__class_Ozero(X0)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).

fof(f277,axiom,
    ! [X2,X0] :
      ( ~ class_RealVector_Oreal__normed__algebra(X0)
      | c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ozero__class_Ozero(X0)),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ozero__left_0) ).

fof(f1959,plain,
    spl0_206,
    inference(avatar_split_clause,[],[f276,f1957]) ).

fof(f1957,plain,
    ( spl0_206
  <=> ! [X0,X1] :
        ( ~ class_RealVector_Oreal__normed__algebra(X0)
        | c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),c_HOL_Ozero__class_Ozero(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).

fof(f276,axiom,
    ! [X0,X1] :
      ( ~ class_RealVector_Oreal__normed__algebra(X0)
      | c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),c_HOL_Ozero__class_Ozero(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ozero__right_0) ).

fof(f1955,plain,
    spl0_205,
    inference(avatar_split_clause,[],[f273,f1953]) ).

fof(f1953,plain,
    ( spl0_205
  <=> ! [X0,X1] :
        ( ~ class_Ring__and__Field_Omult__zero(X0)
        | c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ozero__class_Ozero(X0)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).

fof(f273,axiom,
    ! [X0,X1] :
      ( ~ class_Ring__and__Field_Omult__zero(X0)
      | c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ozero__class_Ozero(X0)),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__left_0) ).

fof(f1951,plain,
    spl0_204,
    inference(avatar_split_clause,[],[f272,f1949]) ).

fof(f1949,plain,
    ( spl0_204
  <=> ! [X0,X1] :
        ( ~ class_Ring__and__Field_Omult__zero(X0)
        | c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),c_HOL_Ozero__class_Ozero(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).

fof(f272,axiom,
    ! [X0,X1] :
      ( ~ class_Ring__and__Field_Omult__zero(X0)
      | c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),c_HOL_Ozero__class_Ozero(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__right_0) ).

fof(f1947,plain,
    spl0_203,
    inference(avatar_split_clause,[],[f271,f1945]) ).

fof(f271,axiom,
    ! [X2,X0] :
      ( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
      | c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ozero__class_Ozero(X0)),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_1) ).

fof(f1943,plain,
    spl0_202,
    inference(avatar_split_clause,[],[f270,f1941]) ).

fof(f270,axiom,
    ! [X0,X1] :
      ( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
      | c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),c_HOL_Ozero__class_Ozero(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_2) ).

fof(f1939,plain,
    spl0_201,
    inference(avatar_split_clause,[],[f251,f1937]) ).

fof(f1937,plain,
    ( spl0_201
  <=> ! [X2,X0,X1] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | X1 = X2
        | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X1,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).

fof(f251,axiom,
    ! [X2,X0,X1] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | X1 = X2
      | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X1,X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus__eq_0) ).

fof(f1935,plain,
    ( spl0_200
    | ~ spl0_60
    | ~ spl0_145 ),
    inference(avatar_split_clause,[],[f1600,f1555,f1143,f1933]) ).

fof(f1933,plain,
    ( spl0_200
  <=> ! [X0] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).

fof(f1600,plain,
    ( ! [X0] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = X0
    | ~ spl0_60
    | ~ spl0_145 ),
    inference(resolution,[],[f1556,f1145]) ).

fof(f1931,plain,
    spl0_199,
    inference(avatar_split_clause,[],[f250,f1929]) ).

fof(f1929,plain,
    ( spl0_199
  <=> ! [X2,X0,X1] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | X1 = X2
        | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X1,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).

fof(f250,axiom,
    ! [X2,X0,X1] :
      ( ~ class_OrderedGroup_Oab__group__add(X0)
      | X1 = X2
      | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X1,X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_1) ).

fof(f1927,plain,
    spl0_198,
    inference(avatar_split_clause,[],[f232,f1925]) ).

fof(f1925,plain,
    ( spl0_198
  <=> ! [X0,X1] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X1
        | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ouminus__class_Ouminus(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).

fof(f232,axiom,
    ! [X0,X1] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X1
      | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ouminus__class_Ouminus(X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__0__iff__equal_0) ).

fof(f1923,plain,
    spl0_197,
    inference(avatar_split_clause,[],[f231,f1921]) ).

fof(f1921,plain,
    ( spl0_197
  <=> ! [X2,X0,X1] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | X1 = X2
        | c_HOL_Ouminus__class_Ouminus(X1,X0) != c_HOL_Ouminus__class_Ouminus(X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).

fof(f231,axiom,
    ! [X2,X0,X1] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | X1 = X2
      | c_HOL_Ouminus__class_Ouminus(X1,X0) != c_HOL_Ouminus__class_Ouminus(X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__iff__equal_0) ).

fof(f1919,plain,
    spl0_196,
    inference(avatar_split_clause,[],[f230,f1917]) ).

fof(f1917,plain,
    ( spl0_196
  <=> ! [X9,X0,X4] :
        ( ~ class_Lattices_Oboolean__algebra(X0)
        | X4 = X9
        | c_HOL_Ouminus__class_Ouminus(X4,X0) != c_HOL_Ouminus__class_Ouminus(X9,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).

fof(f230,axiom,
    ! [X0,X9,X4] :
      ( ~ class_Lattices_Oboolean__algebra(X0)
      | X4 = X9
      | c_HOL_Ouminus__class_Ouminus(X4,X0) != c_HOL_Ouminus__class_Ouminus(X9,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__eq__compl__iff_0) ).

fof(f1915,plain,
    spl0_195,
    inference(avatar_split_clause,[],[f126,f1913]) ).

fof(f1913,plain,
    ( spl0_195
  <=> ! [X4,X0] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Oone__class_Oone(X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),c_HOL_Ozero__class_Ozero(tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).

fof(f126,axiom,
    ! [X0,X4] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Oone__class_Oone(X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),X4),c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__0_0) ).

fof(f1911,plain,
    spl0_194,
    inference(avatar_split_clause,[],[f125,f1909]) ).

fof(f125,axiom,
    ! [X0,X1] :
      ( ~ class_Power_Opower(X0)
      | c_HOL_Oone__class_Oone(X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0_0) ).

fof(f1907,plain,
    spl0_193,
    inference(avatar_split_clause,[],[f36,f1905]) ).

fof(f1905,plain,
    ( spl0_193
  <=> ! [X0,X1] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X1),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).

fof(f36,axiom,
    ! [X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X1),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__square__less__zero_0) ).

fof(f1893,plain,
    ( spl0_192
    | ~ spl0_89
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1597,f1547,f1288,f1891]) ).

fof(f1891,plain,
    ( spl0_192
  <=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(X0,X0,tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).

fof(f1547,plain,
    ( spl0_143
  <=> ! [X4,X0] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X4,X4,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).

fof(f1597,plain,
    ( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(X0,X0,tc_Complex_Ocomplex)
    | ~ spl0_89
    | ~ spl0_143 ),
    inference(resolution,[],[f1548,f1290]) ).

fof(f1548,plain,
    ( ! [X0,X4] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X4,X4,X0) )
    | ~ spl0_143 ),
    inference(avatar_component_clause,[],[f1547]) ).

fof(f1842,plain,
    ( spl0_191
    | ~ spl0_55
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1596,f1547,f1118,f1840]) ).

fof(f1840,plain,
    ( spl0_191
  <=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_HOL_Ominus__class_Ominus(X0,X0,tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).

fof(f1596,plain,
    ( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_HOL_Ominus__class_Ominus(X0,X0,tc_Int_Oint)
    | ~ spl0_55
    | ~ spl0_143 ),
    inference(resolution,[],[f1548,f1120]) ).

fof(f1825,plain,
    spl0_190,
    inference(avatar_split_clause,[],[f819,f1823]) ).

fof(f1823,plain,
    ( spl0_190
  <=> ! [X3] :
        ( ~ c_HOL_Oord__class_Oless(X3,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat),tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).

fof(f819,plain,
    ! [X3] :
      ( ~ c_HOL_Oord__class_Oless(X3,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat),tc_nat)
      | c_HOL_Ozero__class_Ozero(tc_nat) = X3 ),
    inference(forward_demodulation,[],[f141,f377]) ).

fof(f141,axiom,
    ! [X3] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X3
      | ~ c_HOL_Oord__class_Oless(X3,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc0_0) ).

fof(f1821,plain,
    spl0_189,
    inference(avatar_split_clause,[],[f651,f1819]) ).

fof(f1819,plain,
    ( spl0_189
  <=> ! [X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oone__class_Oone(X0)),X1) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).

fof(f651,axiom,
    ! [X0,X1] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oone__class_Oone(X0)),X1) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I11_J_0) ).

fof(f1817,plain,
    spl0_188,
    inference(avatar_split_clause,[],[f650,f1815]) ).

fof(f1815,plain,
    ( spl0_188
  <=> ! [X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),c_HOL_Oone__class_Oone(X0)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).

fof(f650,axiom,
    ! [X0,X1] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),c_HOL_Oone__class_Oone(X0)) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I12_J_0) ).

fof(f1813,plain,
    spl0_187,
    inference(avatar_split_clause,[],[f648,f1811]) ).

fof(f1811,plain,
    ( spl0_187
  <=> ! [X0,X1] :
        ( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oone__class_Oone(X0)),X1) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).

fof(f648,axiom,
    ! [X0,X1] :
      ( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oone__class_Oone(X0)),X1) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1_0) ).

fof(f1806,plain,
    spl0_186,
    inference(avatar_split_clause,[],[f647,f1804]) ).

fof(f647,axiom,
    ! [X0,X1] :
      ( ~ class_OrderedGroup_Omonoid__mult(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oone__class_Oone(X0)),X1) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1__left_0) ).

fof(f1802,plain,
    spl0_185,
    inference(avatar_split_clause,[],[f646,f1800]) ).

fof(f646,axiom,
    ! [X0,X1] :
      ( ~ class_OrderedGroup_Omonoid__mult(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),c_HOL_Oone__class_Oone(X0)) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1__right_0) ).

fof(f1798,plain,
    spl0_184,
    inference(avatar_split_clause,[],[f631,f1796]) ).

fof(f1796,plain,
    ( spl0_184
  <=> ! [X3,X19] :
        ( X3 = X19
        | c_HOL_Oord__class_Oless(X19,X3,tc_nat)
        | c_HOL_Oord__class_Oless(X3,X19,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).

fof(f631,axiom,
    ! [X3,X19] :
      ( X3 = X19
      | c_HOL_Oord__class_Oless(X19,X3,tc_nat)
      | c_HOL_Oord__class_Oless(X3,X19,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).

fof(f1794,plain,
    spl0_183,
    inference(avatar_split_clause,[],[f493,f1792]) ).

fof(f1792,plain,
    ( spl0_183
  <=> ! [X4,X9] :
        ( c_Parity_Oeven__odd__class_Oeven(X4,tc_nat)
        | ~ c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X4),X9),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).

fof(f493,axiom,
    ! [X9,X4] :
      ( c_Parity_Oeven__odd__class_Oeven(X4,tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X4),X9),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__power__nat_0) ).

fof(f1790,plain,
    spl0_182,
    inference(avatar_split_clause,[],[f486,f1788]) ).

fof(f486,axiom,
    ! [X9,X4] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X4),X9),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__product__nat_2) ).

fof(f1786,plain,
    spl0_181,
    inference(avatar_split_clause,[],[f485,f1784]) ).

fof(f1784,plain,
    ( spl0_181
  <=> ! [X4,X9] :
        ( ~ c_Parity_Oeven__odd__class_Oeven(X4,tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X4),X9),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).

fof(f485,axiom,
    ! [X9,X4] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(X4,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X4),X9),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__product__nat_1) ).

fof(f1782,plain,
    spl0_180,
    inference(avatar_split_clause,[],[f415,f1780]) ).

fof(f1780,plain,
    ( spl0_180
  <=> ! [X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0)),X1) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).

fof(f415,axiom,
    ! [X0,X1] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0)),X1) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).

fof(f1778,plain,
    spl0_179,
    inference(avatar_split_clause,[],[f414,f1776]) ).

fof(f1776,plain,
    ( spl0_179
  <=> ! [X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),c_HOL_Ozero__class_Ozero(X0)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).

fof(f414,axiom,
    ! [X0,X1] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),c_HOL_Ozero__class_Ozero(X0)) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).

fof(f1774,plain,
    spl0_178,
    inference(avatar_split_clause,[],[f413,f1772]) ).

fof(f1772,plain,
    ( spl0_178
  <=> ! [X0,X1] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0)),X1) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).

fof(f413,axiom,
    ! [X0,X1] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0)),X1) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).

fof(f1770,plain,
    spl0_177,
    inference(avatar_split_clause,[],[f410,f1768]) ).

fof(f1768,plain,
    ( spl0_177
  <=> ! [X0,X1] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),c_HOL_Ozero__class_Ozero(X0)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).

fof(f410,axiom,
    ! [X0,X1] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),c_HOL_Ozero__class_Ozero(X0)) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).

fof(f1766,plain,
    ( spl0_176
    | ~ spl0_109
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1728,f1668,f1386,f1764]) ).

fof(f1386,plain,
    ( spl0_109
  <=> ! [X4] : ~ c_HOL_Oord__class_Oless(X4,X4,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).

fof(f1728,plain,
    ( ! [X0] : ~ c_HOL_Oord__class_Oless(hAPP(c_Suc,X0),X0,tc_nat)
    | ~ spl0_109
    | ~ spl0_166 ),
    inference(resolution,[],[f1669,f1387]) ).

fof(f1387,plain,
    ( ! [X4] : ~ c_HOL_Oord__class_Oless(X4,X4,tc_nat)
    | ~ spl0_109 ),
    inference(avatar_component_clause,[],[f1386]) ).

fof(f1762,plain,
    spl0_175,
    inference(avatar_split_clause,[],[f409,f1760]) ).

fof(f409,axiom,
    ! [X0,X1] :
      ( ~ class_OrderedGroup_Omonoid__add(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0)),X1) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__0__left_0) ).

fof(f1758,plain,
    spl0_174,
    inference(avatar_split_clause,[],[f408,f1756]) ).

fof(f408,axiom,
    ! [X0,X1] :
      ( ~ class_OrderedGroup_Omonoid__add(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),c_HOL_Ozero__class_Ozero(X0)) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).

fof(f1754,plain,
    spl0_173,
    inference(avatar_split_clause,[],[f237,f1752]) ).

fof(f1752,plain,
    ( spl0_173
  <=> ! [X4,X0] :
        ( ~ class_Ring__and__Field_Oidom(X0)
        | ~ class_Int_Onumber__ring(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X4,X4,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).

fof(f237,axiom,
    ! [X0,X4] :
      ( ~ class_Ring__and__Field_Oidom(X0)
      | ~ class_Int_Onumber__ring(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X4,X4,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_1) ).

fof(f1750,plain,
    spl0_172,
    inference(avatar_split_clause,[],[f225,f1748]) ).

fof(f1748,plain,
    ( spl0_172
  <=> ! [X0,X1] :
        ( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X1
        | c_HOL_Ouminus__class_Ouminus(X1,X0) != X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).

fof(f225,axiom,
    ! [X0,X1] :
      ( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X1
      | c_HOL_Ouminus__class_Ouminus(X1,X0) != X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__zero_0) ).

fof(f1746,plain,
    spl0_171,
    inference(avatar_split_clause,[],[f224,f1744]) ).

fof(f224,axiom,
    ! [X0,X1] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Ouminus__class_Ouminus(X1,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(X0),X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_group__add__class_Odiff__0_0) ).

fof(f1741,plain,
    spl0_170,
    inference(avatar_split_clause,[],[f169,f1739]) ).

fof(f1739,plain,
    ( spl0_170
  <=> ! [X4] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X4),c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).

fof(f169,axiom,
    ! [X4] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X4),c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power__nat__eq_1) ).

fof(f1716,plain,
    ( spl0_169
    | ~ spl0_94
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f1595,f1543,f1313,f1713]) ).

fof(f1713,plain,
    ( spl0_169
  <=> c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).

fof(f1543,plain,
    ( spl0_142
  <=> ! [X0] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).

fof(f1595,plain,
    ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex)
    | ~ spl0_94
    | ~ spl0_142 ),
    inference(resolution,[],[f1544,f1315]) ).

fof(f1544,plain,
    ( ! [X0] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X0),X0) )
    | ~ spl0_142 ),
    inference(avatar_component_clause,[],[f1543]) ).

fof(f1679,plain,
    ( spl0_168
    | ~ spl0_39
    | ~ spl0_141 ),
    inference(avatar_split_clause,[],[f1593,f1539,f1038,f1676]) ).

fof(f1676,plain,
    ( spl0_168
  <=> c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).

fof(f1038,plain,
    ( spl0_39
  <=> class_OrderedGroup_Oordered__ab__group__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).

fof(f1539,plain,
    ( spl0_141
  <=> ! [X0] :
        ( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).

fof(f1593,plain,
    ( c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint)
    | ~ spl0_39
    | ~ spl0_141 ),
    inference(resolution,[],[f1540,f1040]) ).

fof(f1040,plain,
    ( class_OrderedGroup_Oordered__ab__group__add(tc_Int_Oint)
    | ~ spl0_39 ),
    inference(avatar_component_clause,[],[f1038]) ).

fof(f1540,plain,
    ( ! [X0] :
        ( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X0),X0) )
    | ~ spl0_141 ),
    inference(avatar_component_clause,[],[f1539]) ).

fof(f1674,plain,
    spl0_167,
    inference(avatar_split_clause,[],[f637,f1672]) ).

fof(f637,axiom,
    ! [X3] : c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(X3)),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_root__unity_0) ).

fof(f1670,plain,
    spl0_166,
    inference(avatar_split_clause,[],[f614,f1668]) ).

fof(f614,axiom,
    ! [X3,X19] :
      ( ~ c_HOL_Oord__class_Oless(X19,X3,tc_nat)
      | c_HOL_Oord__class_Oless(X19,hAPP(c_Suc,X3),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__SucI_0) ).

fof(f1666,plain,
    spl0_165,
    inference(avatar_split_clause,[],[f613,f1664]) ).

fof(f613,axiom,
    ! [X3,X19] :
      ( c_HOL_Oord__class_Oless(X19,X3,tc_nat)
      | ~ c_HOL_Oord__class_Oless(hAPP(c_Suc,X19),X3,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__lessD_0) ).

fof(f1662,plain,
    spl0_164,
    inference(avatar_split_clause,[],[f593,f1660]) ).

fof(f1660,plain,
    ( spl0_164
  <=> ! [X2,X0,X1] :
        ( ~ class_Orderings_Oorder(X0)
        | ~ c_HOL_Oord__class_Oless(X2,X1,X0)
        | ~ c_HOL_Oord__class_Oless(X1,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).

fof(f593,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Orderings_Oorder(X0)
      | ~ c_HOL_Oord__class_Oless(X2,X1,X0)
      | ~ c_HOL_Oord__class_Oless(X1,X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).

fof(f1658,plain,
    spl0_163,
    inference(avatar_split_clause,[],[f592,f1656]) ).

fof(f1656,plain,
    ( spl0_163
  <=> ! [X4,X0,X9] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_HOL_Oord__class_Oless(X9,X4,X0)
        | ~ c_HOL_Oord__class_Oless(X4,X9,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).

fof(f592,axiom,
    ! [X0,X9,X4] :
      ( ~ class_Orderings_Olinorder(X0)
      | ~ c_HOL_Oord__class_Oless(X9,X4,X0)
      | ~ c_HOL_Oord__class_Oless(X4,X9,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).

fof(f1654,plain,
    spl0_162,
    inference(avatar_split_clause,[],[f591,f1652]) ).

fof(f1652,plain,
    ( spl0_162
  <=> ! [X2,X0,X1] :
        ( ~ class_Orderings_Opreorder(X0)
        | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
        | ~ c_HOL_Oord__class_Oless(X2,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).

fof(f591,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Orderings_Opreorder(X0)
      | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
      | ~ c_HOL_Oord__class_Oless(X2,X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).

fof(f1650,plain,
    spl0_161,
    inference(avatar_split_clause,[],[f555,f1648]) ).

fof(f555,axiom,
    ! [X40,X37] :
      ( X37 = X40
      | hAPP(c_Suc,X37) != hAPP(c_Suc,X40) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).

fof(f1646,plain,
    spl0_160,
    inference(avatar_split_clause,[],[f524,f1644]) ).

fof(f524,axiom,
    ! [X3,X19] :
      ( c_HOL_Oord__class_Oless(X19,X3,tc_nat)
      | c_HOL_Oord__class_Oless(X3,hAPP(c_Suc,X19),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_0) ).

fof(f1642,plain,
    spl0_159,
    inference(avatar_split_clause,[],[f523,f1640]) ).

fof(f523,axiom,
    ! [X3,X19] :
      ( ~ c_HOL_Oord__class_Oless(X19,X3,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X3,hAPP(c_Suc,X19),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_1) ).

fof(f1638,plain,
    spl0_158,
    inference(avatar_split_clause,[],[f481,f1636]) ).

fof(f481,axiom,
    ! [X19] : c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X19),c_HOL_Ozero__class_Ozero(tc_nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__is__0_2) ).

fof(f1634,plain,
    spl0_157,
    inference(avatar_split_clause,[],[f480,f1632]) ).

fof(f1632,plain,
    ( spl0_157
  <=> ! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).

fof(f480,axiom,
    ! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__is__0_1) ).

fof(f1630,plain,
    spl0_156,
    inference(avatar_split_clause,[],[f476,f1628]) ).

fof(f1628,plain,
    ( spl0_156
  <=> ! [X9,X0] :
        ( ~ class_RealVector_Oreal__normed__field(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X0),X9,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).

fof(f476,axiom,
    ! [X0,X9] :
      ( ~ class_RealVector_Oreal__normed__field(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X0),X9,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide_Ozero_0) ).

fof(f1626,plain,
    spl0_155,
    inference(avatar_split_clause,[],[f473,f1624]) ).

fof(f473,axiom,
    ! [X0,X1] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X0),X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__zero__left_0) ).

fof(f1622,plain,
    spl0_154,
    inference(avatar_split_clause,[],[f426,f1620]) ).

fof(f426,axiom,
    ! [X0] :
      ( ~ class_Int_Onumber__ring(X0)
      | c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0) = c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_arith__simps_I31_J_0) ).

fof(f1592,plain,
    spl0_153,
    inference(avatar_split_clause,[],[f606,f1590]) ).

fof(f606,axiom,
    ! [X0] :
      ( ~ class_Int_Onumber__ring(X0)
      | c_HOL_Oone__class_Oone(X0) = c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comp__arith_I110_J_0) ).

fof(f1588,plain,
    spl0_152,
    inference(avatar_split_clause,[],[f532,f1586]) ).

fof(f532,axiom,
    ! [X0,X1] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Oinverse__class_Odivide(X1,c_HOL_Oone__class_Oone(X0),X0) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__1_0) ).

fof(f1584,plain,
    spl0_151,
    inference(avatar_split_clause,[],[f457,f1582]) ).

fof(f1582,plain,
    ( spl0_151
  <=> ! [X3] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X3
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).

fof(f457,axiom,
    ! [X3] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X3
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0I_0) ).

fof(f1580,plain,
    spl0_150,
    inference(avatar_split_clause,[],[f386,f1577]) ).

fof(f1577,plain,
    ( spl0_150
  <=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).

fof(f386,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pos2_0) ).

fof(f1575,plain,
    ( spl0_149
    | ~ spl0_101
    | ~ spl0_134 ),
    inference(avatar_split_clause,[],[f1520,f1496,f1348,f1572]) ).

fof(f1572,plain,
    ( spl0_149
  <=> c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).

fof(f1496,plain,
    ( spl0_134
  <=> ! [X0] :
        ( ~ class_Int_Onumber__ring(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_Int_Onumber__class_Onumber__of(c_Int_OPls,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).

fof(f1520,plain,
    ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_Complex_Ocomplex)
    | ~ spl0_101
    | ~ spl0_134 ),
    inference(resolution,[],[f1497,f1350]) ).

fof(f1497,plain,
    ( ! [X0] :
        ( ~ class_Int_Onumber__ring(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_Int_Onumber__class_Onumber__of(c_Int_OPls,X0) )
    | ~ spl0_134 ),
    inference(avatar_component_clause,[],[f1496]) ).

fof(f1570,plain,
    spl0_148,
    inference(avatar_split_clause,[],[f377,f1567]) ).

fof(f1565,plain,
    spl0_147,
    inference(avatar_split_clause,[],[f258,f1563]) ).

fof(f258,axiom,
    ! [X0,X4] :
      ( ~ class_Lattices_Oboolean__algebra(X0)
      | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X4,X0),X0) = X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__compl_0) ).

fof(f1561,plain,
    spl0_146,
    inference(avatar_split_clause,[],[f256,f1559]) ).

fof(f256,axiom,
    ! [X0,X1] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equation__minus__iff_1) ).

fof(f1557,plain,
    spl0_145,
    inference(avatar_split_clause,[],[f235,f1555]) ).

fof(f235,axiom,
    ! [X0,X1] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__0__right_0) ).

fof(f1553,plain,
    spl0_144,
    inference(avatar_split_clause,[],[f234,f1551]) ).

fof(f1551,plain,
    ( spl0_144
  <=> ! [X4,X0] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X4,X4,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).

fof(f234,axiom,
    ! [X0,X4] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X4,X4,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus__eq_1) ).

fof(f1549,plain,
    spl0_143,
    inference(avatar_split_clause,[],[f233,f1547]) ).

fof(f233,axiom,
    ! [X0,X4] :
      ( ~ class_OrderedGroup_Oab__group__add(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X4,X4,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).

fof(f1545,plain,
    spl0_142,
    inference(avatar_split_clause,[],[f77,f1543]) ).

fof(f77,axiom,
    ! [X0] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__equal__iff__equal_1) ).

fof(f1541,plain,
    spl0_141,
    inference(avatar_split_clause,[],[f74,f1539]) ).

fof(f74,axiom,
    ! [X0] :
      ( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__zero_1) ).

fof(f1531,plain,
    ( spl0_140
    | ~ spl0_68
    | ~ spl0_134 ),
    inference(avatar_split_clause,[],[f1519,f1496,f1183,f1528]) ).

fof(f1528,plain,
    ( spl0_140
  <=> c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).

fof(f1519,plain,
    ( c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_Int_Oint)
    | ~ spl0_68
    | ~ spl0_134 ),
    inference(resolution,[],[f1497,f1185]) ).

fof(f1518,plain,
    spl0_139,
    inference(avatar_split_clause,[],[f655,f1516]) ).

fof(f1516,plain,
    ( spl0_139
  <=> ! [X20,X36] :
        ( X20 = X36
        | c_Int_OBit1(X20) != c_Int_OBit1(X36) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).

fof(f655,axiom,
    ! [X36,X20] :
      ( X20 = X36
      | c_Int_OBit1(X20) != c_Int_OBit1(X36) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I51_J_0) ).

fof(f1514,plain,
    spl0_138,
    inference(avatar_split_clause,[],[f544,f1512]) ).

fof(f1512,plain,
    ( spl0_138
  <=> ! [X20,X36] :
        ( X20 = X36
        | c_Int_OBit0(X36) != c_Int_OBit0(X20) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).

fof(f544,axiom,
    ! [X36,X20] :
      ( X20 = X36
      | c_Int_OBit0(X36) != c_Int_OBit0(X20) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I48_J_0) ).

fof(f1510,plain,
    spl0_137,
    inference(avatar_split_clause,[],[f451,f1508]) ).

fof(f1508,plain,
    ( spl0_137
  <=> ! [X4] :
        ( c_Parity_Oeven__odd__class_Oeven(X4,tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(hAPP(c_Suc,X4),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).

fof(f451,axiom,
    ! [X4] :
      ( c_Parity_Oeven__odd__class_Oeven(X4,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(hAPP(c_Suc,X4),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__Suc_1) ).

fof(f1506,plain,
    spl0_136,
    inference(avatar_split_clause,[],[f450,f1504]) ).

fof(f1504,plain,
    ( spl0_136
  <=> ! [X4] :
        ( ~ c_Parity_Oeven__odd__class_Oeven(X4,tc_nat)
        | ~ c_Parity_Oeven__odd__class_Oeven(hAPP(c_Suc,X4),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).

fof(f450,axiom,
    ! [X4] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(X4,tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(hAPP(c_Suc,X4),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__Suc_0) ).

fof(f1502,plain,
    spl0_135,
    inference(avatar_split_clause,[],[f253,f1500]) ).

fof(f253,axiom,
    ! [X3] :
      ( c_Parity_Oeven__odd__class_Oeven(X3,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_odd__pos_0) ).

fof(f1498,plain,
    spl0_134,
    inference(avatar_split_clause,[],[f123,f1496]) ).

fof(f123,axiom,
    ! [X0] :
      ( ~ class_Int_Onumber__ring(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_Int_Onumber__class_Onumber__of(c_Int_OPls,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_number__of__Pls_0) ).

fof(f1494,plain,
    spl0_133,
    inference(avatar_split_clause,[],[f13,f1492]) ).

fof(f1492,plain,
    ( spl0_133
  <=> ! [X0] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).

fof(f13,axiom,
    ! [X0] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).

fof(f1490,plain,
    spl0_132,
    inference(avatar_split_clause,[],[f12,f1488]) ).

fof(f12,axiom,
    ! [X0] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__one_0) ).

fof(f1483,plain,
    spl0_131,
    inference(avatar_split_clause,[],[f804,f1481]) ).

fof(f1481,plain,
    ( spl0_131
  <=> ! [X48,X0,X49] :
        ( X48 = X49
        | ~ c_fequal(X48,X49,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).

fof(f804,axiom,
    ! [X48,X0,X49] :
      ( X48 = X49
      | ~ c_fequal(X48,X49,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).

fof(f1479,plain,
    spl0_130,
    inference(avatar_split_clause,[],[f545,f1477]) ).

fof(f1477,plain,
    ( spl0_130
  <=> ! [X20] :
        ( c_Int_OPls = X20
        | c_Int_OPls != c_Int_OBit0(X20) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).

fof(f545,axiom,
    ! [X20] :
      ( c_Int_OPls = X20
      | c_Int_OPls != c_Int_OBit0(X20) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I44_J_0) ).

fof(f1475,plain,
    spl0_129,
    inference(avatar_split_clause,[],[f439,f1473]) ).

fof(f1473,plain,
    ( spl0_129
  <=> ! [X36] :
        ( c_Int_OMin = X36
        | c_Int_OMin != c_Int_OBit1(X36) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).

fof(f439,axiom,
    ! [X36] :
      ( c_Int_OMin = X36
      | c_Int_OMin != c_Int_OBit1(X36) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I43_J_0) ).

fof(f1471,plain,
    spl0_128,
    inference(avatar_split_clause,[],[f428,f1469]) ).

fof(f1469,plain,
    ( spl0_128
  <=> ! [X0] :
        ( ~ class_Ring__and__Field_Ozero__neq__one(X0)
        | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oone__class_Oone(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).

fof(f428,axiom,
    ! [X0] :
      ( ~ class_Ring__and__Field_Ozero__neq__one(X0)
      | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oone__class_Oone(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).

fof(f1467,plain,
    spl0_127,
    inference(avatar_split_clause,[],[f138,f1465]) ).

fof(f138,axiom,
    ! [X3] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,X3),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__Suc_0) ).

fof(f1463,plain,
    spl0_126,
    inference(avatar_split_clause,[],[f697,f1461]) ).

fof(f1461,plain,
    ( spl0_126
  <=> ! [X46,X47] :
        ( ~ class_Orderings_Oorder(X47)
        | class_Orderings_Oorder(tc_fun(X46,X47)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).

fof(f697,axiom,
    ! [X46,X47] :
      ( ~ class_Orderings_Oorder(X47)
      | class_Orderings_Oorder(tc_fun(X46,X47)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).

fof(f1459,plain,
    spl0_125,
    inference(avatar_split_clause,[],[f696,f1457]) ).

fof(f1457,plain,
    ( spl0_125
  <=> ! [X46,X47] :
        ( ~ class_Orderings_Opreorder(X47)
        | class_Orderings_Opreorder(tc_fun(X46,X47)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).

fof(f696,axiom,
    ! [X46,X47] :
      ( ~ class_Orderings_Opreorder(X47)
      | class_Orderings_Opreorder(tc_fun(X46,X47)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).

fof(f1455,plain,
    spl0_124,
    inference(avatar_split_clause,[],[f695,f1453]) ).

fof(f695,axiom,
    ! [X46,X47] :
      ( ~ class_Lattices_Oboolean__algebra(X47)
      | class_Lattices_Oboolean__algebra(tc_fun(X46,X47)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oboolean__algebra) ).

fof(f1451,plain,
    spl0_123,
    inference(avatar_split_clause,[],[f625,f1449]) ).

fof(f625,axiom,
    ! [X4] : c_HOL_Oord__class_Oless(X4,hAPP(c_Suc,X4),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq_2) ).

fof(f1447,plain,
    spl0_122,
    inference(avatar_split_clause,[],[f570,f1445]) ).

fof(f1445,plain,
    ( spl0_122
  <=> ! [X4,X0] :
        ( ~ class_Orderings_Opreorder(X0)
        | ~ c_HOL_Oord__class_Oless(X4,X4,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).

fof(f570,axiom,
    ! [X0,X4] :
      ( ~ class_Orderings_Opreorder(X0)
      | ~ c_HOL_Oord__class_Oless(X4,X4,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).

fof(f1443,plain,
    spl0_121,
    inference(avatar_split_clause,[],[f569,f1441]) ).

fof(f1441,plain,
    ( spl0_121
  <=> ! [X4,X0] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_HOL_Oord__class_Oless(X4,X4,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).

fof(f569,axiom,
    ! [X0,X4] :
      ( ~ class_Orderings_Olinorder(X0)
      | ~ c_HOL_Oord__class_Oless(X4,X4,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).

fof(f1439,plain,
    spl0_120,
    inference(avatar_split_clause,[],[f566,f1437]) ).

fof(f1437,plain,
    ( spl0_120
  <=> ! [X4,X0] :
        ( ~ class_Orderings_Oorder(X0)
        | ~ c_HOL_Oord__class_Oless(X4,X4,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).

fof(f566,axiom,
    ! [X0,X4] :
      ( ~ class_Orderings_Oorder(X0)
      | ~ c_HOL_Oord__class_Oless(X4,X4,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).

fof(f1435,plain,
    spl0_119,
    inference(avatar_split_clause,[],[f442,f1433]) ).

fof(f442,axiom,
    ! [X19] : c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(c_Suc,X19),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__neq__Zero_0) ).

fof(f1431,plain,
    spl0_118,
    inference(avatar_split_clause,[],[f171,f1428]) ).

fof(f1428,plain,
    ( spl0_118
  <=> c_FFT__Mirabelle_Oroot(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).

fof(f171,axiom,
    c_FFT__Mirabelle_Oroot(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_root0_0) ).

fof(f1426,plain,
    spl0_117,
    inference(avatar_split_clause,[],[f145,f1423]) ).

fof(f1423,plain,
    ( spl0_117
  <=> c_HOL_Ozero__class_Ozero(tc_nat) = c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).

fof(f145,axiom,
    c_HOL_Ozero__class_Ozero(tc_nat) = c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comp__arith_I113_J_0) ).

fof(f1421,plain,
    spl0_116,
    inference(avatar_split_clause,[],[f84,f1418]) ).

fof(f84,axiom,
    c_HOL_Ozero__class_Ozero(tc_nat) = c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__number__of__Min_0) ).

fof(f1416,plain,
    spl0_115,
    inference(avatar_split_clause,[],[f59,f1414]) ).

fof(f1414,plain,
    ( spl0_115
  <=> ! [X1] : c_FFT__Mirabelle_OIFFT(c_HOL_Ozero__class_Ozero(tc_nat),X1) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).

fof(f59,axiom,
    ! [X1] : c_FFT__Mirabelle_OIFFT(c_HOL_Ozero__class_Ozero(tc_nat),X1) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IFFT_Osimps_I1_J_0) ).

fof(f1411,plain,
    spl0_114,
    inference(avatar_split_clause,[],[f686,f1409]) ).

fof(f1409,plain,
    ( spl0_114
  <=> ! [X20,X36] : c_Int_OBit1(X36) != c_Int_OBit0(X20) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).

fof(f686,axiom,
    ! [X36,X20] : c_Int_OBit1(X36) != c_Int_OBit0(X20),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I49_J_0) ).

fof(f1407,plain,
    spl0_113,
    inference(avatar_split_clause,[],[f617,f1405]) ).

fof(f617,axiom,
    ! [X3] : hAPP(c_Suc,X3) != X3,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).

fof(f1403,plain,
    spl0_112,
    inference(avatar_split_clause,[],[f458,f1401]) ).

fof(f458,axiom,
    ! [X3] : ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less0_0) ).

fof(f1397,plain,
    spl0_111,
    inference(avatar_split_clause,[],[f803,f1395]) ).

fof(f1395,plain,
    ( spl0_111
  <=> ! [X4,X0] : c_fequal(X4,X4,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).

fof(f803,axiom,
    ! [X0,X4] : c_fequal(X4,X4,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).

fof(f1393,plain,
    spl0_110,
    inference(avatar_split_clause,[],[f573,f1390]) ).

fof(f1390,plain,
    ( spl0_110
  <=> c_Int_OPls = c_Int_OBit0(c_Int_OPls) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).

fof(f573,axiom,
    c_Int_OPls = c_Int_OBit0(c_Int_OPls),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Bit0__Pls_0) ).

fof(f1388,plain,
    spl0_109,
    inference(avatar_split_clause,[],[f568,f1386]) ).

fof(f568,axiom,
    ! [X4] : ~ c_HOL_Oord__class_Oless(X4,X4,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_1) ).

fof(f1384,plain,
    spl0_108,
    inference(avatar_split_clause,[],[f546,f1382]) ).

fof(f1382,plain,
    ( spl0_108
  <=> ! [X20] : c_Int_OPls != c_Int_OBit1(X20) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).

fof(f546,axiom,
    ! [X20] : c_Int_OPls != c_Int_OBit1(X20),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I46_J_0) ).

fof(f1380,plain,
    spl0_107,
    inference(avatar_split_clause,[],[f461,f1378]) ).

fof(f1378,plain,
    ( spl0_107
  <=> ! [X20] : c_Int_OMin != c_Int_OBit0(X20) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).

fof(f461,axiom,
    ! [X20] : c_Int_OMin != c_Int_OBit0(X20),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I45_J_0) ).

fof(f1376,plain,
    spl0_106,
    inference(avatar_split_clause,[],[f440,f1373]) ).

fof(f1373,plain,
    ( spl0_106
  <=> c_Int_OMin = c_Int_OBit1(c_Int_OMin) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).

fof(f440,axiom,
    c_Int_OMin = c_Int_OBit1(c_Int_OMin),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I43_J_1) ).

fof(f1371,plain,
    spl0_105,
    inference(avatar_split_clause,[],[f82,f1368]) ).

fof(f1368,plain,
    ( spl0_105
  <=> c_Parity_Oeven__odd__class_Oeven(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).

fof(f82,axiom,
    c_Parity_Oeven__odd__class_Oeven(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__zero__nat_0) ).

fof(f1366,plain,
    ~ spl0_104,
    inference(avatar_split_clause,[],[f452,f1363]) ).

fof(f1363,plain,
    ( spl0_104
  <=> c_Int_OMin = c_Int_OPls ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).

fof(f452,axiom,
    c_Int_OMin != c_Int_OPls,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I37_J_0) ).

fof(f1361,plain,
    spl0_103,
    inference(avatar_split_clause,[],[f800,f1358]) ).

fof(f1358,plain,
    ( spl0_103
  <=> class_Int_Onumber(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).

fof(f800,axiom,
    class_Int_Onumber(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber) ).

fof(f1356,plain,
    spl0_102,
    inference(avatar_split_clause,[],[f799,f1353]) ).

fof(f799,axiom,
    class_Power_Opower(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Power_Opower) ).

fof(f1351,plain,
    spl0_101,
    inference(avatar_split_clause,[],[f798,f1348]) ).

fof(f798,axiom,
    class_Int_Onumber__ring(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber__ring) ).

fof(f1346,plain,
    spl0_100,
    inference(avatar_split_clause,[],[f797,f1343]) ).

fof(f1343,plain,
    ( spl0_100
  <=> class_Int_Oring__char__0(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).

fof(f797,axiom,
    class_Int_Oring__char__0(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Oring__char__0) ).

fof(f1341,plain,
    spl0_99,
    inference(avatar_split_clause,[],[f796,f1338]) ).

fof(f1338,plain,
    ( spl0_99
  <=> class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).

fof(f796,axiom,
    class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) ).

fof(f1336,plain,
    spl0_98,
    inference(avatar_split_clause,[],[f795,f1333]) ).

fof(f1333,plain,
    ( spl0_98
  <=> class_Ring__and__Field_Oring(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).

fof(f795,axiom,
    class_Ring__and__Field_Oring(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring) ).

fof(f1331,plain,
    spl0_97,
    inference(avatar_split_clause,[],[f794,f1328]) ).

fof(f794,axiom,
    class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).

fof(f1326,plain,
    spl0_96,
    inference(avatar_split_clause,[],[f793,f1323]) ).

fof(f1323,plain,
    ( spl0_96
  <=> class_RealVector_Oreal__field(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).

fof(f793,axiom,
    class_RealVector_Oreal__field(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__field) ).

fof(f1321,plain,
    spl0_95,
    inference(avatar_split_clause,[],[f792,f1318]) ).

fof(f1318,plain,
    ( spl0_95
  <=> class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).

fof(f792,axiom,
    class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1) ).

fof(f1316,plain,
    spl0_94,
    inference(avatar_split_clause,[],[f791,f1313]) ).

fof(f791,axiom,
    class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) ).

fof(f1311,plain,
    spl0_93,
    inference(avatar_split_clause,[],[f790,f1308]) ).

fof(f790,axiom,
    class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add) ).

fof(f1306,plain,
    spl0_92,
    inference(avatar_split_clause,[],[f789,f1303]) ).

fof(f1303,plain,
    ( spl0_92
  <=> class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).

fof(f789,axiom,
    class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring) ).

fof(f1301,plain,
    spl0_91,
    inference(avatar_split_clause,[],[f788,f1298]) ).

fof(f788,axiom,
    class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) ).

fof(f1296,plain,
    spl0_90,
    inference(avatar_split_clause,[],[f787,f1293]) ).

fof(f1293,plain,
    ( spl0_90
  <=> class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).

fof(f787,axiom,
    class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero) ).

fof(f1291,plain,
    spl0_89,
    inference(avatar_split_clause,[],[f786,f1288]) ).

fof(f786,axiom,
    class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) ).

fof(f1286,plain,
    spl0_88,
    inference(avatar_split_clause,[],[f785,f1283]) ).

fof(f1283,plain,
    ( spl0_88
  <=> class_Ring__and__Field_Osemiring__0(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).

fof(f785,axiom,
    class_Ring__and__Field_Osemiring__0(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__0) ).

fof(f1281,plain,
    spl0_87,
    inference(avatar_split_clause,[],[f784,f1278]) ).

fof(f1278,plain,
    ( spl0_87
  <=> class_Ring__and__Field_Osemiring__1(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).

fof(f784,axiom,
    class_Ring__and__Field_Osemiring__1(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__1) ).

fof(f1276,plain,
    spl0_86,
    inference(avatar_split_clause,[],[f783,f1273]) ).

fof(f1273,plain,
    ( spl0_86
  <=> class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).

fof(f783,axiom,
    class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1) ).

fof(f1271,plain,
    spl0_85,
    inference(avatar_split_clause,[],[f782,f1268]) ).

fof(f1268,plain,
    ( spl0_85
  <=> class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).

fof(f782,axiom,
    class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one) ).

fof(f1266,plain,
    spl0_84,
    inference(avatar_split_clause,[],[f781,f1263]) ).

fof(f1263,plain,
    ( spl0_84
  <=> class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).

fof(f781,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add) ).

fof(f1261,plain,
    spl0_83,
    inference(avatar_split_clause,[],[f780,f1258]) ).

fof(f1258,plain,
    ( spl0_83
  <=> class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).

fof(f780,axiom,
    class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field) ).

fof(f1256,plain,
    spl0_82,
    inference(avatar_split_clause,[],[f779,f1253]) ).

fof(f1253,plain,
    ( spl0_82
  <=> class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).

fof(f779,axiom,
    class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring) ).

fof(f1251,plain,
    spl0_81,
    inference(avatar_split_clause,[],[f778,f1248]) ).

fof(f1248,plain,
    ( spl0_81
  <=> class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).

fof(f778,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add) ).

fof(f1246,plain,
    spl0_80,
    inference(avatar_split_clause,[],[f777,f1243]) ).

fof(f1243,plain,
    ( spl0_80
  <=> class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).

fof(f777,axiom,
    class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult) ).

fof(f1241,plain,
    spl0_79,
    inference(avatar_split_clause,[],[f776,f1238]) ).

fof(f1238,plain,
    ( spl0_79
  <=> class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).

fof(f776,axiom,
    class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) ).

fof(f1236,plain,
    spl0_78,
    inference(avatar_split_clause,[],[f775,f1233]) ).

fof(f1233,plain,
    ( spl0_78
  <=> class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).

fof(f775,axiom,
    class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).

fof(f1231,plain,
    spl0_77,
    inference(avatar_split_clause,[],[f774,f1228]) ).

fof(f774,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).

fof(f1226,plain,
    spl0_76,
    inference(avatar_split_clause,[],[f773,f1223]) ).

fof(f773,axiom,
    class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero) ).

fof(f1221,plain,
    spl0_75,
    inference(avatar_split_clause,[],[f772,f1218]) ).

fof(f1218,plain,
    ( spl0_75
  <=> class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).

fof(f772,axiom,
    class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors) ).

fof(f1216,plain,
    spl0_74,
    inference(avatar_split_clause,[],[f771,f1213]) ).

fof(f1213,plain,
    ( spl0_74
  <=> class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).

fof(f771,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add) ).

fof(f1211,plain,
    spl0_73,
    inference(avatar_split_clause,[],[f770,f1208]) ).

fof(f1208,plain,
    ( spl0_73
  <=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).

fof(f770,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add) ).

fof(f1206,plain,
    spl0_72,
    inference(avatar_split_clause,[],[f769,f1203]) ).

fof(f769,axiom,
    class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors) ).

fof(f1201,plain,
    spl0_71,
    inference(avatar_split_clause,[],[f768,f1198]) ).

fof(f1198,plain,
    ( spl0_71
  <=> class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).

fof(f768,axiom,
    class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors) ).

fof(f1196,plain,
    spl0_70,
    inference(avatar_split_clause,[],[f767,f1193]) ).

fof(f1193,plain,
    ( spl0_70
  <=> class_Int_Onumber(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).

fof(f767,axiom,
    class_Int_Onumber(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Onumber) ).

fof(f1191,plain,
    spl0_69,
    inference(avatar_split_clause,[],[f766,f1188]) ).

fof(f766,axiom,
    class_Power_Opower(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Power_Opower) ).

fof(f1186,plain,
    spl0_68,
    inference(avatar_split_clause,[],[f765,f1183]) ).

fof(f765,axiom,
    class_Int_Onumber__ring(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Onumber__ring) ).

fof(f1181,plain,
    spl0_67,
    inference(avatar_split_clause,[],[f764,f1178]) ).

fof(f1178,plain,
    ( spl0_67
  <=> class_Int_Oring__char__0(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).

fof(f764,axiom,
    class_Int_Oring__char__0(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Oring__char__0) ).

fof(f1176,plain,
    spl0_66,
    inference(avatar_split_clause,[],[f763,f1173]) ).

fof(f1173,plain,
    ( spl0_66
  <=> class_Orderings_Oorder(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).

fof(f763,axiom,
    class_Orderings_Oorder(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Oorder) ).

fof(f1171,plain,
    spl0_65,
    inference(avatar_split_clause,[],[f762,f1168]) ).

fof(f1168,plain,
    ( spl0_65
  <=> class_Orderings_Olinorder(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).

fof(f762,axiom,
    class_Orderings_Olinorder(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Olinorder) ).

fof(f1166,plain,
    spl0_64,
    inference(avatar_split_clause,[],[f761,f1163]) ).

fof(f1163,plain,
    ( spl0_64
  <=> class_Orderings_Opreorder(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).

fof(f761,axiom,
    class_Orderings_Opreorder(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Opreorder) ).

fof(f1161,plain,
    spl0_63,
    inference(avatar_split_clause,[],[f760,f1158]) ).

fof(f1158,plain,
    ( spl0_63
  <=> class_Ring__and__Field_Oidom(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).

fof(f760,axiom,
    class_Ring__and__Field_Oidom(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oidom) ).

fof(f1156,plain,
    spl0_62,
    inference(avatar_split_clause,[],[f759,f1153]) ).

fof(f1153,plain,
    ( spl0_62
  <=> class_Ring__and__Field_Oring(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).

fof(f759,axiom,
    class_Ring__and__Field_Oring(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oring) ).

fof(f1151,plain,
    spl0_61,
    inference(avatar_split_clause,[],[f758,f1148]) ).

fof(f1148,plain,
    ( spl0_61
  <=> class_Ring__and__Field_Oring__1(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).

fof(f758,axiom,
    class_Ring__and__Field_Oring__1(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oring__1) ).

fof(f1146,plain,
    spl0_60,
    inference(avatar_split_clause,[],[f757,f1143]) ).

fof(f757,axiom,
    class_OrderedGroup_Ogroup__add(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ogroup__add) ).

fof(f1141,plain,
    spl0_59,
    inference(avatar_split_clause,[],[f756,f1138]) ).

fof(f756,axiom,
    class_OrderedGroup_Omonoid__add(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Omonoid__add) ).

fof(f1136,plain,
    spl0_58,
    inference(avatar_split_clause,[],[f755,f1133]) ).

fof(f1133,plain,
    ( spl0_58
  <=> class_Ring__and__Field_Osemiring(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).

fof(f755,axiom,
    class_Ring__and__Field_Osemiring(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Osemiring) ).

fof(f1131,plain,
    spl0_57,
    inference(avatar_split_clause,[],[f754,f1128]) ).

fof(f754,axiom,
    class_OrderedGroup_Omonoid__mult(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Omonoid__mult) ).

fof(f1126,plain,
    spl0_56,
    inference(avatar_split_clause,[],[f753,f1123]) ).

fof(f1123,plain,
    ( spl0_56
  <=> class_Ring__and__Field_Omult__zero(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).

fof(f753,axiom,
    class_Ring__and__Field_Omult__zero(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Omult__zero) ).

fof(f1121,plain,
    spl0_55,
    inference(avatar_split_clause,[],[f752,f1118]) ).

fof(f752,axiom,
    class_OrderedGroup_Oab__group__add(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__group__add) ).

fof(f1116,plain,
    spl0_54,
    inference(avatar_split_clause,[],[f751,f1113]) ).

fof(f1113,plain,
    ( spl0_54
  <=> class_Ring__and__Field_Osemiring__0(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).

fof(f751,axiom,
    class_Ring__and__Field_Osemiring__0(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Osemiring__0) ).

fof(f1111,plain,
    spl0_53,
    inference(avatar_split_clause,[],[f750,f1108]) ).

fof(f1108,plain,
    ( spl0_53
  <=> class_Ring__and__Field_Osemiring__1(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).

fof(f750,axiom,
    class_Ring__and__Field_Osemiring__1(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Osemiring__1) ).

fof(f1106,plain,
    spl0_52,
    inference(avatar_split_clause,[],[f749,f1103]) ).

fof(f1103,plain,
    ( spl0_52
  <=> class_Ring__and__Field_Ocomm__ring__1(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).

fof(f749,axiom,
    class_Ring__and__Field_Ocomm__ring__1(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ocomm__ring__1) ).

fof(f1101,plain,
    spl0_51,
    inference(avatar_split_clause,[],[f748,f1098]) ).

fof(f1098,plain,
    ( spl0_51
  <=> class_Ring__and__Field_Oordered__idom(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).

fof(f748,axiom,
    class_Ring__and__Field_Oordered__idom(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__idom) ).

fof(f1096,plain,
    spl0_50,
    inference(avatar_split_clause,[],[f747,f1093]) ).

fof(f1093,plain,
    ( spl0_50
  <=> class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).

fof(f747,axiom,
    class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ozero__neq__one) ).

fof(f1091,plain,
    spl0_49,
    inference(avatar_split_clause,[],[f746,f1088]) ).

fof(f1088,plain,
    ( spl0_49
  <=> class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).

fof(f746,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__add) ).

fof(f1086,plain,
    spl0_48,
    inference(avatar_split_clause,[],[f745,f1083]) ).

fof(f1083,plain,
    ( spl0_48
  <=> class_Ring__and__Field_Ocomm__semiring(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).

fof(f745,axiom,
    class_Ring__and__Field_Ocomm__semiring(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring) ).

fof(f1081,plain,
    spl0_47,
    inference(avatar_split_clause,[],[f744,f1078]) ).

fof(f1078,plain,
    ( spl0_47
  <=> class_Ring__and__Field_Opordered__ring(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).

fof(f744,axiom,
    class_Ring__and__Field_Opordered__ring(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Opordered__ring) ).

fof(f1076,plain,
    spl0_46,
    inference(avatar_split_clause,[],[f743,f1073]) ).

fof(f1073,plain,
    ( spl0_46
  <=> class_OrderedGroup_Oab__semigroup__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).

fof(f743,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__semigroup__add) ).

fof(f1071,plain,
    spl0_45,
    inference(avatar_split_clause,[],[f742,f1068]) ).

fof(f1068,plain,
    ( spl0_45
  <=> class_OrderedGroup_Ocomm__monoid__mult(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).

fof(f742,axiom,
    class_OrderedGroup_Ocomm__monoid__mult(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__mult) ).

fof(f1066,plain,
    spl0_44,
    inference(avatar_split_clause,[],[f741,f1063]) ).

fof(f1063,plain,
    ( spl0_44
  <=> class_OrderedGroup_Oab__semigroup__mult(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).

fof(f741,axiom,
    class_OrderedGroup_Oab__semigroup__mult(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__semigroup__mult) ).

fof(f1061,plain,
    spl0_43,
    inference(avatar_split_clause,[],[f740,f1058]) ).

fof(f740,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__1) ).

fof(f1056,plain,
    spl0_42,
    inference(avatar_split_clause,[],[f739,f1053]) ).

fof(f1053,plain,
    ( spl0_42
  <=> class_Ring__and__Field_Oordered__semidom(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).

fof(f739,axiom,
    class_Ring__and__Field_Oordered__semidom(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__semidom) ).

fof(f1051,plain,
    spl0_41,
    inference(avatar_split_clause,[],[f738,f1048]) ).

fof(f1048,plain,
    ( spl0_41
  <=> class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).

fof(f738,axiom,
    class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ono__zero__divisors) ).

fof(f1046,plain,
    spl0_40,
    inference(avatar_split_clause,[],[f737,f1043]) ).

fof(f1043,plain,
    ( spl0_40
  <=> class_OrderedGroup_Ocancel__semigroup__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).

fof(f737,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocancel__semigroup__add) ).

fof(f1041,plain,
    spl0_39,
    inference(avatar_split_clause,[],[f736,f1038]) ).

fof(f736,axiom,
    class_OrderedGroup_Oordered__ab__group__add(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oordered__ab__group__add) ).

fof(f1036,plain,
    spl0_38,
    inference(avatar_split_clause,[],[f735,f1033]) ).

fof(f1033,plain,
    ( spl0_38
  <=> class_OrderedGroup_Olordered__ab__group__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).

fof(f735,axiom,
    class_OrderedGroup_Olordered__ab__group__add(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add) ).

fof(f1031,plain,
    spl0_37,
    inference(avatar_split_clause,[],[f734,f1028]) ).

fof(f1028,plain,
    ( spl0_37
  <=> class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).

fof(f734,axiom,
    class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add) ).

fof(f1026,plain,
    spl0_36,
    inference(avatar_split_clause,[],[f733,f1023]) ).

fof(f1023,plain,
    ( spl0_36
  <=> class_Ring__and__Field_Oordered__ring__strict(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).

fof(f733,axiom,
    class_Ring__and__Field_Oordered__ring__strict(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__ring__strict) ).

fof(f1021,plain,
    spl0_35,
    inference(avatar_split_clause,[],[f732,f1018]) ).

fof(f1018,plain,
    ( spl0_35
  <=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).

fof(f732,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocancel__ab__semigroup__add) ).

fof(f1016,plain,
    spl0_34,
    inference(avatar_split_clause,[],[f731,f1013]) ).

fof(f731,axiom,
    class_Ring__and__Field_Oring__no__zero__divisors(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oring__no__zero__divisors) ).

fof(f1011,plain,
    spl0_33,
    inference(avatar_split_clause,[],[f730,f1008]) ).

fof(f1008,plain,
    ( spl0_33
  <=> class_OrderedGroup_Opordered__comm__monoid__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).

fof(f730,axiom,
    class_OrderedGroup_Opordered__comm__monoid__add(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__comm__monoid__add) ).

fof(f1006,plain,
    spl0_32,
    inference(avatar_split_clause,[],[f729,f1003]) ).

fof(f1003,plain,
    ( spl0_32
  <=> class_Ring__and__Field_Oordered__semiring__strict(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).

fof(f729,axiom,
    class_Ring__and__Field_Oordered__semiring__strict(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__semiring__strict) ).

fof(f1001,plain,
    spl0_31,
    inference(avatar_split_clause,[],[f728,f998]) ).

fof(f998,plain,
    ( spl0_31
  <=> class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).

fof(f728,axiom,
    class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oring__1__no__zero__divisors) ).

fof(f996,plain,
    spl0_30,
    inference(avatar_split_clause,[],[f727,f993]) ).

fof(f993,plain,
    ( spl0_30
  <=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).

fof(f727,axiom,
    class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__comm__semiring__strict) ).

fof(f991,plain,
    spl0_29,
    inference(avatar_split_clause,[],[f726,f988]) ).

fof(f988,plain,
    ( spl0_29
  <=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).

fof(f726,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).

fof(f986,plain,
    spl0_28,
    inference(avatar_split_clause,[],[f725,f983]) ).

fof(f983,plain,
    ( spl0_28
  <=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).

fof(f725,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).

fof(f981,plain,
    spl0_27,
    inference(avatar_split_clause,[],[f724,f978]) ).

fof(f978,plain,
    ( spl0_27
  <=> class_Int_Onumber(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).

fof(f724,axiom,
    class_Int_Onumber(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Int_Onumber) ).

fof(f976,plain,
    spl0_26,
    inference(avatar_split_clause,[],[f723,f973]) ).

fof(f723,axiom,
    class_Power_Opower(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Power_Opower) ).

fof(f971,plain,
    spl0_25,
    inference(avatar_split_clause,[],[f722,f968]) ).

fof(f722,axiom,
    class_Orderings_Oorder(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).

fof(f966,plain,
    spl0_24,
    inference(avatar_split_clause,[],[f721,f963]) ).

fof(f963,plain,
    ( spl0_24
  <=> class_Orderings_Olinorder(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).

fof(f721,axiom,
    class_Orderings_Olinorder(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).

fof(f961,plain,
    spl0_23,
    inference(avatar_split_clause,[],[f720,f958]) ).

fof(f958,plain,
    ( spl0_23
  <=> class_Orderings_Opreorder(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).

fof(f720,axiom,
    class_Orderings_Opreorder(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).

fof(f956,plain,
    spl0_22,
    inference(avatar_split_clause,[],[f719,f953]) ).

fof(f719,axiom,
    class_OrderedGroup_Omonoid__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).

fof(f951,plain,
    spl0_21,
    inference(avatar_split_clause,[],[f718,f948]) ).

fof(f948,plain,
    ( spl0_21
  <=> class_Ring__and__Field_Osemiring(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).

fof(f718,axiom,
    class_Ring__and__Field_Osemiring(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).

fof(f946,plain,
    spl0_20,
    inference(avatar_split_clause,[],[f717,f943]) ).

fof(f717,axiom,
    class_OrderedGroup_Omonoid__mult(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).

fof(f941,plain,
    spl0_19,
    inference(avatar_split_clause,[],[f716,f938]) ).

fof(f938,plain,
    ( spl0_19
  <=> class_Ring__and__Field_Omult__zero(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).

fof(f716,axiom,
    class_Ring__and__Field_Omult__zero(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).

fof(f936,plain,
    spl0_18,
    inference(avatar_split_clause,[],[f715,f933]) ).

fof(f933,plain,
    ( spl0_18
  <=> class_Ring__and__Field_Osemiring__0(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).

fof(f715,axiom,
    class_Ring__and__Field_Osemiring__0(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).

fof(f931,plain,
    spl0_17,
    inference(avatar_split_clause,[],[f714,f928]) ).

fof(f928,plain,
    ( spl0_17
  <=> class_Ring__and__Field_Osemiring__1(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).

fof(f714,axiom,
    class_Ring__and__Field_Osemiring__1(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).

fof(f926,plain,
    spl0_16,
    inference(avatar_split_clause,[],[f713,f923]) ).

fof(f923,plain,
    ( spl0_16
  <=> class_Ring__and__Field_Ozero__neq__one(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).

fof(f713,axiom,
    class_Ring__and__Field_Ozero__neq__one(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).

fof(f921,plain,
    spl0_15,
    inference(avatar_split_clause,[],[f712,f918]) ).

fof(f918,plain,
    ( spl0_15
  <=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).

fof(f712,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).

fof(f916,plain,
    spl0_14,
    inference(avatar_split_clause,[],[f711,f913]) ).

fof(f913,plain,
    ( spl0_14
  <=> class_Ring__and__Field_Ocomm__semiring(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).

fof(f711,axiom,
    class_Ring__and__Field_Ocomm__semiring(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).

fof(f911,plain,
    spl0_13,
    inference(avatar_split_clause,[],[f710,f908]) ).

fof(f908,plain,
    ( spl0_13
  <=> class_OrderedGroup_Oab__semigroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).

fof(f710,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).

fof(f906,plain,
    spl0_12,
    inference(avatar_split_clause,[],[f709,f903]) ).

fof(f903,plain,
    ( spl0_12
  <=> class_OrderedGroup_Ocomm__monoid__mult(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).

fof(f709,axiom,
    class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__mult) ).

fof(f901,plain,
    spl0_11,
    inference(avatar_split_clause,[],[f708,f898]) ).

fof(f898,plain,
    ( spl0_11
  <=> class_OrderedGroup_Oab__semigroup__mult(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

fof(f708,axiom,
    class_OrderedGroup_Oab__semigroup__mult(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).

fof(f896,plain,
    spl0_10,
    inference(avatar_split_clause,[],[f707,f893]) ).

fof(f707,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).

fof(f891,plain,
    spl0_9,
    inference(avatar_split_clause,[],[f706,f888]) ).

fof(f706,axiom,
    class_Ring__and__Field_Oordered__semidom(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).

fof(f886,plain,
    spl0_8,
    inference(avatar_split_clause,[],[f705,f883]) ).

fof(f883,plain,
    ( spl0_8
  <=> class_Ring__and__Field_Ono__zero__divisors(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

fof(f705,axiom,
    class_Ring__and__Field_Ono__zero__divisors(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).

fof(f881,plain,
    spl0_7,
    inference(avatar_split_clause,[],[f704,f878]) ).

fof(f878,plain,
    ( spl0_7
  <=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

fof(f704,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).

fof(f876,plain,
    spl0_6,
    inference(avatar_split_clause,[],[f703,f873]) ).

fof(f873,plain,
    ( spl0_6
  <=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

fof(f703,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).

fof(f871,plain,
    spl0_5,
    inference(avatar_split_clause,[],[f702,f868]) ).

fof(f868,plain,
    ( spl0_5
  <=> class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

fof(f702,axiom,
    class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).

fof(f866,plain,
    spl0_4,
    inference(avatar_split_clause,[],[f701,f863]) ).

fof(f863,plain,
    ( spl0_4
  <=> class_Ring__and__Field_Oordered__semiring__strict(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f701,axiom,
    class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring__strict) ).

fof(f861,plain,
    spl0_3,
    inference(avatar_split_clause,[],[f700,f858]) ).

fof(f858,plain,
    ( spl0_3
  <=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f700,axiom,
    class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) ).

fof(f856,plain,
    spl0_2,
    inference(avatar_split_clause,[],[f699,f853]) ).

fof(f853,plain,
    ( spl0_2
  <=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f699,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).

fof(f851,plain,
    spl0_1,
    inference(avatar_split_clause,[],[f698,f848]) ).

fof(f848,plain,
    ( spl0_1
  <=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f698,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SWV712-1 : TPTP v8.1.2. Released v4.1.0.
% 0.14/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n009.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Tue Apr 30 04:51:41 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.35  % (10556)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.41  % (10559)WARNING: value z3 for option sas not known
% 0.20/0.41  % (10557)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.20/0.41  % (10558)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.20/0.41  % (10560)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.20/0.41  % (10559)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.20/0.41  % (10561)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.20/0.41  % (10562)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.20/0.41  % (10563)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 1.35/0.57  TRYING [1]
% 1.35/0.59  TRYING [2]
% 2.49/0.73  % (10561)First to succeed.
% 2.49/0.76  % (10561)Refutation found. Thanks to Tanya!
% 2.49/0.76  % SZS status Unsatisfiable for theBenchmark
% 2.49/0.76  % SZS output start Proof for theBenchmark
% See solution above
% 2.49/0.77  % (10561)------------------------------
% 2.49/0.77  % (10561)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 2.49/0.77  % (10561)Termination reason: Refutation
% 2.49/0.77  
% 2.49/0.77  % (10561)Memory used [KB]: 6454
% 2.49/0.77  % (10561)Time elapsed: 0.342 s
% 2.49/0.77  % (10561)Instructions burned: 856 (million)
% 2.49/0.77  % (10561)------------------------------
% 2.49/0.77  % (10561)------------------------------
% 2.49/0.77  % (10556)Success in time 0.406 s
%------------------------------------------------------------------------------